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Getting Started with Abaqus: Keywords Edition

1. Figure 10 44 Element numbers Ifyou wish to create the entire model using Abaqus CAE refer to Example axisymmetric mount Section 10 7 of Getting Started with Abaqus Interactive Edition 10 7 5 Reviewing the input file the model data We review the model data including the geometry definition nodes and elements and the material properties 10 60 EXAMPLE AXISYMMETRIC MOUNT SUSBESSESBESSESEESEESEESEEELEE Node set MIDDLE SPC aon i i i CELE EE EEE Ee o i SN Figure 10 45 Node set MIDDLE and pressure loading G N Model description The input file should contain a suitable description of the analysis HEADING Axisymmetric mount analysis under axial loading S I Units m kg N sec Nodal coordinates and element connectivity There will be at least two ELEMENT option blocks in the input file since two different types of elements are used in the simulation It is a good idea to check that the element types are correct and that the element sets containing the elements have descriptive names The ELEMENT options in your input file should look like ELEMENT TYPE CAX41I
2. 0 8 0 6 Nominal Stress Pa 0 2 0 0 0 0 0 5 1 0 1 5 2 0 2 5 30 KI 4 0 Nominal Strain Figure 10 48 Comparison of experimental data UNIAXIAL and Abaqus results UNI COMP uniaxial tension MATERIAL NAME STEEL ELASTIC 2 0E11 0 3 10 64 EXAMPLE AXISYMMETRIC MOUNT x X PLANAR_COMP 6 PLANAR x10 Nominal Stress Pa 0 5 poe a won Pa De E Mie dl 0 0 0 5 1 0 13 2 0 259 3 0 59 4 0 Nominal Strain Figure 10 49 Comparison of experimental data PLANAR and Abaqus results PLANAR COMP planar shear 10 7 6 Reviewing the input the history data We now discuss the history data associated with this problem including the time incrementation parameters boundary conditions loading and output requests Including nonlinear geometry and specifying the initial increment size When hyperelastic materials are used in a model Abaqus assumes that it may undergo large deformations But large deformations and other nonlinear geometric effects are included only if the NLGEOM parameter is set to YES on the STEP option Therefore you must include it in this simulation or Abaqus will terminate the analysis with an input error The STEP option should look like STEP NLGEOM YES The simulation will be a static analysis with a total step time of 1 0 Specify the initial time increment to be 1 100th of the total step time
3. Avg 75 4 000e 08 8 879e 06 Step Step 1 Increment 1 Step Time 2 2200E 16 Primary Var S Mises F x Deformed Var U Deformation Scale Factor 2 968e 01 Figure 4 32 Mises stress through the lug thickness 1 Dos i fli 1 are displayed as indicated by the check marks beneath the on cut iii and below cut aj symbols To translate or rotate the cut choose Translate or Rotate from the list of available motions and enter a value or drag the slider at the bottom of the View Cut Manager 4 To view the full model again toggle off Cut 4 in the View Cut Manager For more information on view cuts see Chapter 80 Cutting through a model of the Abaqus CAE User s Manual Maximum and minimum values The maximum and minimum values of a variable in a model can be determined easily To display the minimum and maximum values of a contour variable 1 From the main menu bar select Viewport Viewport Annotation Options then click the Legend tab in the dialog box that appears The Legend options become available 2 Toggle on Show min max values 3 Click OK The contour legend changes to report the minimum and maximum contour values 4 31 5 EXAMPLE CONNECTING LUG One of the goals of this example is to determine the deflection of the lug in the negative 2 direction You can contour the displacement component of the lug in the 2 direction to determine its peak disp
4. where D and n are material constants 40 and 5 in this case When the RATE DEPENDENT option is included the yield stress effectively increases as the strain rate increases Therefore because the elastic modulus is higher than the plastic modulus we expect a stiffer response in the analysis with rate dependence Both the displacement history of the central portion of the plate shown in Figure 10 35 and the history of plastic strain shown in Figure 10 36 confirm that the response is indeed stiffer when rate dependence is included 10 6 Hyperelasticity We now turn our attention to another class of material nonlinearity namely the nonlinear elastic response exhibited by rubber materials 10 49 HYPERELASTICITY 50 00 40 00 E 30 00 E Q O amp P A 20 00 JA No Rate Dep Rate Dep 10 00 0 00 0 00 0 01 0 02 0 03 0 04 0 05 Time s Figure 10 35 Displacement of the central node with and without rate dependence x10 4 40 00 35 00 30 00 25 00 20 00 Plastic Energy J 15 00 No Rate Dep 10 00 Rate Dep 5 00 0 00 0 00 0 01 0 02 0 03 0 04 0 05 Time s Figure 10 36 Plastic strain energy with and without rate dependence 10 50 HYPERELASTICITY 10 6 1 Introduction The stress strain behavior of typical rubber materials shown in Figure 10 37 is elastic but highly nonlinear Stress Strain Figure 10 37 Typical stress strain curve for rubber This type of m
5. 12 10 1 Coordinate system While the circuit board will be dropped at an angle it is easiest to use the SYSTEM option to define the mesh aligned with a local rectangular coordinate system as shown in Figure 12 49 The SYSTEM option transforms nodal coordinates from the local coordinate system to the global coordinate system This option allows you to define the circuit board in the x z plane of the local coordinate system which is rotated by the desired angle relative to the global coordinate system The SYSTEM option defines a new coordinate system by specifying three points a local origin a point on the local x axis and a point in the local x y plane Before defining the nodes for the circuit board use the following option to tilt the mesh so that it lands on its corner 12 59 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST circuit board 150 foam local packaging coordinate system Z T Material properties Circuit board material plastic E 45x 10 Pa v 0 3 p 500 kg m Foam packaging material is crushable foam E 3x10 Pa v 0 0 p 100 kg m Foam plasticity data are given in the text Figure 12 49 Dimensions in millimeters and material properties SYSTEM Ong Oss Ose 257 707 25 5 707 5 All subsequent nodal definitions will be in this local coordinate system To reset the coordinate system to the default use another SYSTEM option with no data lines
6. 9 21 EXAMPLE STRESS WAVE PROPAGATION IN A BAR pos 0425 poo 0 5 S33 0 75 x10 0 00 20 00 40 00 60 00 80 00 Stress S33 Pa 100 00 120 00 0 00 0 05 0 10 0 15 0 20 x10 Total time s Figure 9 i i g 9 Time history of stress S33 at three points alon the length of the bar 0 25 m 0 5 m and 0 75 m SS KKSSSSSSOSOSSSS SS SILLS SSH SSS SSS ST SSS SS ISEEET ELE LEE EEE EH SSS SSS VISSSSHKHVS SOL NSS SSS gt Q SSS SST HLT a H H O HH E H r HE r CE ee aT H TEI N Prr HE Hi FA ELD RRRS lt N SSRS cnn anann FRR SBAS Snn SSSQVSgsssssspypp yy SSSPEELLE PPL SSS HHH Coo HHH 7 f i i aM Ly LN Wy 0 Y h Poy LZ LZ LLLI N i OH OOH H HHHH 50x10x10 LZLLZI 27 LIZ 7777 ZZ ZZ LZ LZ Lz LZ LLII LLLLLLD LLLLLLZ Perr LZ 50x10x5 LZ LZ TAFA Z Z7 LZ A Z Z7 aa LOI H m LZ L m Figure 9 10 Meshes from least to most refined Table 9 1 shows how th e CPU time n E E l ormalized with respect to the co bae onie ere na oa Problem The first half of the table DA a AA the result l uations presented in this guide th ee s obtained by running the analyses in Abaqus Explicit oa a Phen ne a ae table provides workstation 9
7. This expression is commonly referred to as the Mooney Rivlin material model If Co 1s also zero the material is called neo Hookean The other hyperelastic models are similar in concept and are described in Hyperelasticity Section 22 5 of the Abaqus Analysis User s Manual You must provide Abaqus with the relevant material parameters to use a hyperelastic material For the polynomial form these are C and D It is possible that you will be supplied with these parameters when modeling hyperelastic materials however more likely you will be given test data for 10 53 HYPERELASTICITY the materials that you must model Fortunately Abaqus can accept test data directly and calculate the material parameters for you using a least squares fit 10 6 4 Defining hyperelastic behavior using test data A convenient way of defining a hyperelastic material is to supply Abaqus with experimental test data Abaqus then calculates the constants using a least squares method Abaqus can fit data for the following experimental tests e Uniaxial tension and compression e Equibiaxial tension and compression e Planar tension and compression pure shear e Volumetric tension and compression The deformation modes seen in these tests and the Abaqus input options used to define the data for each are shown in Figure 10 38 Unlike plasticity data the test data for hyperelastic materials must be given to Abaqus as nominal stress and nominal strain v
8. 0 585 0 0192 Area 1 5 I torsional rigidity lt n gt lt n gt lt n gt lt Young s modulus gt lt torsional shear modulus gt CENTROID 0 1 642857 SHEAR CENTER 0 1 202857 It is also possible to define the beam nodes and shell nodes separately and connect the beam and shell using a rigid beam constraint between the two nodes See Linear constraint equations Section 34 2 1 of the Abaqus Analysis User s Manual for further details 6 2 Formulation and integration All beam elements in Abaqus are beam column elements meaning they allow axial bending and torsional deformation The Timoshenko beam elements also consider the effects of transverse shear deformation 5 FORMULATION AND INTEGRATION 6 2 1 Shear deformation The linear elements B21 and B31 and the quadratic elements B22 and B32 are shear deformable Timoshenko beams thus they are suitable for modeling both stout members in which shear deformation is important and slender beams in which shear deformation is not important The cross sections of these elements behave in the same manner as the cross sections of the thick shell elements as illustrated in Figure 6 7 b and discussed in Shell formulation thick or thin Section 5 2 dw y p dw dx Neutral dx AXIS Neutral axliS Transverse Transverse E section 7 section Ea Zs Deformation of cross section Deformation of cross section
9. 12 90 COMPATIBILITY BETWEEN Abaqus Standard AND Abaqus Explicit LEP Max CalcAfterFilter bw500 x1 E 6 lan LEP Max FilterAfterCalc bw500 80 60 40 Strain 20 0 5 10 15 20 x1 E 3 Time s Figure 12 67 Principal logarithmic strain calculated before and after filtering cutoff frequency 500 Hz from aliased data In addition it may not be obvious when results have been over filtered or aliased if additional data are not available for comparison A good strategy is to choose a relatively high output rate and use the Abaqus Explicit filters to prevent aliasing of the history output so that valid and rich results are written to the output database You may even wish to request output at every increment for a couple of critical locations After the analysis completes use the postprocessing tools in Abaqus Viewer to quickly and iteratively apply additional filtering as desired 12 11 Compatibility between Abaqus Standard and Abaqus Explicit There are fundamental differences in the mechanical contact algorithms in Abaqus Standard and Abaqus Explicit These differences are reflected in how contact conditions are defined The main differences are the following e For contact pairs Abaqus Standard typically uses a pure master slave relationship for the contact constraints by default see Defining contact pairs in Abaqus Standard Section 35 3 1 of the Abaqus Analysis User s Manual the nodes of the slave
10. 6 1 1 Section points When you specify BEAM SECTION Abaqus calculates the beam element s response at an array of section points throughout the beam cross section The number of section points as well as the section point locations are shown in Beam cross section library Section 29 3 9 of the Abaqus Analysis User s Manual Element output variables such as stress and strain are available at any of the section points however by default output is provided at only a select number of section points as listed in Beam cross section library Section 29 3 9 of the Abaqus Analysis User s Manual All the section points for a rectangular cross section SECTION RECT are shown in Figure 6 2 21 23 Integration 2 points SX 9 Array of section points at each 1 integration point Nodes 3 5 Figure 6 2 Integration and default section points in a B32 rectangular beam element For this cross section output 1s provided at points 1 5 21 and 25 by default The beam element shown in Figure 6 2 uses a total of 50 section points 25 at each of the two integration points to calculate its stiffness When you specify BEAM GENERAL SECTION Abaqus does not calculate the beam s response at the section points Instead it uses the section engineering properties to determine the section response Therefore Abaqus uses section points only as locations for output and you need to specify the section points at which you desire output Use
11. The plot created by these commands is shown in Figure 11 13 The axial stress history of the same element during Step 3 can be plotted by itself by selecting only the RESTART curve see Figure 11 14 x1 E9 0 80 0 70 ORIGINAL RESTART 0 60 0 50 Y v Aa 0 40 O Se mjd u 0 30 0 20 0 10 0 00 0 0 0 5 1 0 1 5 2 0 Total Time Figure 11 13 History of axial stress in the pipe 11 6 Related Abaqus examples e Deep drawing of a cylindrical cup Section 1 3 4 of the Abaqus Example Problems Manual 11 24 SUMMARY x1 E9 0 80 0 65 Stress S11 10 1 2 1 4 1 6 1 8 2 0 Total Time Figure 11 14 History of axial stress in the pipe during Step 3 Linear analysis of the Indian Point reactor feedwater line Section 2 2 2 of the Abaqus Example Problems Manual Vibration of a cable under tension Section 1 4 3 of the Abaqus Benchmarks Manual Random response to jet noise excitation Section 1 4 10 of the Abaqus Benchmarks Manual Summary An Abaqus simulation can include any number of steps Implicit and explicit steps are not allowed in the same analysis job 11 25 SUMMARY e An analysis step is a period of time during which the response of the model to a specified set of loads and boundary conditions is calculated The character of this response is determined by the particular analysis procedure used during the step e The response of a structure in a general
12. YMAX 7 915E 04 x1 E6 Peak tensile point 0 05 Probe this point 0 05 0 00 0 10 0 20 0 30 0 40 0 50 Time Figure 7 9 History of the reaction forces at the attached nodes To query the X Y plot 1 2 3 From the main menu bar select Tools Query The Query dialog box appears Click Probe values in the Visualization Module Queries field The Probe Values dialog box appears Select the point indicated in Figure 7 9 The Y coordinate of this point is 40 30 kN which corresponds to the value of the reaction force in the 1 direction 7 21 EFFECT OF DAMPING 7 6 Effect of the number of modes For this simulation 30 modes were used to represent the dynamic behavior of the structure The total modal effective mass for all of these modes was well over 90 of the mass of the structure that can move in the y and zdirections indicating that the dynamic representation is adequate Figure 7 10 shows the displacement in the direction of degree of freedom 2 at node 104 versus time and illustrates the effect of using fewer modes on the quality of the results If you look at the table of effective mass you will see that the first significant mode in the 2 direction is mode 3 which accounts for the lack of response when only two modes are used The displacement of this node in the direction of degree of freedom 2 for the analyses using five modes and 30 modes is similar after 0 2 seconds however the early resp
13. Abaqus 612 Getting Started with Abaqus Keywords Edition 2 FS PnULIA Getting Started with Abaqus Keywords Edition Legal Notices CAUTION This documentation is intended for qualified users who will exercise sound engineering judgment and expertise in the use of the Abaqus Software The Abaqus Software is inherently complex and the examples and procedures in this documentation are not intended to be exhaustive or to apply to any particular situation Users are cautioned to satisfy themselves as to the accuracy and results of their analyses Dassault Systemes and its subsidiaries including Dassault Systemes Simulia Corp shall not be responsible for the accuracy or usefulness of any analysis performed using the Abaqus Software or the procedures examples or explanations in this documentation Dassault Syst mes and its subsidiaries shall not be responsible for the consequences of any errors or omissions that may appear in this documentation The Abaqus Software is available only under license from Dassault Syst mes or its subsidiary and may be used or reproduced only in accordance with the terms of such license This documentation is subject to the terms and conditions of either the software license agreement signed by the parties or absent such an agreement the then current software license agreement to which the documentation relates This documentation and the software described in this documentation are subject to change witho
14. By default Abaqus Standard allows a maximum of five cutbacks of increment size in an increment before stopping the analysis In Abaqus Standard you can also add the INC parameter to specify the maximum number of increments allowed during the step Abaqus Standard terminates the analysis with an error message if it needs more increments than this limit to complete the step The default number of increments for a step 1s 100 if significant nonlinearity is present in the simulation the analysis may require many more increments The INC parameter specifies an upper limit on the number of increments that Abaqus Standard can use rather than the number of increments it must use For example a step involving nonlinear geometry with a maximum of 150 increments would be specified as STEP NLGEOM YES INC 150 8 10 THE SOLUTION OF NONLINEAR PROBLEMS In a nonlinear analysis a step takes place over a finite period of time although this time has no physical meaning unless inertial effects or rate dependent behavior are present In Abaqus Standard you specify the initial time increment AT initial and the total step time 7 4 on the data line of the procedure option used in the step For example STATIC 0 1 1 0 A Total step time T total Initial time increment AT iria defines a static analysis that occurs over 1 0 units of time and has an initial increment of 0 1 The ratio of the initial time increment to the step t
15. Computer Methods in Applied Mechanics and Engineering vol 43 251 276 1984 e Flanagan D P and T Belytschko A Uniform Strain Hexahedron and Quadrilateral with Hourglass Control International Journal for Numerical Methods in Engineering vol 17 679 706 1981 e Puso M A A Highly Efficient Enhanced Assumed Strain Physically Stabilized Hexahedral Element International Journal for Numerical Methods in Engineering vol 49 1029 1064 2000 Incompatible mode elements e Simo J C and M S Rifai A Class of Assumed Strain Methods and the Method of Incompatible Modes International Journal for Numerical Methods in Engineering vol 29 1595 1638 1990 4 53 SUMMARY 4 7 Summary The formulation and order of integration used in a continuum element can have a significant effect on the accuracy and cost of the analysis First order linear elements using full integration are prone to shear locking and normally should not be used First order reduced integration elements are prone to hourglassing sufficient mesh refinement minimizes this problem When using first order reduced integration elements in a simulation where bending deformation will occur use at least four elements through the thickness Hourglassing is rarely a problem in the second order reduced integration elements in Abaqus Standard You should consider using these elements for most general applications when there is no c
16. Displacement U2 at tip S b31 alpha std b31 alpha xpl 30 00 b33 zeta std 0 00 0 05 0 10 0 15 0 20 0 25 0 30 0 35 0 40 0 45 0 50 Time Figure 7 13 Comparison of tip displacements obtained from Abaqus Standard and Abaqus Explicit 7 9 Other dynamic procedures We now briefly review the other dynamic procedures available in Abaqus namely linear modal dynamics and nonlinear dynamics 7 26 OTHER DYNAMIC PROCEDURES 7 9 1 Linear modal dynamics There are several other linear dynamic procedures in Abaqus Standard that employ the modal superposition technique Unlike MODAL DYNAMIC which calculates the response in the time domain these procedures provide results in the frequency domain which can give additional insight into the behavior of the structure A complete description of these procedures is given in Dynamic stress displacement analysis Section 6 3 of the Abaqus Analysis User s Manual Steady state dynamics The STEADY STATE DYNAMICS option calculates the amplitude and phase of the structure s response caused by harmonic excitation over a user specified range of frequencies Typical examples include the following e The response of car engine mounts over a range of engine operating speeds e Rotating machinery in buildings e Components on aircraft engines Response spectrum The RESPONSE SPECTRUM option provides an estimate of the peak response displacement stress etc when a structure i
17. Figure 12 13 Smoothing an analytical rigid surface Rigid surface normals Start of line segments End of line segments Figure 12 14 Normals for an analytical rigid surface The normals for a rigid surface created from rigid elements are defined by the faces specified on the SURFACE option creating the surface 12 5 Abaqus Standard 2 D example forming a channel This simulation of the forming of a channel in a long metal sheet illustrates the use of rigid surfaces and some of the more complex techniques often required for a successful contact analysis in Abaqus Standard The problem consists of a strip of deformable material called the blank and the tools the punch die and blank holder that contact the blank The tools are modeled as analytical rigid surfaces because they are much stiffer than the blank Figure 12 15 shows the basic arrangement of the components The blank 1s 1 mm thick and is squeezed between the blank holder and the die The blank holder force is 440 KN This force in conjunction with the friction between the blank and blank holder and the blank and die controls how the blank material 1s drawn into the die during the forming process You have been asked to determine the forces acting on the punch during the forming process You also must assess how well the channel is formed with these particular settings for the blank holder force and the coefficient of friction between the tools and blank
18. The default view is isometric Try rotating the model to find a better view of the first eigenmode similar to that shown in Figure 11 10 Natural frequency modes 1 and 2 47 1 Hz The base state undeformed configuration is the deformed shape from Step 1 Figure 11 10 First and second eigenmode shapes of the pipe section under the tensile load the modes lie in planes orthogonal to each other Since this is a linear perturbation step the undeformed shape is the shape of the structure in the base state This makes it easy to see the motion relative to the base state Use the Frame Selector to plot the other mode shapes You will discover that this model has many repeated eigenmodes This is a result of the symmetric nature of the pipe s cross section which yields two eigenmodes 11 15 RESTART ANALYSIS for each natural frequency corresponding to the 1 2 and 1 3 planes The second eigenmode shape is shown in Figure 11 10 Some of the higher vibrational mode shapes are shown in Figure 11 11 Natural frequency modes 3 and 4 118 4 Hz Natural frequency modes 5 and 6 218 5 Hz Figure 11 11 Shapes of eigenmodes 3 through 6 corresponding mode shapes lie in planes orthogonal to each other The natural frequency associated with each eigenmode is reported in the plot title The lowest natural frequency of the pipe section when the 4 MN tensile load is applied is 47 1 Hz The tensile loading has increased the stiff
19. The model data section begins with the element definitions which summarize all the model data The model data also include the material description It is always a good idea to check that Abaqus has interpreted the material properties you gave in the input file correctly Mistakes in the material properties can sometimes cause subtle errors that are difficult to detect from the results It is easier to check the data here ELEMENT DEFINITIONS NUMBER TYPE PROPERTY NODES FORMING ELEMENT REFERENCE 11 T2D2 1 101 102 12 T2D2 1 102 103 13 T2D2 1 101 104 14 T2D2 1 102 104 15 T2D2 1 102 105 16 T2D2 1 103 105 17 T2D2 1 104 105 SOLID SECTION 8 PROPERTY NUMBER 1 MATERIAL NAME STEEL ATTRIBUTES 1 96300E 05 0 0000 0 0000 HOURGLASS CONTROL STIFFNESS 3 84615E 08 USED WITH LOWER ORDER REDUCED INTEGRATED SOLID ELEMENTS LIKE CPS4R CPE4RH C3D8R MATERIAL DESCRIPTION MATERIAL NAME STEEL ELASTIC YOUNG S POISSON S MODULUS RATIO 2 00000E 11 0 30000 2 22 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST ELEMENT SETS SET FRAME MEMBERS 11 12 13 14 15 16 17 NODE SETS SET NALL MEMBERS 101 102 103 104 105 NODE DEFINITIONS NODE COORDINATES SINGLE POINT CONSTRAINTS NUMBER TYPE PLUS DOF 101 0 0000 0 0000 0 0000 ENCASTRE 102 1 0000 0 0000 0 0000 103 2 0000 0 0000 0 0000 2 104 0 50000 0 86600 0 0000 105 1 5000 0 86600 0 0000 History data loads and database output The history data are presented below in two sections The first line of
20. 0 40 0 40 0 20 0 20 NORMALIZED TIP DISPLACEMENT NORMALIZED TIP DISPLACEMEN 0 00 0 00 0 00 10 00 20 00 30 00 40 00 0 00 10 00 20 00 30 00 40 00 SKEW ANGLE Degrees SKEW ANGLE Degrees Parallel distortion Trapezoidal distortion Figure 4 12 Effect of parallel and trapezoidal distortion of incompatible mode elements Three types of plane stress elements in Abaqus Standard are compared the fully integrated linear element the reduced integration quadratic element and the linear incompatible mode element The fully integrated linear elements produce poor results in all cases as expected On the other hand the reduced integration quadratic elements give very good results that do not deteriorate until the elements are badly distorted When the incompatible mode elements are rectangular even a mesh with just one element through the thickness of the cantilever gives results that are very close to the theoretical value However even quite small levels of trapezoidal distortion make the elements much too stiff Parallel distortion also reduces the accuracy of the element but to a lesser extent Incompatible mode elements are useful because they can provide high accuracy at a low cost if they are used appropriately However care must be taken to ensure that the element distortions are small which may be difficult when meshing complex geometries therefore you should again consider using the reduced integration quadrat
21. 12 60 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST 12 10 22 Mesh design The overall mesh for this problem is shown in Figure 12 50 NN femma Y JN N AN MRK RY X Y Figure 12 50 Mesh of the circuit board and foam packaging Define the circuit board so that the shell normals are in the direction indicated Defining the bottom corner of the foam packaging as the origin of your model will ensure the correct positioning of the circuit board and packaging Since the ground onto which the board will be dropped 1s effectively rigid use a single R3D4 element for this part of the model The packaging 1s a three dimensional solid structure that should be modeled using C3D8R elements The circuit board itself can be considered as a thin flat plate with various chips attached to it Therefore model the circuit board with S4R elements and model the chips with MASS elements Since you will be using shell elements for the circuit board Abaqus Explicit will by default use the original shell element thickness when checking for contact The circuit board and its slot in the foam packaging are both the same thickness 2 mm so that there is a snug fit between the two bodies In this example the circuit board is a mesh of 10 x 10 S4R elements and the foam packaging is a mesh of 6 x 7 x 15 elements as shown in Figure 12 51 12 61 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST SSS SSS f f ff Figure 12 51 Packaging
22. 12 16 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL Punch force Blank holder force symmetry Blank me Die Final punch position x Figure 12 15 Forming analysis A two dimensional plane strain model will be used The assumption that there is no strain in the out of plane direction of the model is valid if the structure is long in this direction Only half of the channel needs to be modeled because the forming process is symmetric about a plane along the center of the channel The model will use contact pairs rather than general contact since general contact is not available for analytical rigid surfaces in Abaqus Standard The dimensions of the various components are shown in Figure 12 16 12 5 1 Coordinate system Two dimensional plane strain models are defined by default in the global 1 2 plane as shown in Figure 12 16 For the forming simulation place the origin of this plane at the bottom left hand corner of the blank Figure 12 16 The 1 direction will be normal to the symmetry plane which is located atx 0 12 5 2 Mesh design The mesh for this simulation can be divided into the deformable blank and the rigid tools Blank Once again the element type should be selected before the mesh 1s designed The mesh used for the blank should consist of four rows of 100 CPE4R elements see Figure 12 17 Four rows of 12 17 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL symmetry plane 1 x Fi
23. 5 576E 03 AT NODE 559 DOF 3 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE AVERAGE MOMENT 1 12 TIME AVG MOMENT 1 12 LARGEST RESIDUAL MOMENT 3 273E 03 AT NODE 1104 DOF 5 LARGEST INCREMENT OF ROTATION 1 598E 02 AT NODE 159 DOF 5 LARGEST CORRECTION TO ROTATION 1 598E 02 AT NODE 159 DOF 5 ROTATION CORRECTION TOO LARGE COMPARED TO ROTATION INCREMENT 8 18 EXAMPLE NONLINEAR SKEW PLATE In this example the initial time increment is 0 1 as specified in the input file The average force for the increment is 12 2 N and q has the same value since this is the first increment The largest residual force in the model r az is 749 N which is clearly greater than 0 005 x 9 Th az occurred at node 1051 in degree of freedom 1 Abaqus must also check for equilibrium of the moments in the model since this model includes shell elements The moment rotation field also failed to satisfy the equilibrium check Although failure to satisfy the equilibrium check is enough to cause Abaqus to try another iteration you should also examine the displacement correction In the first iteration of the first increment of the first step the largest increment of displacement Au _ and the largest correction Max to displacement c z are both 5 576 x 10 m and the largest increment of rotation and correction to rotation are both 1 598 x 10 radians Since the incremental values and the corrections are always equal in the first iteration of the fir
24. Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST A3 N 403 NSET BOTCHIP ALL A3_ANTIALIASING N 403 NSET CHIPS A3_ANTIALIASING N 403 NSET BOTCHIP LARGEINC x1 E3 2 0 a 15 Se c 10 O i 1 T a k ile i 5 08 I T i 3 E ARIARI IRIE O 0 0 e LI iA e a lt fe i ra 2 0 5 ji D gt 10 i ANO AW E O 0 5 10 15 x1 E 3 Time s Figure 12 63 Filtered acceleration with different output sampling rates Another issue to note is that there is a time delay in the acceleration results recorded every 0 7 ms This time delay or phase shift affects all real time filters The filter must have some input in order to produce output consequently the filtered result will include some time delay While some time delay is introduced for all real time filtering the time delay becomes more pronounced as the filter cutoff frequency decreases the filter must have input over a longer span of time in order to remove lower frequency content Increasing the filter order an option if you have created a user defined filter rather than using the second order built in anti aliasing filter also results in an increase in the output time delay For more information see Filtering output and operating on output in Abaqus Explicit in Output to the output database Section 4 1 3 of the Abaqus Analysis User s Manual Use the real time filtering functionality with caution In this example we would not have been ab
25. Abaqus Viewer reports the element ID and type by default and the value of the Mises stress at each integration point starting with the first integration point The Mises stress values at the integration points are all lower than the values reported in the contour legend and also below the yield stress of 580 MPa You can click mouse button 1 to store probed values 5 Click Cancel when you have finished probing the results The fact that the extrapolated values are so different from the integration point values indicates that there 1s a rapid variation of stress across the elements and that the mesh is too coarse for accurate stress calculations This extrapolation error will be less significant if the mesh is refined but will 10 22 5 EXAMPLE CONNECTING LUG WITH PLASTICITY always be present to some extent Therefore always use nodal values of element variables with caution Contour plot of equivalent plastic strain The equivalent plastic strain in a material PEEQ is a scalar variable that is used to represent the material s inelastic deformation If this variable is greater than zero the material has yielded Those parts of the lug that have yielded can be identified in a contour plot of PEEQ by selecting Primary from the list of variable types on the left side of the Field Output toolbar and selecting PEEQ from the list of output variables Any areas in the model plotted in a dark color in Abaqus Viewer still have elastic material be
26. Create elements in your model that correspond to the elements shown in Figure 6 15 but remember that your numbering may be different Having the same numbering will make defining some modeling features easier however There are several element sets that you will need in this simulation As the elements are defined they are grouped into following element sets OUTA 100 101 102 103 104 105 106 BRACEA 110 111 112 113 114 OUTB 200 201 202 203 204 205 206 BRACEB 210 211 212 213 214 CROSSEL 300 301 302 303 304 305 306 307 where these element numbers refer to those elements shown in Figure 6 15 The element sets OUTA and OUTB contain the main outer members for the two truss structures Element sets BRACEA and 6 16 EXAMPLE CARGO CRANE BRACEB contain the elements modeling the internal bracing within each truss structure Element set CROSSEL contains the cross bracing that connects the two truss structures Beam element properties Since the material behavior in this simulation is assumed to be linear elastic use the BEAM GENERAL SECTION option to define the section properties All of the beams in this structure have a box shaped cross section A box section is specified using the parameter SECTION BOX The first data line contains the section dimensions which are the dimensions a b t1 t2 t3 and t4 shown in Figure 6 16 for a box section The dimensions shown in Figure 6 16 are fo
27. Ensure that the end of the step definition is clearly marked with an END STEP option 10 7 7 Running the analysis Store your input options in a file called mount inp The input options for the model discussed in the above sections can be found in Axisymmetric mount Section A 10 Since the nonlinear nature of the simulation means that it may take some time to complete use the following command to run the analysis in the background abaqus job mount When the job has completed check the data file mount dat for errors If there are any correct the input file and rerun the analysis If necessary compare your input with that shown in Axisymmetric mount Section A 10 10 67 5 EXAMPLE AXISYMMETRIC MOUNT 10 7 8 We briefly review the results associated with the polynomial fit of the test data Results The hyperelastic material parameters In this simulation you specified that the material is incompressible 0 The incompressibility is assumed since no volumetric test data were provided To simulate compressible behavior you must provide volumetric test data in addition to the other test data You also specified that Abaqus should use a first order polynomial strain energy function This form of the hyperelasticity model is known as the Mooney Rivlin material model The hyperelastic material coefficients C9 Co1 and D that Abaqus calculates from the material test data are given in the data file moun
28. FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE NOTE THE SOLUTION APPEARS TO BE DIVERGING CONVERGENCE IS JUDGED UNLIKELY Now that you have reviewed the early increments of the simulation move to the end of the message file and review the last increment Abaqus attempted You will see that Abaqus is using a very small increment size on the order of 1 0 x 10 in this final increment because of the many cut backs The iteration summaries for the last increment are shown below Abaqus makes two attempts to find a solution in this final increment but it must cut back the time increment in each 10 16 EXAMPLE CONNECTING LUG WITH PLASTICITY attempt because the strain increments are so large that it does not even try to perform the plasticity calculations This check on the magnitude of the total strain increment is another example of the many automatic solution controls Abaqus uses to ensure that the solution obtained for your simulation is both accurate and efficient The automatic solution controls are suitable for almost all simulations Therefore you do not have to worry about providing parameters to control the solution algorithm you only have to be concerned with the input data for your model INCREMENT 24 STARTS ATTEMPT NUMBER 1 TIME INCREMENT 2 250E 05 WARNING THE STRAIN INCREMENT HAS EXCEEDED FIFTY TIMES THE STRAIN TO CAUSE FIRST YIELD AT 152 POINTS WARNING THE STRAIN INCREMENT IS SO LARGE THAT THE PROGRAM WILL NO
29. Figure 6 7 Behavior of transverse beam sections in a slender beams and b thick beams Abaqus assumes the transverse shear stiffness of these beam elements to be linear elastic and constant In addition these beams are formulated so that their cross sectional area can change as a function of the axial deformation an effect that 1s considered only in geometrically nonlinear simulations see Chapter 8 Nonlinearity in which the POISSON parameter on the beam section property option has a nonzero value These elements can provide useful results as long as the cross section dimensions are less than 1 10 of the typical axial dimensions of the structure which is generally considered to be the limit of the applicability of beam theory if the beam cross section does not remain plane under bending deformation beam theory is not adequate to model the deformation The cubic elements available in Abaqus Standard the so called Euler Bernoulli beam elements B23 and B33 do not model shear flexibility The cross sections of these elements remain perpendicular to the beam axis see Figure 6 7 a Therefore the cubic beam elements are most effective for modeling structures with relatively slender members Since cubic elements model a cubic variation of displacement along their lengths a structural member often can be modeled with a single cubic element for a static analysis and with a small number of elements for a dynamic analysis These element
30. Plot forceDisp std and forceDisp xpl in the viewport There is significantly more noise in the Abaqus Explicit results compared to the Abaqus Standard results because Abaqus Explicit simulates a quasi static response while Abaqus Standard solves for true static equilibrium Some of the noise in the Abaqus Explicit history data was removed during the analysis by the built in anti aliasing filter specified on the output request Now you will use an Abaqus Viewer X Y data filter to remove more of the solution noise from the Abaqus Explicit force displacement curve The Abaqus Viewer X Y data filters should only be applied to X Y data whose X value is time This avoids confusion regarding the meaning of the filter cutoff frequency and prevents problems with the data regularization that is performed internally before the filter is applied Consequently you will not filter forceDisp xpl1 directly but rather you will filter U2 xp1 and RF2 xp1 individually before combining them to create a new force displacement curve It is best to apply the same filter operations both during the analysis and during postprocessing to any two X Y data objects that will be combined This will ensure that any distortions due to filtering such as time delays are uniformly applied to the combined data 13 20 9 10 11 12 13 14 15 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit In the Operate on XY Data dialog box filter the force history
31. Step 7 Stand on sink Figure 11 7 Steps in the manufacture and use of a sink 11 8 EXAMPLE VIBRATION OF A PIPING SYSTEM The following procedures in Abaqus Standard are always linear perturbation steps BUCKLE e FREQUENCY e MODAL DYNAMIC e RANDOM RESPONSE e RESPONSE SPECTRUM and e STEADY STATE DYNAMICS The STATIC procedure can be either a general or linear perturbation procedure Include the PERTURBATION parameter on the STEP option to make a static step a linear perturbation procedure 11 3 Example vibration of a piping system In this example you will study the vibrational frequencies of a 5 m long section of a piping system The pipe is made of steel and has an outer diameter of 18 cm and a 2 cm wall thickness see Figure 11 8 nT Se ee ee ee ee Global 1 axis D m Origin Wall thickness 0 02m Figure 11 8 Portion of piping system being analyzed It is clamped firmly at one end and can move only axially at the other end This 5 m portion of the piping system may be subjected to harmonic loading at frequencies up to 50 Hz The lowest vibrational mode of the unloaded structure is 40 1 Hz but this value does not consider how the loading applied to the piping structure may affect its response To ensure that the section does not resonate you have been asked to determine the magnitude of the in service load that is required so that its lowest vibrational mode is higher than 50 Hz You are to
32. The explicit central difference operator satisfies the dynamic equilibrium equations at the beginning of the increment t the accelerations calculated at time t are used to advance the velocity solution to time t At 2 and the displacement solution to time t At For linear and nonlinear problems alike explicit methods require a small time increment size that depends solely on the highest natural frequency of the model and is independent of the type and duration of loading Simulations typically require a large number of increments however due to the fact that a global set of equations is not solved in each increment the cost per increment of an explicit method is much smaller than that of an implicit method The small increments characteristic of an explicit dynamic method make Abaqus Explicit well suited for nonlinear analysis 8 2 1 Steps increments and iterations This section introduces some new vocabulary for describing the various parts of an analysis It is important that you clearly understand the difference between an analysis step a load increment and an iteration e The load history for a simulation consists of one or more steps You define the steps which generally consist of an analysis procedure option loading options and output request options Different loads boundary conditions analysis procedure options and output requests can be used in each step For example Step 1 Hold a plate between rigid jaws St
33. The procedure option block should look like STATIC O1 1 0 Boundary conditions Specify symmetry boundary conditions on the nodes lying on the symmetry plane In this model the symmetry conditions prevent the nodes from moving in degree of freedom 2 axially as shown in Figure 10 50 10 65 5 EXAMPLE AXISYMMETRIC MOUNT AAAAAA AAAA AAAA AAAA AAA AAAA AAAA AA 4 oe a SH tH oe os N mr Figure 10 50 Boundary conditions on the rubber mount Symmetry conditions that constrain motion in the global 2 direction can be applied using the YSYMM type boundary condition or you can simply constrain the 2 direction In this case the BOUNDARY option block has the following format BOUNDARY MIDDLE 2 2 0 0 No boundary constraints are needed in the radial direction global 1 direction because the axisymmetric nature of the model does not allow the structure to move as a rigid body in the radial direction Abaqus will allow nodes to move in the radial direction even those initially on the axis of symmetry 1 e those with a radial coordinate of 0 0 if no boundary conditions are applied to their radial displacements degree of freedom 1 Since you
34. U1 2 2 Translation in the 2 direction U2 3 Translation in the 3 direction U3 4 Rotation about the 1 direction UR1 5 Rotation about the 2 direction UR2 6 Rotation about the 3 direction UR3 dof 4 dof 6 The degrees of freedom active at a node depend on the type of elements attached to that node Chapter 3 Finite Elements and Rigid Bodies describes the active degrees of freedom for some of the elements available in Abaqus The two dimensional truss element T2D2 has two degrees of freedom active at each node translation in the 1 and 2 directions dof 1 and dof 2 respectively Constraints on nodes are defined by using the BOUNDARY option and specifying the constrained degrees of freedom Each data line is of the form lt node number gt lt first dof gt lt last dof gt lt magnitude of displacement gt The first degree of freedom and last degree of freedom are used to give a range of degrees of freedom that will be constrained For example the following statement constrains degrees of freedom 1 2 and 3 at node 101 to have zero displacement the node cannot move in either the global 1 2 or 3 direction 101 1 3 0 0 If the magnitude of the displacement is not specified on the data line it is assumed to be zero If the node is constrained in one direction only the third field should be blank or equal to the second EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST field For example to const
35. When discussing this equation with reference to convergence and nonlinearity we write it as P I 0 For the complete two element three node structure we therefore modify the signs and rewrite the equilibrium equation as A QUICK REVIEW OF THE FINITE ELEMENT METHOD ine K ky 0 u P K K K K gt u 0 lo 0 Ko Ko u In an implicit method such as that used in Abaqus Standard this system of equations can then be solved to obtain values for the three unknown variables u u and P u is specified in the problem as 0 0 Once the displacements are known we can go back and use them to calculate the stresses in the truss elements Implicit finite element methods require that a system of equations is solved at the end of each solution increment In contrast to implicit methods an explicit method such as that used in Abaqus Explicit does not require the solving of a simultaneous system of equations or the calculation of a global stiffness matrix Instead the solution is advanced kinematically from one increment to the next The extension of the finite element method to explicit dynamics is covered in the following section 1 6 2 Stress wave propagation illustrated This section attempts to provide some conceptual understanding of how forces propagate through a model when using the explicit dynamics method In this illustrative example we consider the propagation of a stress wave along a rod modeled with three
36. an internal set is created by Abaqus that can be used for visualization purposes To display a subset of the model 1 In the Results Tree double click Display Groups The Create Display Group dialog box opens 2 From the Item list select Elements From the Method list select Internal sets Once you have selected these items the list on the right hand side of the Create Display Group dialog box shows the available selections 3 Using this list identify the set that contains the elements at the bottom of the hole Toggle on Highlight items in viewport below the list so that the outlines of the elements in the selected set are highlighted in red 4 32 EXAMPLE CONNECTING LUG 4 When the highlighted set corresponds to the group of elements at the bottom of the hole click P Replace D to replace the current model display with this element set Abaqus Viewer displays the specified subset of your model 5 Click Dismiss to close the Create Display Group dialog box When creating an Abaqus model you may want to determine the face labels for a solid element For example you may want to verify that the correct load ID was used when applying pressure loads or when defining surfaces for contact In such situations you can use the Visualization module to display the mesh after you have run a datacheck analysis that creates an output database file To display the face identification labels and element numbers on the undeforme
37. double click XY Data The Create XY Data dialog box appears Choose Path as the X Y data source and click Continue The XY Data from Path dialog box appears with the path that you created visible in the list of available paths If the undeformed model shape is currently displayed the path you select is highlighted in the plot 3 Toggle on Include intersections under Point Locations 4 Accept True distance as the selection in the X Values region of the dialog box Click Field Output in the Y Values region of the dialog box to open the Field Output dialog box Select the S33 stress component and click OK The field output variable in the XY Data from Path dialog box changes to indicate that stress data in the 3 direction S33 will be created Note Abaqus Viewer may warn you that the field output variable will not affect the current image Leave the plot state As is and click OK to continue Click Step Frame in the Y Values region of the XY Data from Path dialog box 8 In the Step Frame dialog box that appears choose frame 1 which is the second of the five 10 11 12 recorded frames The first frame listed frame 0 is the base state of the model at the beginning of the step Click OK The Y Values region of the XY Data from Path dialog box changes to indicate that data from Step 1 frame 1 will be created To save the X Y data click Save As The Save XY Data As dialog box appears Nam
38. icon to the left of a topic heading to expand it The headings of the subtopics appear under the topic heading and the sign changes to indicating that the section is expanded If appears beside a subsection there are no further levels within that section to expand To collapse an expanded section of the table of contents click next to the topic heading SUPPORT 7 In the search panel in the navigation frame type any word that appears in the text frame on the right and click Search When the search is complete the table of contents frame displays the number of hits next to each topic heading and all hits become highlighted in the text frame Click Next Match or Previous Match in the navigation frame to move through the document from one hit to the next You can enter a single word or a phrase in the search panel and you can use the character as a wildcard For detailed instructions on using the search capabilities of the online documentation see Using Abaqus Online Documentation 8 Close the web browser windows 1 5 Support Both technical engineering support for problems with creating a model or performing an analysis and systems support for installation licensing and hardware related problems for Abaqus are offered through a network of local support offices Regional contact information is listed in the front of each Abaqus manual and is accessible from the Locations page at www simulia com Support is also
39. if the small piece of material is modeled using a single element its deformed shape is like that shown in Figure 4 5 Cae Figure 4 5 Deformation of a fully integrated linear element subjected to bending moment M For visualization dotted lines that pass through the integration points are plotted It is apparent that the upper line has increased in length indicating that the direct stress in the 1 direction 01 1s tensile Similarly the length of the lower dotted line has decreased indicating that c11 1s compressive The length of the vertical dotted lines has not changed assuming that displacements are small therefore 022 at all integration points is zero All this is consistent with the expected state of stress of a small piece of material subjected to pure bending However at each integration point the angle between the vertical and horizontal lines which was initially 90 has changed This indicates that the shear stress c12 at 4 4 ELEMENT FORMULATION AND INTEGRATION these points is nonzero This is incorrect the shear stress in a piece of material under pure bending is zero This spurious shear stress arises because the edges of the element are unable to curve Its presence means that strain energy is creating shearing deformation rather than the intended bending deformation so the overall deflections are less the element is too stiff Shear locking only affects the performance of fully integrated linear elem
40. increment 1s Le Altable Cd We then assumed that the characteristic element length L is the smallest element dimension whereas Abaqus Explicit actually determines the characteristic element length based on the overall size and shape ofthe element Another complication is that Abaqus Explicit employs a global stability estimator which allows a larger stable time increment to be used These factors make it difficult to predict the stable time increment accurately before running the analysis However since the trends follow nicely from the simplified theory it is straightforward to predict how the stable time increment will change with mesh refinement 9 4 7 How the material affects the stable time increment and CPU time The same wave propagation analysis performed on different materials would take different amounts of CPU time depending on the wave speed of the material For example if we were to change the material from steel to aluminum the wave speed would change from 5 15 x 10 m s to 9 23 5 DAMPING OF DYNAMIC OSCILLATIONS E 70x109 Pa ca 4 5 09 x 10 m s p 2700 kg m The change from aluminum to steel has minimal effect on the stable time increment because the stiffness and the density differ by nearly the same amount In the case of lead the difference is more substantial as the wave speed decreases to E 14 x 109 Pa ca 4f 5 1 12 x 10 m s p 11240 kg m which is
41. no stiffness to resist the applied load two elements through width Linear reduced integration elements tend to be too flexible because they suffer from their own numerical problem called hourglassing Again consider a single reduced integration element modeling a small piece of material subjected to pure bending see Figure 4 8 MCE k Figure 4 8 Deformation of a linear element with reduced integration subjected to bending moment M Neither of the dotted visualization lines has changed in length and the angle between them is also unchanged which means that all components of stress at the element s single integration point are zero 4 1 ELEMENT FORMULATION AND INTEGRATION This bending mode of deformation is thus a zero energy mode because no strain energy is generated by this element distortion The element is unable to resist this type of deformation since it has no stiffness in this mode In coarse meshes this zero energy mode can propagate through the mesh producing meaningless results In Abaqus a small amount of artificial hourglass stiffness is introduced in first order reduced integration elements to limit the propagation of hourglass modes This stiffness is more effective at limiting the hourglass modes when more elements are used in the model which means that linear reduced integration elements can give acceptable results as long as a reasonably fine mesh is used The errors seen with the finer meshes of l
42. on either the deformed or the undeformed plots Use the Normals options in the Common Plot Options dialog box to do this and confirm that the surface normals are in the correct directions Abaqus Standard may still have some problems with contact simulations even when the contact surfaces are all defined correctly One reason for these problems may be the default convergence tolerances and limits on the number of iterations they are quite rigorous In contact analyses it is sometimes better to allow Abaqus Standard to iterate a few more times rather than abandon the increment and try again This is why Abaqus Standard makes the distinction between severe discontinuity iterations and equilibrium iterations during the simulation The PRINT CONTACT YES option is essential for almost every contact analysis The information this option provides in the message file can be vital for spotting mistakes or problems For example chattering can be spotted because the same slave node will be seen to be involved in all of the severe discontinuity iterations If you see this you will have to modify the mesh in the region around that node or add constraints to the model Contact data in the message file can also identify regions where only a single slave node is interacting with a surface This is a very unstable situation and can cause convergence problems Again you should modify the model to increase the number of elements in such regions 12 28 Abaqus
43. 0 400 0 300 0 200 0 100 0 STRESS INVARIANT MISES 0 0 0 0 2 0 4 0 6 0 8 0 10 0 STRAIN E11 x10 Figure 10 17 Mises stress vs direct strain E11 along the lug in the corner element Maximum strain 0 01 This stress strain curve contains another apparent error It appears that the material yields at 250 MPa which is well below the initial yield stress However this error is caused by the fact that Abaqus Viewer connects the data points on the curve with straight lines If you limit the increment size the additional points on the graph will provide a better display of the material response and show yield occurring at exactly 380 MPa 10 27 5 EXAMPLE BLAST LOADING ON A STIFFENED PLATE The results from this second simulation indicate that the lug will withstand this 60 kN load if the steel hardens after it yields Taken together the results of the two simulations demonstrate that it is very important to determine the actual post yield hardening behavior of the steel If the steel has very little hardening the lug may collapse under the 60 kN load Whereas if it has moderate hardening the lug will probably withstand the load although there will be extensive plastic yielding in the lug see Figure 10 14 However even with plastic hardening the factor of safety for this loading will probably be very small 10 5 Example blast loading on a stiffened plate The previous example illustrated some of the co
44. 0 00 0 01 0 02 0 03 0 04 0 05 Time s Figure 10 28 Central node displacement as a function of time To generate a history plot of the central node displacement 1 In the Results Tree double click the history output data named Spatial displacement U2 at the node in the center of the plate set NOUT Save the current X Y data in the Results Tree click mouse button 3 on the data name and select Save As from the menu that appears Name the data DISP The units of the displacements in this plot are meters Modify the data to create a plot of displacement in millimeters versus time by creating a new data object In the Results Tree expand the XYData container The DISP data are listed underneath In the Results Tree double click X YData then select Operate on XY data in the Create XY Data dialog box Click Continue In the Operate on XY Data dialog box multiply DISP by 1000 to create the plot with the displacement values in millimeters instead of meters The expression at the top of the dialog box should appear as DISP 1000 10 42 6 7 8 EXAMPLE BLAST LOADING ON A STIFFENED PLATE Click Plot Expression to see the modified X Y data Save the data as U2 _ BASE Close the Operate on XY Data dialog box Click the Axis Options ii tool in the toolbox In the Axis Options dialog box change the X axis title to Time s and the Y axis title to Displacement mm Click OK to close the di
45. 0 29902E6 0 3 0 32455E6 0 4 0 34935E6 0 5 0 37326E6 0 6 0 39617E6 0 7 0 41801E6 0 8 0 43872E6 0 9 0 45827E6 1 0 0 49384E6 1 2 0 52484E6 1 4 0 55153E6 1 6 0 57431E6 1 8 0 59359E6 2 0 0 62936H6 2 5 0 65199E6 3 0 0 68334E6 5 0 0 68833E6 10 0 Boundary conditions The rigid surface representing the floor is fully constrained by applying a fixed boundary condition to the reference node which was previously defined as node set REF BOUNDARY REF ENCASTRE Initial conditions The circuit board and foam packaging is given an initial velocity of 4 43 m s in the global 3 direction corresponding to the velocity at the end of a meter free fall INITIAL CONDITIONS TYPE VELOCITY BOARD 3 4 43 PACK 3 4 43 Defining contact Either contact algorithm could be used for this problem However the definition of contact using the contact pair algorithm would be more cumbersome since unlike general contact the surfaces involved in contact pairs cannot span more than one body We use the general contact algorithm in this example to demonstrate the simplicity of the contact definition for more complex geometries 12 68 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST First a named contact property is defined using the SURFACE INTERACTION option a friction coefficient of 0 3 is defined SURFACE INTERACTION NAME FRIC FRICTION 0 3 Use the CONTACT option to define a general contact interaction Use
46. 005 0 005 0 005 0 005 0 1118 0 0 0 9936 200 E9 80 E9 The dimensions of the beam sections for the bracing members are shown in Figure 6 17 Both the cross bracing and the bracing within each truss structure have the same beam section geometry but they do not share the same orientation of the beam section axes Therefore separate BEAM GENERAL SECTION options must be used The bracing is made from the same steel as the main members to 0 003 b 0 03 r mea Figure 6 17 Cross section geometry and dimensions in m of the bracing members The approximate n vector for the internal truss bracing is the same as for the main members of the respective truss structures The following input defines the element properties of this bracing BEAM GENERAL SECTION SECTION BOX ELSET BRACEA 0 03 0 03 0 003 0 003 0 003 0 003 0 1118 0 0 0 9936 200 E9 80 E9 BEAM GENERAL SECTION SECTION BOX ELSET BRACEB 0 03 0 03 0 003 0 003 0 003 0 003 0 1118 0 0 0 9936 200 E9 80 E9 We make some assumptions so that the orientation of the cross bracing is somewhat easier to specify All of the beam normals n2 vectors should lie approximately in the plane of the plan view of the cargo crane see Figure 6 12 This plane is skewed slightly from the global 1 3 plane Again a simple method for defining such an orientation is to provide an approximate n vector that is orthogonal to this plane on the element property option
47. 1 17 1 0 3 3 0 953 0 953 6 599e 005 1 18 1U 0 2 2 0 953 0 953 9 899e 005 1 18 2 0 2 2 0 953 0 953 2 475e 005 1 19 1 0 3 3 0 953 0 953 3 712e 005 1 20 1U 0 1 1 0 953 0 953 5 568e 005 1 20 2 0 3 3 0 953 0 953 1 392e 005 1 21 1 0 3 3 0 953 0 953 2 088e 005 1 22 1U 0 1 1 0 953 0 953 3 132e 005 1 22 2 0 2 2 0 953 0 953 1 000e 005 1 23 1 0 3 3 0 953 0 953 1 500e 005 1 24 1U 0 1 1 0 953 0 953 2 250e 005 THE ANALYSIS HAS NOT BEEN COMPLETED Abaqus was able to apply only 95 of the prescribed load to the model and still obtain a converged solution The status file shows that Abaqus reduced the size of the time increment which is shown in the last right hand column many times during the simulation and stopped the analysis in the 10 14 EXAMPLE CONNECTING LUG WITH PLASTICITY 24th increment You will have to look at the information in the message file to understand why Abaqus terminated the simulation early Message file The message file lug_plas msg contains detailed information about the simulation s progress see Results Section 8 4 3 for more information about the format of the message file Look at the information for the first increment in the analysis it 1s also shown below you will discover that the model s initial behavior is linear and the displacement correction is ignored because the residual force is essentially zero The model s behavior was also linear in the second increment INCREMENT 1 STARTS ATTEMPT
48. 12 27 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL 2 167 2 0 4 4 1 95 0 952 0 002239 2 168 1 1 3 4 1 96 0 956 0 003358 2 169 1 2 2 4 1 96 0 961 0 005037 2 170 1 1 3 4 1 97 0 968 0 007556 2 171 1 3 3 6 1 98 0 980 0 01133 2 172 1U 4 0 4 1 98 0 980 0 01700 2 172 2 1 3 4 1 98 0 984 0 004250 2 173 1 3 2 5 1 99 0 990 0 006375 2 174 1U 4 0 4 1 99 0 990 0 009563 2 174 2 3 2 5 1 99 0 993 0 002391 2 175 1 1 2 3 2 00 0 996 0 003586 2 176 1 4 1 5 2 00 1 00 0 003721 THE ANALYSIS HAS COMPLETED SUCCESSFULLY This simulation contains many severe discontinuity iterations The message file will be quite large because of the number of iterations in the analysis Although it might be tempting to limit the information written to this file generally this should not be done because this information is the main source of diagnostic data that Abaqus provides during the simulation 12 5 8 Troubleshooting Abaqus Standard contact analyses Contact analyses are generally more difficult to complete than just about any other type of simulation in Abaqus Standard Therefore it is important to understand all of the options available to help you with contact analyses If a contact analysis runs into difficulty the first thing to check is whether the contact surfaces are defined correctly The easiest way to do this is to run a datacheck analysis and plot the surface normals in Abaqus Viewer You can plot all of the normals for both surfaces and structural elements
49. 14 15 16 Select all five curves Click mouse button 3 and select Plot from the menu that appears to view the X Y plot Next you will customize the appearance of the plot begin by changing the line styles of the curves Open the Curve Options dialog box In this dialog box apply different line styles and thicknesses to each of the curves displayed in the viewport Next reposition the legend so that it appears inside the plot Double click the legend to open the Chart Legend Options dialog box In this dialog box switch to the Area tabbed page and toggle on Inset In the viewport drag the legend over the plot Now change the format of the X axis labels In the viewport double click the X axis to access the X Axis options in the Axis Options dialog box In this dialog box switch to the Axes tabbed page and select the Engineering label format for the X axis The energy histories appear as shown in Figure 12 57 12 73 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST Artificial Energy Internal Energy Kinetic Energy Plastic Dissipation Strain Energy Energy J 0 5 10 15 20 x1 E 3 Time s Figure 12 57 Energy results versus time First consider the kinetic energy history At the beginning of the simulation the components are in free fall and the kinetic energy is large The initial impact deforms the foam packaging thus reducing the kinetic energy The components then bounce an
50. 22 EXAMPLE STRESS WAVE PROPAGATION IN A BAR Table 9 1 Mesh refinement and solution time Simplified Theory Theory Atetable Number of a Max Number of Normalized a BNA a on oat Time For the theoretical results we choose the coarsest mesh 25 x 5 x 5 as the base state and we define the stable time increment the number of elements and the CPU time as variables A B and C respectively As the mesh is refined two things happen the smallest element dimension decreases and the number of elements in the mesh increases Each of these effects increases the CPU time In the first level of refinement the 50 x 5 x 5 mesh the smallest element dimension is cut in half and the number of elements is doubled increasing the CPU time by a factor of four over the previous mesh However further doubling the mesh to 50 x 10 x 5 does not change the smallest element dimension it only doubles the number of elements Therefore the CPU time increases by only a factor of two over the 50 x 5 x 5 mesh Further refining the mesh so that the elements are uniform and square in the 50 x 10 x 10 mesh again doubles the number of elements and the CPU time This simplified calculation predicts quite well the trends of how mesh refinement affects the stable time increment and CPU time However there are reasons why we did not compare the predicted and actual stable time increment values First recall that we made the approximation that the stable time
51. 3 4 of the Abaqus Analysis User s Manual If you intend to model curved beam structures you should use one of the two methods described earlier to define the ny direction directly allowing you great control in modeling the curvature Even 5 BEAM CROSS SECTION GEOMETRY if you intend to model a structure made up of straight beams curvature may be introduced as normals are averaged at shared nodes You can rectify this problem by defining the beam normals directly as explained previously 6 1 4 Nodal offsets in beam sections When beam elements are used as stiffeners for shell models it is convenient to have the beam and shell elements share the same nodes By default shell element nodes are located at the midplane of the shell and beam element nodes are located somewhere in the cross section of the beam Hence if the shell and beam elements share the same nodes the shell and the beam stiffener will overlap unless the beam cross section is offset from the location of the node see Figure 6 5 Same node used for shell and beam elements Shell section DS i e e a b Figure 6 5 Using beams as stiffeners for shell models a without offset of beam sections b with offset of beam sections With beam section types I TRAPEZOID and ARBITRARY it is possible to specify that the section geometry is located at some distance from the origin of the section s local coordinate system which is located at the element s
52. A solver problem will occur during the solution stage and may cause the simulation to stop prematurely Abaqus Standard will issue a warning message if it detects a solver problem during a simulation It is important that you learn to interpret such error messages If you see a numerical singularity or zero pivot warning message during a static stress analysis you should check whether all or part of your model lacks constraints against rigid body translations or rotations Rigid body motions can consist of both translations and rotations of the components The potential rigid body motions depend on the dimensionality of the model Dimensionality Possible Rigid Body Motion Three dimensional Translation in the 1 2 and 3 directions Rotation about the 1 2 and 3 axes Axisymmetric Translation in the 2 direction Rotation about the 3 axis axisymmetric rigid bodies only Plane stress Translation in the 1 and 2 directions Plane strain Rotation about the 3 axis By default the 1 2 and 3 directions are aligned with the axes of a global Cartesian coordinate system discussed later 2 3 5 FORMAT OF THE INPUT FILE In a dynamic analysis inertia forces prevent the model from undergoing infinite motion instantaneously as long as all separate parts in the model have some mass therefore solver problem warnings in a dynamic analysis usually indicate some other modeling problem such as excessive plasticity Ana
53. ALLSE The end of the step 1s indicated with the END STEP option 12 10 7 Running the analysis Run the analysis using the following command abaqus job circuit analysis This analysis is somewhat more complicated than the previous analyses in this guide and it may take 45 minutes or more to run to completion depending on the power of your computer Status file Information concerning the initial stable time increment can be found at the top of the status file The 10 most critical elements 1 e those resulting in the smallest time increments are also shown in rank order 3 49594E 02 1 076765E 02 Total mass in model Center of mass of model 4 948691E 02 8 492255E 02 Moments of Inertia About Center of Mass About Origin I XX 6 655668E 05 4 042925E 04 I YY 9 949297E 05 3 556680E 04 I ZZ 6 893156E 05 1 585989E 04 I XY 1 344118E 05 5 187227E 06 I YZ 5 240504E 06 1 521594E 04 I ZX 3 958677E 05 7 155426E 05 The stable time increment estimate for each element is based on linearization about the initial state Initial time increment 8 80392E 07 Statistics for all elements Mean 1 04795E 05 Standard deviation 3 99235E 06 Most critical elements Element number Rank Time increment Increment ratio 98 1 8 803920E 07 1 000000E 00 83 2 8 803923E 07 9 999997E 01 80 3 8 803923E 07 9 999996E 01 79 4 8 803925E 07 9 999995E 01 71 5 8 803925E 07 9 999994E 01 30 6 8 803926E 07 9 999993E 01 36 7 8 803926
54. Abaqus Viewer to review all of the results from this simulation so all printed output requests have been deleted The resulting output request option in your input file appears below OUTPUT FIELD FREQUENCY 1 VARIABLE PRESELECT You will need to save some history data in the output database file to use with the X Y plotting capability in Abaqus Viewer The displacements for node set HOLEBOT which should already exist are stored using the following option OUTPUT HISTORY FREQUENCY 1 NODE OUTPUT NSET HOLEBOT U You also want detailed results for one of the elements along the built in end of the lug see Figure 10 9 element 206 Figure 10 9 Element 206 This is element 206 in the mesh generated by the commands found in Connecting lug with plasticity Section A 8 the element in this location may have a different number in your model This element is chosen because it 1s the element for which the stresses are most likely to be largest in magnitude In the input file for this example an element set has been created that contains the element and saves the stresses S stress invariants SINV plastic strains PE and strains E for that element set in the output database file The necessary option blocks are shown below ELEMENT OUTPUT ELSET EL206 S SINV PE E ELSET ELSET EL206 206 10 13 5 EXAMPLE CONNECTING LUG WITH PLASTICITY Note The ELSET option used to define the element set appears after
55. Create a default field output request and two history output requests In the first request displacement history for the set TIP in the second request reaction force history for the set ATTACH For your simulation the option block defining the output requests should look similar to the following NSET NSET TIP 104 OUTPUT FIELD VARIABLE PRESELECT OUTPUT HISTORY VARIABLE PRESELECT NODE OUTPUT NSET TIP U NODE OUTPUT NSET ATTACH RF Terminate the step with END STEP 8 Save the input file as dynamics xpl inp and submit for analysis abaqus job dynamics xpl inp 7 25 5 OTHER DYNAMIC PROCEDURES When the job completes navigate to the directory containing the output database file dynamics xpl1 odb and type the command abaqus viewer odb dynamics xpl at the operating system prompt to examine the results in Abaqus Viewer In particular compare the tip displacement history obtained earlier from Abaqus Standard with that obtained from Abaqus Explicit As shown in Figure 7 13 there are small differences in the response These differences are due to the different element and damping types used for the modal dynamic analysis In fact if the Abaqus Standard analysis is modified to use B31 elements and mass proportional damping the results produced by the two analysis products are nearly indistinguishable see Figure 7 13 which confirms the accuracy of the modal dynamic procedure k10 10 00 20 00
56. DISP 1 171E 05 AT NODE 5817 DOF 2 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 3 AVERAGE FORCE 801 TIME AVG FORCE 461 LARGEST RESIDUAL FORCE 1 755E 02 AT NODE 12855 DOF 1 LARGEST INCREMENT OF DISP 2 691E 04 AT NODE 815 DOF 2 LARGEST CORRECTION TO DISP 1 054E 07 AT NODE 817 DOF 2 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED ITERATION SUMMARY FOR THE INCREMENT 3 TOTAL ITERATIONS OF WHICH 10 15 5 EXAMPLE CONNECTING LUG WITH PLASTICITY 0 ARE SEVERE DISCONTINUITY ITERATIONS AND 3 ARE EQUILIBRIUM ITERATIONS TIME INCREMENT COMPLETED 0 300 FRACTION OF STEP COMPLETED 0 700 STEP TIME COMPLETED 0 700 TOTAL TIME COMPLETED 0 700 Abaqus attempts to find a solution in the fourth increment using an increment size of 0 3 which means it is applying 30 of the total load or 18 MPa during this increment After several iterations Abaqus issues warning messages that the strain increments it calculated exceed the strain at initial yield by 50 times After a few more iterations Abaqus determines that the solution in this increment is not going to converge instead it is diverging Therefore Abaqus abandons this attempt at finding a solution reduces the increment size to 25 of the value used in the first attempt and tries a second attempt at finding a solution This reduction in increment size is called a cut back With the smaller increment size Abaqus finds a converged solution in just a f
57. ELSET PLATE ELEMENT TYPE CAX4H ELSET RUBBER Node sets Check that the node set MIDDLE has been created If it has not add it using an editor Property definition Two element property definitions are required one for the elements modeling the rubber and one for those modeling the plates The following element property definitions should be in your model SOLID SECTION MATERIAL RUBBER ELSET RUBBER SOLID SECTION MATERIAL STEEL ELSET PLATE 10 61 5 EXAMPLE AXISYMMETRIC MOUNT Material properties hyperelastic model for the rubber You have been given some experimental test data shown in Figure 10 46 for the rubber material used in the mount Three different sets of test data a uniaxial test a biaxial test and a planar shear test are available You decide to have Abaqus calculate the appropriate hyperelastic material constants from the test data You are not sure how large the strains will be in the rubber mount but you suspect that they will be under 2 0 Xx x UNIAXIAL 6 E E BIAXIAL x1 O PLANAR 2 4 Nominal Stress Pa 0 0 0 5 1 0 12 2 0 2 5 3 0 3 5 4 0 Nominal Strain Figure 10 46 Material test data for the rubber material The test data for the biaxial and planar tests go well beyond this magnitude so you decide to perform a one element simulation of the experimental tests to confirm that the coefficients that Abaqus calculates from the test data are adequate Use a first
58. FACTOR AFTER TOO MANY EQUILIBRIUM ITERATIONS 0 7500 CUT BACK FACTOR AFTER TOO MANY SEVERE DISCONTINUITY ITERATIONS 0 2500 CUT BACK FACTOR AFTER PROBLEMS IN ELEMENT ASSEMBLY 0 2500 INCREASE FACTOR AFTER TWO INCREMENTS THAT CONVERGE QUICKLY 1 500 MAX TIME INCREMENT INCREASE FACTOR ALLOWED 1 500 MAX TIME INCREMENT INCREASE FACTOR ALLOWED DYNAMICS 1 250 MAX TIME INCREMENT INCREASE FACTOR ALLOWED DIFFUSION 2 000 MINIMUM TIME INCREMENT RATIO FOR EXTRAPOLATION TO OCCUR 0 1000 MAX RATIO OF TIME INCREMENT TO STABILITY LIMIT 1 000 FRACTION OF STABILITY LIMIT FOR NEW TIME INCREMENT 0 9500 TIME INCREMENT INCREASE FACTOR BEFORE A TIME POINT 1 000 GLOBAL STABILIZATION CONTROL IS NOT USED PRINT OF INCREMENT NUMBER TIME ETC EVERY 1 INCREMENTS Abaqus lists a summary of each iteration in the message file after the lists of tolerances and controls It prints the values of the largest residual force r __ largest increment of displacement Auga the largest correction to displacement c and the time averaged force q It also prints the nodes and degrees of freedom DOF at which r Auga and ca occur A similar summary is Max printed for rotational degrees of freedom INCREMENT 1 STARTS ATTEMPT NUMBER 1 TIME INCREMENT 0 100 CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 1 AVERAGE FORCE 12 2 TIME AVG FORCE 12 2 LARGEST RESIDUAL FORCE 749 AT NODE 1051 DOF 1 LARGEST INCREMENT OF DISP 5 576E 03 AT NODE 559 DOF 3 LARGEST CORRECTION TO DISP
59. NORMAL option takes precedence Abaqus again defines the n direction as no x t The ny direction that you provide need not be orthogonal to the beam element tangent t When you provide the ng direction the local beam element tangent is redefined as the value of the cross product n X n It is quite possible in this situation that the redefined local beam tangent t will not align with the beam axis as defined by the vector from the first to the second node If the ng direction subtends an angle greater than 20 with the plane perpendicular to the element axis Abaqus issues a warning message in the data file The example presented in Example cargo crane Section 6 4 explains how to assign the beam cross section orientation in your model 6 1 3 Beam element curvature The curvature of beam elements is based on the orientation of the beam s n direction relative to the beam axis If the ng direction and the beam axis are not orthogonal 1 e the beam axis and the tangent t do not coincide the beam element is considered to be curved initially Since the behavior of curved beams is different from the behavior of straight beams you should always check your model to ensure that the correct normals and hence the correct curvatures are used For beams and shells Abaqus uses the same algorithm to determine the normals at nodes shared by several elements A description is given in Beam element cross section orientation Section 29
60. OF DOF IF DISCON ITERS ITERS TIME TIME LPF TIME LPF MONITOR RIKS ITERS FREQ 1 1 1 0 1 1 0 200 0 200 0 2000 1 2 1 0 1 1 0 400 0 400 0 2000 1 3 1 0 3 3 0 700 0 700 0 3000 1 4 1 0 7 7 1 00 1 00 0 3000 In this simulation there is very little information of interest in the message file There are no warnings issued during the analysis so you can proceed directly to postprocessing the results with Abaqus Viewer 10 4 7 Postprocessing the results Start Abaqus Viewer and use the following command to review the results of the second analysis abaqus viewer odb lug plas hard Deformed model shape and peak displacements Plot the deformed model shape with these new results and change the deformation scale factor to 2 to obtain a plot similar to Figure 10 12 The displayed deformations are double the actual deformations Contour plot of Mises stress Contour the Mises stress in the model Create a filled contour plot using ten contour intervals on the actual deformed shape of the lug 1 e set the deformation scale factor to 1 0 with the plot title and state blocks suppressed Use the view manipulation tools to position and size the model to obtain a plot similar to that shown in Figure 10 13 Do the values listed in the contour legend surprise you The maximum stress 1s greater than 580 MPa which should not be possible since the material was assumed to be perfectly plastic at this stress magnitude This misleading result occurs because of th
61. STARTED WITH Abaqus The CATIA V5 Associative Interface creates a link between CATIA V5 and Abaqus CAE that allows you to transfer model data and propagate design changes from CATIA V5 to Abaqus CAE The SolidWorks Associative Interface creates a link between SolidWorks and Abaqus CAE that allows you to transfer model data and propagate design changes from SolidWorks to Abaqus CAE The Pro ENGINEER Associative Interface creates a link between Pro ENGINEER and Abaqus CAE that allows you to transfer model data and propagate design changes between Pro ENGINEER and Abaqus CAE The Geometry Translator for CATIA V4 allows you to import the geometry of CATIA V4 format parts and assemblies directly into Abaqus CAE The Geometry Translator for Parasolid allows you to import the geometry of Parasolid format parts and assemblies directly into Abaqus CAE In addition the Abaqus CAE Associative Interface for NX creates a link between NX and Abaqus CAE that allows you to transfer model data and propagate design changes between NX and Abaqus CAE The Abaqus CAE Associative Interface for NX can be purchased and downloaded from Elysium Inc www elysiuminc com The geometry translators are not discussed in this guide Translator utilities Abaqus provides the following translators for converting entities from third party preprocessors to input for Abaqus analyses or for converting output from Abaqus analyses to entities for third party postprocessors
62. Source 1 ODB lug odb Step Step 1 Frame Increment 1 Step Time 2 2200E 16 Loc 1 Integration point values from source 1 Output sorted by column Element Label Field Output reported at nodes for part PART 1 1 Element Int S Mises S S11 S S22 Ss S33 Ss S12 Label Pt Loc 1 Loc 1 Loc 1 Loc 1 Loc 1 s S13 S S23 Loc 1 Loc 1 206 1 293 921E 06 281 921E 06 8 1398E 06 13 8667E 06 6 99752E 06 11 6881E 06 1 15564E 06 206 2 286 9E 06 347 661E 06 87 6292E 06 81 1577E 06 49 8957E 06 42 7097E 06 3 12903E 06 206 3 196 605E 06 183 407E 06 1 32717E 06 8 90914E 06 33 674E 06 6 34469E 06 1 77895E 06 206 4 168 508E 06 194 713E 06 38 9812E 06 38 4224E 06 24 4931E 06 27 2442E 06 3 10456E 06 206 5 306 077E 06 303 672E 06 1 19087E 06 2 78165E 06 8 25811E 06 4 05888E 06 184 07E 03 206 6 271 531E 06 329 68E 06 79 7248E 06 74 0551E 06 56 4163E 06 9 20019E 06 78 3313E 03 206 7 205 123E 06 199 438E 06 7 85751E 06 1 07157E 06 34 4693E 06 2 34785E 06 546 279E 03 206 8 157 315E 06 180 601E 06 33 2797E 06 32 7648E 06 30 9435E 06 5 64979E 06 74 1186E 03 1236 1 205 096E 06 199 458E 06 7 88628E 06 1 07185E 06 34 4032E 06 2 3479E 06 545 449E 03 1236 2 157 301E 06 180 618E 06 33 2934E 06 32 7715E 06 30 9083E 06 5 65027E 06 74 2669E 03 1236 3 306 071E 06 303 67E 06 1 18777E 06 2 78175E 06 8 2327E 06 4 05827E 06 185 017E 03 1236 4 271 48E 06 329 625E 06 79 7048E 06 74 0391E 06 56 3889E 06 9 19885E 06 78 2027E 03 1236
63. Standard to perform design sensitivity calculations Abaqus Design is not discussed in this guide Abaqus AMS Abaqus AMS 1s an optional capability that can be added to Abaqus Standard It uses the automatic multi level substructuring AMS eigensolver during a natural frequency extraction Abaqus AMS is not discussed in this guide Abaqus Foundation Abaqus Foundation offers more efficient access to the linear static and dynamic analysis functionality in Abaqus Standard Abaqus Foundation is not discussed in this guide Abaqus Interface for Moldflow The Abaqus Interface for Moldflow translates finite element model information from a Moldflow analysis to write a partial Abaqus input file The Abaqus Interface for Moldflow is not discussed in this guide Abaqus Interface for MSC ADAMS The Abaqus Interface for MSC ADAMS allows Abaqus finite element models to be included as flexible components within the MSC ADAMS family of products The interface is based on the component mode synthesis formulation of ADAMS Flex The Abaqus Interface for MSC ADAMS is not discussed in this guide Geometry translators Abaqus provides the following translators for converting geometry from third party CAD systems to parts and assemblies for Abaqus CAE e The SIMULIA Associative Interface for Abaqus CAE creates a link between CATIA V6 and Abaqus CAE that allows you to transfer model data and propagate design changes from CATIA V6 to Abaqus CAE 5 GETTING
64. THE FOLLOWING TABLE IS PRINTED FOR ALL ELEMENTS WITH TYPE T2D2 AT THE INTEGRATION POINTS ELEMENT PT FOOT S11 NOTE 11 1 1 4706E 08 12 1 1 4706E 08 13 1 2 9412E 08 14 1 2 9412E 08 15 1 2 9412E 08 16 1 2 9412E 08 17 1 2 9412E 08 MAXIMUM 2 9412E 08 ELEMENT 14 MINIMUM 2 9412E 08 ELEMENT 17 Node output NODE OUTPUT THE FOLLOWING TABLE IS PRINTED FOR ALL NODES NODE FOOT U1 U2 NOTE 102 7 3531E 04 4 6698E 03 103 1 4706E 03 0 000 104 1 4706E 03 2 5472E 03 105 0 000 2 5472E 03 2 27 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST MAXIMUM 1 4706E 03 0 000 AT NODE 104 101 MINIMUM 0 000 4 6698E 03 AT NODE 101 102 THE FOLLOWING TABLE IS PRINTED FOR ALL NODES NODE FOOT RF1 RF2 NOTE 101 9 0949E 13 5000 103 0 000 5000 MAXIMUM 0 000 5000 AT NODE 102 103 MINIMUM 9 0949E 13 0 000 AT NODE 101 102 Are the nodal displacements and peak stresses in the individual members reasonable for this hoist and these applied loads It is always a good idea to check that the results of the simulation satisfy basic physical principles In this case check that the external forces applied to the hoist sum to zero in both the vertical and horizontal directions What nodes have vertical forces applied to them What nodes have horizontal forces Do the results from your simulation match those shown here Abaqus also creates several other files during a simulation One such file the output database file frame odb can be u
65. The current area is related to the original area by l A A7 Substituting this definition of A into the definition of true stress gives OF Fl l a Mel A y where l lo can also be written as TE noms Making this final substitution provides the relationship between true stress and nominal stress and strain C one al za Pnom These relationships are valid only prior to necking The PLASTIC option in Abaqus defines the post yield behavior for most metals Abaqus approximates the smooth stress strain behavior of the material with a series of straight lines joining the given data points Any number of points can be used to approximate the actual material behavior therefore it is possible to use a very close approximation of the actual material behavior The data on the PLASTIC option define the true yield stress of the material as a function of true plastic strain The first piece of data given defines the initial yield stress of the material and therefore should have a plastic strain value of zero The strains provided in material test data used to define the plastic behavior are not likely to be the plastic strains in the material Instead they will probably be the total strains in the material You must decompose these total strain values into the elastic and plastic strain components The plastic strain is obtained by subtracting the elastic strain defined as the value of true stress divided by the Young s modulus from th
66. The nodal displacements are appended to the report file 7 In the Variable tabbed page of the Report Field Output dialog box toggle off U Spatial displacement and select RF1 and RF2 from the list of available RF Reaction force variables 8 In the Data region at the bottom of the Setup tabbed page toggle on Column totals 9 Click OK The reaction forces are appended to the report file and the Report Field Output dialog box closes Open the file Frame rpt in a text editor The contents of this file are shown below Your node and element numbering may be different Very small values may also be calculated differently depending on your system Stress output Field Output Report Source 1 ODB frame odb Step Step 1 Frame Increment 1 Step Time 2 2200E 16 Loc 1 Integration point values from source 1 Output sorted by column Element Label Field Output reported at integration points for part PART 1 1 Element Int S S11 Label Pt Loc 1 11 1 147 062E 06 12 1 147 062E 06 13 1 294 118E 06 14 1 294 118E 06 15 1 294 118E 06 16 1 294 118E 06 1 294 125E 06 2 35 Minimum At Element Int Pt Maximum At Element Int Pt Displacement output Field Output Report Source 1 ODB Step Frame frame odb Step 1 Increment Loc 1 1 Step Time Nodal values from source 1 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST 294 125E 06 17 1 294 118E 06 15 1 2 2200E 16
67. Using the field output toolbar Section 42 5 2 of the Abaqus CAE User s Manual Abaqus Viewer offers many options to customize contour plots To see the available options click the Contour Options a tool in the toolbox By default Abaqus Viewer automatically 4 28 EXAMPLE CONNECTING LUG 8 879e 06 Step Step 1 Increment 1 Step Time 2 2200E 16 Primary Var S Mises z xX Deformed Var U Deformation Scale Factor 2 968e 01 Figure 4 30 Filled contour plot of Mises stress computes the minimum and maximum values shown in your contour plots and evenly divides the range between these values into 12 intervals You can control the minimum and maximum values Abaqus Viewer displays for example to examine variations within a fixed set of bounds as well as the number of intervals To generate a customized contour plot 1 In the Basic tabbed page of the Contour Plot Options dialog box drag the Contour Intervals slider to change the number of intervals to nine 2 In the Limits tabbed page of the Contour Plot Options dialog box choose Specify beside Max then enter a maximum value of 400E 6 3 Choose Specify beside Min then enter a minimum value of 60E 6 4 Click OK Abaqus Viewer displays your model with the specified contour option settings as shown in Figure 4 31 this figure shows Mises stress your plot will show whichever output variable you have chosen These settings re
68. Velocity the bottom chip in the Z direction 6 In the Operate on XY Data dialog box integrate acceleration A3 a second time to calculate chip displacement The expression at the top of the dialog box should appear as integrate integrate A3 4 43 7 Click Plot Expression to plot the calculated displacement curve 12 76 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST Notice that the Y value type is length In order to plot the calculated displacement with the same Y axis as the displacement output recorded during the analysis we must save the X Y data and change the Y value type to displacement 8 Click Save As to save the calculated displacement curve as U3 from A3 10 11 12 In the XYData container of the Results Tree click mouse button 3 on U3 from A3 and select Edit from the menu that appears In the Edit XY Data dialog box choose Displacement as the Y value type In the Results Tree double click U3 from A3 to recreate the calculated displacement plot with the displacement Y value type In the Results Tree click mouse button 3 on the displacement U3 history output for node 403 and select Add to Plot from the menu that appears The X Y plot appears in the viewport As before customize the plot appearance to obtain a plot similar to Figure 12 60 Again the curve you produced by integrating the acceleration data may be different from the one pictured here The reason for this will be discus
69. WHEN THERE IS ZERO FLUX 1 000E 03 CRITERION FOR RESIDUAL MOMENT FOR A LINEAR INCREMENT 1 000E 08 FIELD CONVERSION RATIO 1 00 CRITERION FOR ZERO MOMENT REL TO TIME AVRG MAX MOMENT 1 000E 05 VOLUMETRIC STRAIN COMPATIBILITY TOLERANCE FOR HYBRID SOLIDS 1 000E 05 AXIAL STRAIN COMPATIBILITY TOLERANCE FOR HYBRID BEAMS 1 000E 05 TRANS SHEAR STRAIN COMPATIBILITY TOLERANCE FOR HYBRID BEAMS 1 000E 05 SOFT CONTACT CONSTRAINT COMPATIBILITY TOLERANCE FOR P gt P0 5 000E 03 SOFT CONTACT CONSTRAINT COMPATIBILITY TOLERANCE FOR P 0 0 0 100 DISPLACEMENT COMPATIBILITY TOLERANCE FOR DCOUP ELEMENTS 1 000E 05 ROTATION COMPATIBILITY TOLERANCE FOR DCOUP ELEMENTS 1 000E 05 EQUILIBRIUM WILL BE CHECKED FOR SEVERE DISCONTINUITY ITERATIONS TIME INCREMENTATION CONTROL PARAMETERS FIRST EQUILIBRIUM ITERATION FOR CONSECUTIVE DIVERGENCE CHECK 4 EQUILIBRIUM ITERATION AT WHICH LOG CONVERGENCE RATE CHECK BEGINS 8 EQUILIBRIUM ITERATION AFTER WHICH ALTERNATE RESIDUAL IS USED 9 MAXIMUM EQUILIBRIUM ITERATIONS ALLOWED 16 EQUILIBRIUM ITERATION COUNT FOR CUT BACK IN NEXT INCREMENT 10 MAXIMUM EQUILIB ITERS IN TWO INCREMENTS FOR TIME INCREMENT INCREASE 4 MAXIMUM ITERATIONS FOR SEVERE DISCONTINUITIES 50 MAXIMUM CUT BACKS ALLOWED IN AN INCREMENT 5 MAXIMUM DISCON ITERS IN TWO INCREMENTS FOR TIME INCREMENT INCREASE 50 MAXIMUM CONTACT AUGMENTATIONS FOR SURFACE BEHAVIOR AUGMENTED LAGRANGE 6 CUT BACK FACTOR AFTER DIVERGENCE 0 2500 CUT BACK FACTOR FOR TOO SLOW CONVERGENCE 0 5000 CUT BACK
70. You can create X Y plots from field and history output To create X Y plots of the internal and kinetic energy as a function of time 1 In the Results Tree expand the History Output container underneath the output database named lug xpl odb 2 The list of all the variables in the history portion of the output database appears these are the only history output variables you can plot From the list of available output variables double click ALLIE to plot the internal energy for the whole model 4 43 5 EXAMPLE CONNECTING LUG Abaqus reads the data for the curve from the output database file and plots the graph shown in Figure 4 37 ALLIE for Whole Model fi i l J 0 0 1 0 2 0 3 0 4 0 5 0 x1 E 3 Figure 4 37 Internal energy for the whole model 3 Repeat this procedure to plot ALLKE the kinetic energy for the whole model shown in Figure 4 38 ALLKE for Whole Model 05 D 1 L l L l 1 1 Jo 1 0 20 3 0 4 0 5 0 x1 3 Time Figure 4 38 Kinetic energy for the whole model 4 44 EXAMPLE CONNECTING LUG Both the internal energy and the kinetic
71. a positive clearance to closed clearance equal to zero sometimes makes it difficult to complete contact simulations in Abaqus Standard the same is not true for Abaqus Explicit since iteration is not required for explicit methods Alternative enforcement methods e g penalty are available for contact pairs as discussed in Contact constraint enforcement methods in Abaqus Standard Section 37 1 2 of the Abaqus Analysis User s Manual Penalty enforcement of the contact constraints is the only option available for general contact Other sources of information include Common difficulties associated with contact modeling in Abaqus Standard Section 38 1 2 of the Abaqus Analysis User s Manual Common difficulties associated with contact modeling using contact pairs in Abaqus Explicit Section 38 2 2 of the Abaqus Analysis User s Manual the Modeling Contact with Abaqus Standard lecture notes and the Advanced Topics Abaqus Explicit lecture notes 12 2 2 Sliding of the surfaces In addition to determining whether contact has occurred at a particular point an Abaqus analysis also must calculate the relative sliding of the two surfaces This can be a very complex calculation therefore 12 2 INTERACTION BETWEEN SURFACES Abaqus makes a distinction between analyses where the magnitude of sliding is small and those where the magnitude of sliding may be finite It 1s much less expensive computationally to model
72. analysis is due to reductions in the stable time increment The stable time increment is discussed further in Chapter 9 Nonlinear Explicit Dynamics Since the response of a nonlinear system is not a linear function of the magnitude of the applied load it is not possible to create solutions for different load cases by superposition Each load case must be defined and solved as a separate analysis 8 1 Sources of nonlinearity There are three sources of nonlinearity in structural mechanics simulations e Material nonlinearity e Boundary nonlinearity e Geometric nonlinearity 8 1 1 Material nonlinearity This type of nonlinearity is probably the one that you are most familiar with and is covered in more depth in Chapter 10 Materials Most metals have a fairly linear stress strain relationship at low strain values but at higher strains the material yields at which point the response becomes nonlinear and irreversible see Figure 8 2 Rubber materials can be approximated by a nonlinear reversible elastic response see Figure 8 3 Material nonlinearity may be related to factors other than strain Strain rate dependent material data and material failure are both forms of material nonlinearity Material properties can also be a function of temperature and other predefined fields 8 1 2 Boundary nonlinearity Boundary nonlinearity occurs if the boundary conditions change during the analysis Consider the cantilever bea
73. analysis step may be either linear or nonlinear e The starting condition for each general step is the ending condition of the previous general step Thus the model s response evolves during a sequence of general steps in a simulation e Linear perturbation steps available only in Abaqus Standard calculate the linear response of the structure to a perturbation load The response is reported relative to the base state defined by the condition of the model at the end of the last general step e In general steps the OP parameter on any loading options such as BOUNDARY CLOAD and DLOAD controls how the values specified with these options interact with those values defined in previous steps e Analyses can be restarted as long as a restart file is saved Restart files can be used to continue an interrupted analysis or to add additional load history to the simulation 11 26 INTERACTION BETWEEN SURFACES 12 Contact Many engineering problems involve contact between two or more components In these problems a force normal to the contacting surfaces acts on the two bodies when they touch each other If there is friction between the surfaces shear forces may be created that resist the tangential motion sliding of the bodies The general aim of contact simulations is to identify the areas on the surfaces that are in contact and to calculate the contact pressures generated In a finite element analysis contact conditions are a specia
74. and Figure 13 10 respectively Kinetic Energy 2 00 4 00 6 00 x10 Time Figure 13 9 Kinetic energy history for forming analysis attempt 1 The kinetic energy history shown in Figure 13 9 oscillates significantly In addition the kinetic energy history has no clear relation to the forming of the blank which indicates the inadequacy of this analysis In this analysis the punch velocity remains constant while the kinetic energy which is primarily due to the motion of the blank is far from constant 13 14 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit x10 2 00 1 60 1 20 0 80 Internal Energy 0 40 0 00 L l 0 00 2 00 4 00 6 00 x10 Time Figure 13 10 Internal energy history for forming analysis attempt 1 Comparing Figure 13 9 and Figure 13 10 shows that the kinetic energy is a small fraction less than 1 of the internal energy through all but the very beginning of the analysis The criterion that kinetic energy must be small relative to internal energy has been satisfied even for this severe loading case Although the kinetic energy of the model is a small fraction of the internal energy it is still quite noisy Therefore we should change the simulation in some way to obtain a smoother response 13 5 2 Forming analysis attempt 2 Even if the punch actually moves at a nearly constant velocity the
75. and J L Sanders On the Best First Order Linear Shell Theory Progress in Applied Mechanics The Prager Anniversary Volume 129 140 1963 Advanced computational shell theory e Ashwell D G and R H Gallagher Finite Elements for Thin Shells and Curved Members John Wiley amp Sons 1976 e Hughes T J R T E Tezduyar Finite Elements Based upon Mindlin Plate Theory with Particular Reference to the Four Node Bilinear Isoparametric Element Journal of Applied Mechanics 587 596 1981 e Simo J C D D Fox and M S Rifai On a Stress Resultant Geometrically Exact Shell Model Part III Computational Aspects of the Nonlinear Theory Computer Methods in Applied Mechanics and Engineering vol 79 21 70 1990 5 28 5 8 SUMMARY Summary The cross section behavior of shell elements can be determined using numerical integration through the shell thickness SHELL SECTION or using a cross section stiffness calculated at the beginning of the analysis SHELL GENERAL SECTION SHELL GENERAL SECTION is efficient but it can be used only with linear materials SHELL SECTION can be used with both linear and nonlinear materials Numerical integration 1s performed at a number of section points through the shell thickness These section points are the locations at which element variables can be output The default outermost section points lie on the surfaces of the shell The direction of a sh
76. and normal throughout the deformation Hence transverse shear strains are assumed to vanish y 0 Figure 5 5 b illustrates the transverse shear behavior of thick shells material lines that are initially normal to the shell surface do not necessarily remain normal to the surface throughout the deformation thus adding transverse shear flexibility y 0 5 6 SHELL FORMULATION THICK OR THIN d AW y dw W dx dx Neutral dx AXIS Neutral a ri b axis Transverse section Transverse section Deformation of cross section Deformation of cross section Figure 5 5 Behavior of transverse shell sections in a thin shells and b thick shells Abaqus offers multiple classes of shell elements distinguished by the element s applicability to thin and thick shell problems General purpose shell elements are valid for use with both thick and thin shell problems In certain cases for specific applications enhanced performance can be obtained by using the special purpose shell elements available in Abaqus Standard The special purpose shell elements fall into two categories thin only shell elements and thick only shell elements All special purpose shell elements provide for arbitrarily large rotations but only small strains The thin only shell elements enforce the Kirchhoff constraint that is plane sections normal to the midsection of the shell remain normal to the midsurface The Kirchhoff constraint is enforced eithe
77. and require the use of excessively small time increments 10 6 3 Strain energy potential Abaqus uses a strain energy potential U rather than a Young s modulus and Poisson s ratio to relate stresses to strains in hyperelastic materials Several different strain energy potentials are available a polynomial model the Ogden model the Arruda Boyce model the Marlow model and the van der Waals model Simpler forms of the polynomial model are also available including the Mooney Rivlin neo Hookean reduced polynomial and Yeoh models The polynomial form of the strain energy potential is one that is commonly used Its form is N N zs E 1 U C3 Se XY Guth 9h 3 V5 aD where U is the strain energy potential Je is the elastic volume ratio J and Jy are measures of the distortion in the material and N C and D are material parameters which may be functions of temperature The C parameters describe the shear behavior of the material and the D parameters introduce compressibility If the material is fully incompressible a condition not allowed in Abaqus Explicit all the values of D are set to zero and the second part of the equation shown above can be ignored If the number of terms N is one the initial shear modulus jg and bulk modulus Ko are given by Ho 2 Co1 Cio and 2 5 If the material is also incompressible the equation for the strain energy density is Ko U Cro Ly _ 3 Co1 Ie 3
78. applied loads and Epw Ecw and Emw are the work done by contact penalties by constraint penalties and by propelling added mass respectively Hy pr is the external heat energy through external fluxes The sum of these energy components is 4q1 which should be constant In the numerical model o is only approximately constant generally with an error of less than 1 Internal energy The internal energy is the sum of the recoverable elastic strain energy Eg the energy dissipated through inelastic processes such as plasticity p the energy dissipated through viscoelasticity or creep cp the artificial strain energy 4 the energy dissipated through damage Epmnp the energy dissipated through distortion control pc and the fluid cavity energy Epc Er Eg Ep Ecp Ea Epmb Epc Erc The artificial strain energy includes energy stored in hourglass resistances and transverse shear in shell and beam elements Large values of artificial strain energy indicate that mesh refinement or other changes to the mesh are necessary 9 27 ENERGY BALANCE Viscous energy The viscous energy is the energy dissipated by damping mechanisms including bulk viscosity damping and material damping A fundamental variable in the global energy balance viscous energy is not part of the energy dissipated through viscoelasticity or inelastic processes External work of applied forces The external work is integrated forward continuously defined
79. are modeled with analytical rigid surfaces A rigid body reference node will be assigned to each of these surfaces when they are created If you did not create these rigid body reference nodes during preprocessing add the following option block to your model NODE NSET REFPUNCH 7000 0 000 0 06 NODE NSET REFHOLD 8000 0 1 0 06 NODE NSET REFDIE 9000 0 1 0 06 NSET NSET NOUT REFDIE REFHOLD REFPUNCH Each node is placed in a node set to make the input file easy to read While someone unfamiliar with the specific mesh used in the simulation may not know why boundary conditions are applied to node 7000 they might be able to guess why boundary conditions were applied to the REFPUNCH node All reference nodes are also assigned to a set named NOUT to facilitate the history output requests that will follow To ensure that an analytical rigid surface s normals point toward the deformable surfaces that the rigid surface will contact the segments composing the rigid surface must be defined in a particular order For example to create the correct normals for the surface PUNCH define the surface from the top right corner to the bottom left corner of the punch The following input to the model creates the surface PUNCH SURFACE TYPE SEGMENTS NAME PUNCH FILLET RADIUS 0 001 START 0 050 0 060 LINE 0 050 0 006 CIRCL 0 045 0 001 0 045 0 006 LINE 0 010 0 001 RIGID BODY ANALYTICAL SURFACE PUNCH REF NODE 7000 12 22 Ab
80. are partially attenuated To compensate for this the built in anti aliasing filter has a cutoff frequency that is one sixth of the sample rate a value lower than the Nyquist frequency of one half the sample rate In most cases including this example this cutoff frequency 1s adequate to ensure that all frequency content above the Nyquist frequency has been removed before the data are written to the output database Abaqus Explicit does not check to ensure that the specified output time interval provides an appropriate cutoff frequency for the internal anti aliasing filter for example Abaqus does not check that only the noise of the signal is eliminated When the acceleration data are recorded every 0 07 ms the internal anti aliasing filter 1s applied with a cutoff frequency of 2 4 kHz This cutoff frequency is nearly the same value we previously determined to be the maximum physically meaningful frequency for the model more than two orders of magnitude less than the maximum frequency the stable time increment can capture The 0 07 ms output interval was intentionally chosen for this example to avoid filtering frequency content that could be physically meaningful Next we will study the results when the anti aliasing filter is applied with a sample interval that is too large To plot the filtered acceleration histories 1 Inthe Results Tree double click the acceleration A3 history output for the node set Bot Chip all 2 Select the two fil
81. as damping Damping is usually assumed to be viscous or proportional to velocity The dynamic equilibrium equation can be rewritten to include damping as M I P 0 I Ku C where C is the damping matrix for the structure and is the velocity of the structure The dissipation of energy is caused by a number of effects including friction at the joints of the structure and localized material hysteresis Damping is a convenient way of including the important absorption of energy without modeling the effects in detail In Abaqus Standard the eigenmodes are calculated for the undamped system yet most engineering problems involve some kind of damping however small The relationship between the damped natural frequency and the undamped natural frequency for each mode is wa wy l1 where Wd is the damped eigenvalue E 5 is the damping ratio which is the fraction of critical damping is the damping of that mode shape and Cox is the critical damping The eigenfrequencies of the damped system are very close to the corresponding quantities for the undamped system for small values of lt 0 1 As increases the undamped eigenfrequencies become less accurate and as approaches 1 the use of undamped eigenfrequencies becomes invalid If a structure is critically damped 1 after any disturbance it will return to its initial static configuration as quickly as possible without overshooting Figure 7
82. be defined in the next section Setting OFFSET to SPOS offsets the midsurface of the plate one half of the shell thickness away from the nodes The effect is to make the PLATE nodes lie on the SPOS shell face instead of on the shell midsurface The purpose of the shell offset in this case is to allow the stiffeners to butt up against the plate without overlapping any material with the plate Figure 10 21 shows the cross section of the joint between the stiffener and panel using the OFFSET parameter stiffener nodes lie ra on shell midsurface stiffener plate nodes lie on shell SPOS or SNEG face base plate plate midsurface Figure 10 21 Stiffener joint in which the plate s midsurface is offset from its nodes If the stiffener and base plate elements are joined at common nodes at their midsurfaces an area of material overlaps as shown in Figure 10 22 10 32 EXAMPLE BLAST LOADING ON A STIFFENED PLATE overlapping material Figure 10 22 Overlapping material if OFFSET were not used If the thicknesses of the plate and stiffener is small in comparison to the overall dimensions of the structure this overlapping material and the extra stiffness it would create has little effect on the analysis results However if the stiffener is short in comparison to its width or to the thickness of the base plate the additional stiffness of the overlapping material could affect the response of the whole structure Mat
83. built in anti aliasing filter Use node set BotChip largelInc 12 80 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST OUTPUT HISTORY TIME INTERVAL 0 7E 3 FILTER ANTIALIASING NODE OUTPUT NSET BotChip largeInc U3 V3 A3 When you are finished there will be four history output requests for the bottom chip the original one and the three added here Evaluating the filtered acceleration of the bottom chip When the analysis completes test the plausibility of the acceleration history output for the bottom chip recorded every 0 07 ms using the built in anti aliasing filter Do this by saving and then integrating the filtered acceleration data A3 ANTIALIASING for node 403 in set CHIPS and comparing the results to recorded velocity and displacement data just as you did earlier for the unfiltered version of these results This time you should find that the velocity and displacement curves calculated by integrating the filtered acceleration are very similar to the velocity and displacement values written to the output database during the analysis You may also have noticed that the velocity and displacement results are the same regardless of whether or not the built in anti aliasing filter is used This is because the highest frequency content of the nodal velocity and displacement curves is much less than half the sampling rate Consequently no aliasing occurred when the data was recorded without filtering and when the built in anti alia
84. called necking as the material fails see Figure 10 2 The engineering stress force per unit undeformed area in the metal is known as the nominal stress with the conjugate nominal strain length change per unit undeformed length The nominal stress in the metal as it is necking is much lower than the material s ultimate strength This material behavior is caused by the geometry of the test specimen the nature of the test itself and the stress and strain measures used For example testing the same material in compression produces a stress strain plot that does not have a necking region because the specimen is not going to thin as it deforms under compressive loads A mathematical model describing the plastic behavior of metals should be able to account for differences in the compressive and tensile behavior independent of the structure s geometry or the nature of the applied loads This goal can be accomplished 10 3 PLASTICITY IN DUCTILE METALS if the familiar definitions of nominal stress F A o and nominal strain Al lo where the subscript 0 indicates a value from the undeformed state of the material are replaced by new measures of stress and strain that account for the change in area during the finite deformations 10 2 2 Stress and strain measures for finite deformations Strains in compression and tension are the same only if considered in the limit as Al dl 0 i e dl cS dl 4 p In l l
85. data consist of the following e Geometry Nodal coordinates Element connectivity Element section properties e Material properties Heading The first option in any Abaqus input file must be HEADING The data lines that follow the HEADING option are lines of text describing the problem being simulated You should provide an accurate description to allow the input file to be identified at a later date Moreover it is often helpful to specify the system of units directions of the global coordinate system etc For example the HEADING option block for the hoist problem contains the following HEADING Two dimensional overhead hoist frame SI units kg m s N l axis horizontal 2 axis vertical Data file printing options By default Abaqus will not print an echo of the input file or the model and history definition data to the printed output dat file However it is recommended that you check your model and history 2 11 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST definition in a datacheck run before performing the analysis The datacheck run is discussed later in this chapter To request a printout of the input file and of the model and history definition data add the following statement to the input file PREPRINT ECHO YES MODEL YES HISTORY YES Nodal coordinates The coordinates of each node can be defined once you select the mesh design and node numbering scheme For this problem use the nu
86. data from the Abaqus Standard analysis as U2 std and RF2 std respectively The number of the punch reference node is 7000 Similarly save punch displacement U2 and reaction force RF2 history data from the Abaqus Explicit analysis as U2 xp1 and RF2 xp1 respectively Next you will operate on saved X Y data to create the force displacement curves In the force displacement plot we would like the downward motion of the punch to be represented as a positive value therefore when you create the force displacement curves include a negative sign before the displacement history data so that motion in the negative 2 direction will be positive In the Results Tree double click X YData then select Operate on XY data in the Create XY Data dialog box Click Continue In the Operate on XY Data dialog box combine the force and displacement history data from the Abaqus Standard analysis to create a force displacement curve The expression at the top of the dialog box should appear as combine U2 std RF2 std 5 Click Save As to save the calculated displacement curve as forceDisp std 6 In the Operate on XY Data dialog box combine the force and displacement history data from the Abaqus Explicit analysis to create a force displacement curve The expression at the top of the dialog box should appear as combine U2 xpl RF2 xpl 7 Click Save As to save the calculated displacement curve as forceDisp xpl 8
87. database file from the restart analysis should be used by giving the following command abaqus viewer odb pipe 2 Plotting the eigenmodes of the pipe Plot the same six eigenmode shapes of the pipe section for this simulation as were plotted in the previous analysis The eigenmode shapes can be plotted using the procedures described for the original analysis These eigenmodes and their natural frequencies are shown in Figure 11 12 again the corresponding mode shapes lie in planes orthogonal to each other 11 21 EXAMPLE RESTARTING THE PIPE VIBRATION ANALYSIS Natural frequency modes 1 and 2 53 1 Hz Natural frequency modes 3 and 4 127 5 Hz Natural frequency modes 5 and 6 228 9 Hz Figure 11 12 Shapes and frequencies of eigenmodes 1 through 6 with 8 MN tensile load Under 8 MN of axial load the lowest mode is now at 53 1 Hz which is greater than the required minimum of 50 Hz If you want to find the exact load at which the lowest mode is just above 50 Hz you can repeat this restart analysis and change the value of the applied load Plotting X Y graphs from field data for selected steps Use the field data stored in the output database files pipe odb and pipe 2 odb to plot the history of the axial stress in the pipe for the whole simulation To generate a history plot of the axial stress in the pipe for the restart analysis 1 In the Results Tree double click XYData The Create XY Data dialog box appea
88. default no minimum or maximum frequency or shift is used If the structure is not constrained against rigid body modes the shift value should be set to a small negative value to remove numerical problems associated with rigid body motion The form of the FREQUENCY option block is FREQUENCY lt number of eigenvalues gt lt min frequency gt lt max frequency gt lt shift point gt The step and procedure option blocks for this simulation are STEP PERTURBATION Frequency extraction of the first 30 modes 7 11 5 EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING FREQUENCY 30 In structural dynamic analysis the response is usually associated with the lower modes However enough modes should be extracted to provide a good representation of the dynamic response of the structure One way of checking that a sufficient number of eigenvalues has been extracted is to look at the total effective mass in each degree of freedom which indicates how much of the mass is active in each direction of the extracted modes The effective masses are tabulated in the data file under the eigenvalue output Ideally the sum of the modal effective masses for each mode in each direction should be at least 90 of the total mass This is discussed further in Effect of the number of modes Section 7 6 Boundary conditions The boundary conditions are the same as in the static analysis Output By default Abaqus writes the mode shapes to the
89. deformed shape From the main menu bar select Plot Deformed Shape or use the Ea tool in the toolbox Figure 4 24 displays the deformed model shape at the end of the analysis What is the displacement magnification level Changing the view The default view is isometric You can change the view using the options in the View menu or the view tools in the View Manipulation toolbar You can also specify a view by entering values for rotation angles viewpoint zoom factor or fraction of viewport to pan Direct view manipulation is also available using the 3D compass To manipulate the view using the 3D compass e Click and drag one of the straight axes of the 3D compass to pan along an axis e Click and drag any of the quarter circular faces on the 3D compass to pan along a plane e Click and drag one of the three arcs along the perimeter of the 3D compass to rotate the model about the axis that is perpendicular to the plane containing the arc e Click and drag the free rotation handle the point at the top of the 3D compass to rotate the model freely about its pivot point 4 23 5 EXAMPLE CONNECTING LUG THE FOLLOWING TABLE IS PRINTED FOR NODES BELONGING TO NODE SET LHEND NODE FOOT RF1 RF2 RF3 NOTE 3241 872 9 765 2 936 5 3243 1 0792E 04 139 6 2692 3245 2544 29 24 636 7 3247 3471 248 1 879 4 3249 0 1244 366 6 9 4686E 02 3251 3473 247 2 879 7 3253 2543 29 40 636 9 3255 1 0792E 04 140 0 2692 3257 87
90. direction is blue the material 2 direction is yellow and the 3 direction if it is present is red 3 To view the initial material orientation select Result Step Frame In the Step Frame dialog box that appears select Increment 0 Click Apply Abaqus displays the initial material directions 4 To restore the display to the results at the end of the analysis select the last increment available in the Step Frame dialog box and click OK 12 71 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST Animation of results You will create a time history animation of the deformation to help you visualize the motion and deformation of the circuit board and foam packaging during impact To create a time history animation 1 2 Plot the deformed model shape at the end of the analysis From the main menu bar select Animate Time History The animation of the deformed model shape begins From the main menu bar select View Parallel to turn off perspective In the context bar click it to pause the animation after a full cycle has been completed In the context bar click and then select a node on the foam packaging near one of the corners that impacts the floor When you restart the animation the camera will move with the selected node If you zoom in on the node it will remain in view throughout the animation Note To reset the camera to follow the global coordinate system click in the context bar While you view
91. displacements are scaled automatically to ensure that they are clearly visible The scale factor 1s displayed in the state block In this case the displacements have been scaled by a factor of 42 83 To change the deformation scale factor 1 From the main menu bar select Options Common or use the 1234 tool in the toolbox 2 From the Common Plot Options dialog box click the Basic tab if it is not already selected 3 From the Deformation Scale Factor area toggle on Uniform and enter 10 0 in the Value field 4 Click Apply to redisplay the deformed shape The state block displays the new scale factor 5 To return to automatic scaling of the displacements repeat the above procedure and in the Deformation Scale Factor field toggle on Auto compute 6 Click OK to close the Common Plot Options dialog box 2 32 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST To superimpose the undeformed model shape on the deformed model shape 1 3 4 5 LJ Click the Allow Multiple Plot States tool in the toolbox to allow multiple plot states in the viewport then click the tool or select Plot Undeformed Shape to add the undeformed shape plot to the existing deformed plot in the viewport By default Abaqus Viewer plots the deformed model shape in green and the superimposed undeformed model shape in a translucent white The plot options for the superimposed image are controlled separately from those of the E primary
92. each integration point in each element Some elements in Abaqus can use full or reduced integration a choice that can have a significant effect on the accuracy of the element for a given problem as discussed in detail in Element formulation and integration Section 4 1 Abaqus uses the letter R at the end of the element name to distinguish reduced integration elements unless they are also hybrid elements in which case the element name ends with the letters RH For example CAX4 is the 4 node fully integrated linear axisymmetric solid element and CAXAR is the reduced integration version of the same element Abaqus Standard offers both full and reduced integration elements Abaqus Explicit offers only reduced integration elements with the exception of the modified tetrahedron and triangle elements and the fully integrated first order shell membrane and brick elements 3 1 2 Continuum elements Among the different element families continuum or solid elements can be used to model the widest variety of components Conceptually continuum elements simply model small blocks of material in a component Since they may be connected to other elements on any of their faces continuum elements like bricks in a building or tiles in a mosaic can be used to build models of nearly any shape subjected to nearly any loading Abaqus has stress displacement nonstructural and coupled field continuum elements this guide will discuss only
93. each other 12 46 DEFINING CONTACT IN Abaqus Explicit 12 8 1 Abaqus Explicit contact formulation The contact formulation in Abaqus Explicit includes the constraint enforcement method the contact surface weighting and the sliding formulation Constraint enforcement method For general contact CONTACT Abaqus Explicit enforces contact constraints using a penalty contact method which searches for node into face and edge into edge penetrations in the current configuration The penalty stiffness that relates the contact force to the penetration distance is chosen automatically by Abaqus Explicit so that the effect on the time increment 1s minimal yet the penetration is not significant The contact pair algorithm CONTACT PAIR uses a kinematic contact formulation by default that achieves precise compliance with the contact conditions using a predictor corrector method The increment at first proceeds under the assumption that contact does not occur If at the end of the increment there is an overclosure the acceleration is modified to obtain a corrected configuration in which the contact constraints are enforced The predictor corrector method used for kinematic contact is discussed in more detail in Contact constraint enforcement methods in Abaqus Explicit Section 37 2 3 of the Abaqus Analysis User s Manual some limitations of this method are discussed in Common difficulties associated with contact modeling using contact pair
94. easy to use in that you need only specify the number of modes required or the maximum frequency of interest 7 1 2 Modal superposition The natural frequencies and mode shapes of a structure can be used to characterize its dynamic response to loads in the linear regime The deformation of the structure can be calculated from a combination of the mode shapes of the structure using the modal superposition technique Each mode shape is multiplied by a scale factor The vector of displacements in the model u is defined as CoO u gt adi 11 where is the modal displacement and is the generalized coordinate of mode 7 This technique is valid only for simulations with small displacements linear elastic materials and no contact conditions in other words linear problems In structural dynamic problems the response of a structure usually is dominated by a relatively small number of modes making modal superposition a particularly efficient method for calculating the response of such systems Consider a model containing 10 000 degrees of freedom Direct integration of the dynamic equations of motion would require the solution of 10 000 simultaneous equations at each point in time If the structural response is characterized by 100 modes only 100 equations need to be solved every time increment Moreover the modal equations are uncoupled whereas the original equations of motion are coupled There is an initial cost in calculating the mode
95. elastic material The material behavior is characterized by two constants Young s modulus E and Poisson s ratio v A material definition in the Abaqus input file starts with a MATERIAL option The parameter NAME is used to associate a material with an element section property For example SOLID SECTION ELSET FRAME MATERIAL STEEL 1 963E 5 MATERIAL NAME STEEL Material suboptions directly follow their associated MATERIAL option Several suboptions may be required to complete the material definition All material suboptions are associated with the material that is listed on the most recent MATERIAL option until another MATERIAL option or a non material option block is given Without considering thermal expansion effects which would be defined with the EXPANSION material suboption one material suboption ELASTIC is required to define a linear elastic material The form of this option block is x ELASTIC lt E gt lt v gt Therefore the complete isotropic linear elastic material definition for the hoist members which are made of steel should be entered into your input file as MATERIAL NAME STEEL ELASTIC 200 E9 0 3 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST The model definition portion of this problem is now complete since all the components describing the structure have been specified 2 3 9 History data The history data define the sequence of events for the simulation This loading history is
96. elements as shown in Figure 1 6 We will study the state of the rod as we increment through time Figure 1 6 Initial configuration of a rod with a concentrated load P at the free end In the first time increment node 1 has an acceleration u4 as a result of the concentrated force P applied to it The acceleration causes node 1 to have a velocity which in turn causes a strain rate Ee1 in element 1 The increment of strain Ae in element 1 is obtained by integrating the strain rate through the time of increment 1 The total strain 1s the sum of the initial strain 9 and the increment in strain In this case the initial strain is zero Once the element strain has been calculated the element stress 0 11 1S obtained by applying the material constitutive model For a linear elastic material the stress is simply the elastic modulus times the total strain This process is shown in Figure 1 7 Nodes 2 and 3 do not move in the first increment since no force is applied to them A QUICK REVIEW OF THE FINITE ELEMENT METHOD 1 2 2 3 3 4 is P 5 Uy z fiat E ee AE f enat l fol E AE Oel Feo Figure 1 7 Configuration at the end of increment 1 of a rod with a concentrated load P at the free end In the second increment the stresses in element 1 apply internal element forces to the nodes associated with element 1 as shown in Figure 1 8 These element stresses are th
97. energy show oscillations that reflect the vibrations of the lug Throughout the simulation kinetic energy is transformed into internal strain energy and vice versa Since the material is linear elastic total energy is conserved This can be seen by plotting ETOTAL the total energy of the system together with ALLIE and ALLKE The value of ETOTAL is approximately zero throughout the course of the analysis Energy balances in dynamic analysis are discussed further in Chapter 9 Nonlinear Explicit Dynamics We will examine the nodal displacements at the bottom of the lug hole to evaluate the significance of geometrically nonlinear effects in this simulation To generate a plot of displacement versus time 1 2 Plot the deformed shape of the lug In the Results Tree double click XY Data In the Create XY Data dialog box that appears select ODB field output as the source and click Continue In the XY Data from ODB Field Output dialog box that appears select Unique Nodal as the type of position from which the X Y data should be read Click the arrow next to U Spatial displacement and toggle on U2 as the displacement variable for the X Y data Select the Elements Nodes tab Choose Pick from viewport as the selection method for identifying the node for which you want X Y data Click Edit Selection In the viewport select one of the nodes on the bottom of the hole as shown in Figure 4 39 if necessary chan
98. energy to have confidence in the results Figure 13 23 shows a plot of these two energies the static stabilization energy is indeed small and thus has not significantly affected the results Summary If a quasi static analysis is performed in its natural time scale the solution should be nearly the same as a truly static solution It is often necessary to use load rate scaling or mass scaling to obtain a quasi static solution using less CPU time The loading rate often can be increased somewhat as long as the solution does not localize If the loading rate is increased too much inertial forces adversely affect the solution Mass scaling is an alternative to increasing the loading rate When using rate dependent materials mass scaling is preferable because increasing the loading rate artificially changes the material properties 13 28 SUMMARY x10 2 50 2 00 1 50 ALLIE Whole Model ALLSD Whole Model Energy 1 00 0 50 0 00 0 00 0 20 0 40 0 60 0 80 1 00 Time Figure 13 23 Internal and static stabilization energy histories In a static analysis the lowest modes of the structure dominate the response Knowing the lowest natural frequency and correspondingly the period of the lowest mode you can estimate the time required to obtain the proper static response It may be necessary to run a series of analyses at varying loading rates to determine an acceptable loading rate The k
99. entirely by nodal forces moments and displacements rotations Prescribed boundary conditions also contribute to the external work 9 6 2 Output of the energy balance Each of the energy quantities can be requested as output and can be plotted as time histories summed over the entire model particular element sets individual elements or as energy density within each element The variable names associated with the energy quantities summed over the entire model or element sets are as listed in Table 9 2 Table 9 2 Whole model energy output variables Variable Name Energy Quantity ALLIE Internal energy Er ALLIE ALLSE ALLPD ALLCD ALLAE ALLDMD ALLDC ALLFC ALLWK NPW ALLOW ALLMIW ALLDM 9 28 9 7 SUMMARY Variable Name Energy Quantity ALLDC Energy dissipated by distortion control Epc ALLFC Fluid cavity energy negative of work done by fluid cavities kro ETOTAL Energy balance Eror Er Ey Erp Exe Erge Ew Epw Ecw Emw EprF In addition Abaqus Explicit can produce element level energy output and energy density output as listed in Table 9 3 Table 9 3 Whole element energy output variables Summary e Abaqus Explicit uses a central difference rule to integrate the kinematics explicitly through time e The explicit method requires many small time increments Since there are no simultaneous equations to solve each increment is inexpensive e The explicit
100. explicit analyses the large strain shell elements are appropriate If however the analysis involves small membrane strains and arbitrarily large rotations the small strain shell elements are more computationally efficient The S4RS and S3RS elements do not consider warping while the S4RSW element does The shell formulations available in Abaqus are discussed in detail in Chapter 5 Using Shell Elements Degrees of freedom The three dimensional elements in Abaqus Standard whose names end in the number 5 e g S4R5 STRI65 have 5 degrees of freedom at each node three translations and two in plane rotations i e no rotations about the shell normal However all six degrees of freedom are activated at a node if required for example if rotational boundary conditions are applied or if the node is on a fold line of the shell The remaining three dimensional shell elements have six degrees of freedom at each node three translations and three rotations The axisymmetric shells have three degrees of freedom associated with each node jl Translation in the r direction 2 Translation in the z direction 6 Rotation in the r z plane Element properties Use either the SHELL GENERAL SECTION or the SHELL SECTION option to define the thickness and material properties for a set of shell elements These two options have similar formats 3 10 FINITE ELEMENTS SHELL SECTION ELSET lt element set name gt MATERIAL lt materi
101. first order 4 node element As is the case for many options in Abaqus both element numbers and element sets can be used the use of element sets can make the definition of large surfaces much easier It is valid to specify both element sets and individual elements in the same SURFACE option block as shown in Figure 12 5 and the example below The surface TOPSURF consists of the element faces shown in Figure 12 5 and is created as follows ELSET ELSET TOP GENERATE 5 8 SURFACE NAME TOPSURF TOP S3 5 S4 8 S2 Figure 12 5 Face numbers and elements that form the surface TOPSURF Abaqus can determine the free faces of two and three dimensional continuum elements automatically and use them to create a surface To use this capability simply include all the elements whose free faces make up the surface on the data lines of the SURFACE option Either 12 7 a DEFINING CONTACT IN Abaqus Standard element sets or individual element numbers can be used If elements in the interior of the body are included Abaqus will ignore them For example the surface shown in Figure 12 5 could also be defined using SURFACE NAME TOPSURF TOP Surfaces on shell membrane and rigid elements For shell membrane and rigid elements you must specify which side of the element forms the contact surface The side in the direction of the positive element normal is called SPOS while the side in the direction of the negative element normal
102. following ELEMENT TYPE S8R5 ELSET PLATE In some examples the name given for the ELSET parameter is not a descriptive name like PLATE If necessary you may want to change these values because meaningful names for node and element sets make input files easy to understand Node sets The three node sets shown in Figure 5 12 will be useful in completing the model of the plate These node sets are described in the input file using NSET option blocks Defining alternative material directions If you use the default material directions the direct stress in the material 1 direction 011 will contain contributions from both the axial stress produced by the bending of the plate and the stress transverse to the axis of the plate It will be easier to interpret the results if the material directions are aligned with the axis of the plate and the transverse direction Therefore a local rectangular coordinate system is needed in which the local x direction lies along the axis of the plate 1 e at 30 to the global 1 axis and the local y direction is also in the plane of the plate As you learned in Shell material directions Section 5 3 the ORIENTATION option defines such a local coordinate system Choose point a see Figure 5 8 to have coordinates 10 0E 2 5 77E 2 0 so that z x tan 30 and point b to have coordinates 5 77E 2 10 E 2 0 You must also specify which axis is not projected onto the shell s
103. for a linear perturbation step is called the base state of the model If the first step in a simulation is a linear perturbation step the base state is the state of the model specified using the INITIAL CONDITIONS option Otherwise the base state is the state of the simulation at the end of the last general step prior to the linear perturbation step Although the response of the structure during the perturbation step is by definition linear the model may have a nonlinear response in previous general steps For models with a nonlinear response in the prior general steps Abaqus Standard uses the current elastic modulus as the linear stiffness for perturbation procedures This modulus is the initial elastic modulus for elastic plastic materials and the tangent modulus for hyperelastic materials see Figure 11 5 the moduli used for other material models are described in General and linear perturbation procedures Section 6 1 3 of the Abaqus Analysis User s Manual 11 4 LINEAR PERTURBATION ANALYSIS tangent modulus Force Base state Displacement Figure 11 5 For hyperelastic materials the tangent modulus is used as the stiffness in linear perturbation steps that occur after general nonlinear steps The loads in the perturbation step should be sufficiently small that the model s response would not deviate much from that predicted with the tangent modulus If the simulation includes contact the contact state between two s
104. for quadratic interpolation and 3 for cubic interpolation The use of beam elements is discussed in Chapter 6 Using Beam Elements Beam element library Linear quadratic and cubic beams are available in two and three dimensions Cubic beams are not available in Abaqus Explicit 3 12 FINITE ELEMENTS Degrees of freedom Three dimensional beams have six degrees of freedom at each node three translational degrees of freedom 1 3 and three rotational degrees of freedom 4 6 Open section type beams such as B31OS are available in Abaqus Standard and have an additional degree of freedom 7 that represents the warping of the beam cross section Two dimensional beams have three degrees of freedom at each node two translational degrees of freedom 1 and 2 and one rotational degree of freedom 6 about the normal to the plane of the model Element properties Use either the BEAM SECTION or the BEAM GENERAL SECTION option to define the geometry of the beam cross section the nodal coordinates define only the length If you specify the BEAM SECTION option the beam cross section is defined geometrically and the MATERIAL parameter refers to a material property definition Abaqus calculates the cross section behavior of the beam by numerical integration over the cross section allowing both linear and nonlinear material behavior The BEAM GENERAL SECTION option allows you to define the cross section behavio
105. frame parameter specifies that the jobname for this analysis is frame All the files associated with this analysis will have this jobname as their identifier which allows them to be recognized easily 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST The analysis will run interactively and messages similar to those shown below will appear on your screen Abaqus JOB frame Abaqus 6 12 1 Begin Analysis Input File Processor 9 23 2010 9 26 43 AM Run pre exe Abaqus License Manager checked out the following licenses Abaqus Foundation checked out 3 tokens 9 23 2010 9 26 45 AM End Analysis Input File Processor Begin Abaqus Standard Datacheck Begin Abaqus Standard Analysis 9 23 2010 9 26 45 AM Run standard exe Abaqus License Manager checked out the following licenses Abaqus Foundation checked out 3 tokens 2 23 2010 9 26 45 AM End Abaqus Standard Analysis Abaqus JOB frame COMPLETED When the datacheck analysis is complete you will find that a number of additional files have been created by Abaqus If any errors are encountered during the datacheck analysis messages will be written to the data file frame dat This data file is a text file that can be viewed in an editor or printed Try viewing the data file in a text editor The file can contain lines up to 256 characters long so the editor should be able to accommodate that many characters Header page The data file starts with a header page that contains information ab
106. from the end of the previous increment Even though a given analysis may require a large number of time increments using the explicit method the analysis can be more efficient in Abaqus Explicit if the same analysis in Abaqus Standard requires many iterations Another advantage of Abaqus Explicit is that it requires much less disk space and memory than Abaqus Standard for the same simulation For problems in which the computational cost of the two programs may be comparable the substantial disk space and memory savings of Abaqus Explicit make it attractive 2 4 2 Cost of mesh refinement in implicit and explicit analyses Using the explicit method the computational cost is proportional to the number of elements and roughly inversely proportional to the smallest element dimension Mesh refinement therefore increases the computational cost by increasing the number of elements and reducing the smallest element dimension As an example consider a three dimensional model with uniform square elements If the mesh 1s refined by a factor of two in all three directions the computational cost increases by a factor of 2 x 2 x 2 as a result of the increase in the number of elements and by a factor of 2 as a result of the decrease in the smallest element dimension The total computational cost of the analysis increases by a factor of 2 2 42 2 5 SUMMARY or 16 by refining the mesh Disk space and memory requirements are proportional to the nu
107. if you are interested in using them in your models read about them in Part VI Elements of the Abaqus Analysis User s Manual The first letter or letters of an element s name indicate to which family the element belongs For example the S in S4R indicates this is a shell element while the C in C3D8I indicates this is a continuum element Degrees of freedom The degrees of freedom dof are the fundamental variables calculated during the analysis For a stress displacement simulation the degrees of freedom are the translations at each node Some element families such as the beam and shell families have rotational degrees of freedom as well For a heat transfer simulation the degrees of freedom are the temperatures at each node a heat transfer analysis therefore requires the use of different elements than a stress analysis since the degrees of freedom are not the same The following numbering convention is used for the degrees of freedom in Abaqus l Translation in direction 1 2 Translation in direction 2 3 Translation in direction 3 3 2 FINITE ELEMENTS Rotation about the 1 axis Rotation about the 2 axis Rotation about the 3 axis Warping in open section beam elements Acoustic pressure pore pressure or hydrostatic fluid pressure Electric potential Re Oo CO l A WN AA 1 Temperature or normalized concentration in mass diffusion analysis for continuum elements or temperature at the first point through the th
108. improved solution 12 74 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST Evaluating acceleration histories at the chips The next result we wish to examine is the acceleration of the chips attached to the circuit board Excessive accelerations during impact may damage the chips Therefore in order to assess the desirability of the foam packaging we need to plot the acceleration histories of the three chips Since we expect the accelerations to be greatest in the 3 direction we will plot the variable A3 To plot acceleration histories 1 In the Results Tree filter the History Output container according to A3 select the acceleration A3 of the nodes 60 357 and 403 in the set CHIPS and plot the three X Y data objects The X Y plot appears in the viewport As before customize the plot appearance to obtain a plot similar to Figure 12 58 x1 E3 60 NSET CHIPS 357 NSET CHIPS 403 NSET CHIPS 2 0 10 oe il whe we Bt ta aH judy 24 sahi E SPT eee A MARY fi l 4 i Hea IN piy val w ths a eae W ra athe 2 ls HU 1 uy wt aM iy My Hh i Aa Ui nih We 0 0 aa Ta ee rete wee ee we eRe Be SSS SS eee m A a eie 1 0 Vertical Acceleration m s 2 0 0 5 10 15 20 x1 E 3 Time s Figure 12 58 Acceleration of the three chips in the Z direction Next we will evaluate the plausibility of the acceleration data recorded at the bottom chip
109. in the mode with the highest frequency Recall that critical damping defines the limit between oscillatory and non oscillatory motion in the context of free damped vibration Abaqus Explicit always introduces a small amount of damping in the form of bulk viscosity to control high frequency oscillations Perhaps contrary to engineering intuition damping always reduces the stability limit The actual highest frequency in the system is based on a complex set of interacting factors and it is not computationally feasible to calculate its exact value Alternately we use a simple estimate that is 9 6 AUTOMATIC TIME INCREMENTATION AND STABILITY efficient and conservative Instead of looking at the global model we estimate the highest frequency of each individual element in the model which is always associated with the dilatational mode It can be shown that the highest element frequency determined on an element by element basis 1s always higher than the highest frequency in the assembled finite element model Based on the element by element estimate the stability limit can be redefined using the element length L and the wave speed of the material ca e Atstable Cd For most element types a distorted quadrilateral element for example the above equation is only an estimate of the actual element by element stability limit because it is not clear how the element length should be determined As an approximation the shortest element
110. integrity under this drop load 1 damping 5 damping 10 damping REACTION FORCE RF1 0 00 010 0 20 030 0 40 0 50 STEP TIME Figure 7 11 Effect of damping ratio on the pull out force Comparison with direct time integration Since this is a transient dynamic analysis it is natural to consider how the results compare with those obtained using direct integration of the equations of motion Direct integration can be performed with either implicit Abaqus Standard or explicit Abaqus Explicit methods Here we extend the analysis to use the explicit dynamics procedure A direct comparison with the results presented earlier is not possible since the B33 element type and direct modal damping are not available in Abaqus Explicit Thus in the Abaqus Explicit analysis the element type is changed to B31 and Rayleigh damping is used in place of direct modal damping 1 23 5 COMPARISON WITH DIRECT TIME INTEGRATION Save a copy of dynamics inp as dynamics xpl inp All subsequent changes should be made to dynamics xpl inp To modify the model 1 Change the element type to B31 for all elements in the model You can perform this change by modifying the TYPE parameter on the ELEMENT option ELEMENT TYPE B31 2 Add mass proportional damping to the bracing section properties To do this add the following DAMPING option to the end of the material data option block for the bracing section DAMPING ALPHA 15 This state
111. is called SNEG as shown in Figure 12 6 As discussed in Chapter 5 Using Shell Elements the connectivity of an element defines the positive element normal The positive element normals can be viewed in Abaqus Viewer n Side SPOS gt Ns Olt SNEG Figure 12 6 Surfaces on a two dimensional shell or rigid element The following option block defines surface SURF 1 as the surface composed of all the SPOS faces of the elements in element set SHELLS SURFACE NAME SURF1 SHELLS SPOS Restrictions on the types of surfaces that can be created in Abaqus are discussed in Surface definition Section 2 3 of the Abaqus Analysis User s Manual please read them before beginning a contact simulation Rigid surfaces Rigid surfaces are the surfaces of rigid bodies They can be defined as an analytical shape or they can be based on the underlying surfaces of elements associated with the rigid body Analytical rigid surfaces are created by defining a series of connected lines arcs and parabolas The parameter ANALYTICAL SURFACE on the RIGID BODY option binds an analytical rigid surface defined with the TYPE parameter on the SURFACE option with a rigid body The RIGID BODY option must be defined in the model definition The TYPE parameter on the SURFACE option defines the dimensionality of the surface and it has three possible values 12 8 DEFINING CONTACT IN Abaqus Standard e Use TYPE SEGMENTS to define a two dimensio
112. is used throughout this guide Users working in the systems labeled US Unit should be careful with the units of density often the densities given in handbooks of material properties are multiplied by the acceleration due to gravity 2 3 2 Coordinate systems You also need to decide which coordinate system to use The global coordinate system in Abaqus is a right handed rectangular Cartesian system For this example define the global l axis to be the horizontal axis of the hoist and the global 2 axis to be the vertical axis Figure 2 3 The global 3 axis is normal to the plane of the framework The origin x1 0 x2 0 r3 0 is the bottom left hand corner of the frame Figure 2 3 Coordinate system and origin for model For two dimensional problems such as this one Abaqus requires that the model lie in a plane parallel to the global 1 2 plane 2 3 3 Mesh You must select the element types and design the mesh Creating a proper mesh for a given problem requires experience For this example you will use a single truss element to model each member of the frame as shown in Figure 2 4 2 9 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST lt q Nodes Truss elements Figure 2 4 Finite element mesh A truss element which can carry only tensile and compressive axial loads is ideal for modeling pin jointed frameworks such as the overhead hoist Truss elements are described in Truss elements Section 3 1 5 an
113. l axis on the deformed model shape The deformation scale factor is chosen automatically since geometric nonlinearity was not considered in the analysis Open the Common Plot Options dialog box and select a Uniform deformation scale factor of 1 0 Color contour plots of this type typically are not very useful for one dimensional elements such as beams A more useful plot is a bending moment type plot which you can produce using the contour options 4 m From the main menu bar select Options Contour or use the Contour Options 5 tool in the toolbox The Contour Plot Options dialog box appears by default the Basic tab is selected In the Contour Type field toggle on Show tick marks for line elements Click OK The plot shown in Figure 6 21 appears The magnitude of the variable at each node is now indicated by the position at which the contour curve intersects a tick mark drawn perpendicular to the element This bending moment type plot can be used for any variable not just bending moments for any one dimensional element including trusses and axisymmetric shells as well as beams Related Abaqus examples Detroit Edison pipe whip experiment Section 2 1 2 of the Abaqus Example Problems Manual Buckling analysis of beams Section 1 2 1 of the Abaqus Benchmarks Manual Crash simulation of a motor vehicle Section 1 3 14 of the Abaqus Benchmarks Manual Geometrically non
114. maximum Mises stress at the built in end is approximately 306 MPa THE FOLLOWING TABLE IS PRINTED AT THE INTEGRATION POINTS FOR ELEMENT TYPE C3D20R AND ELEMENT SET BUILTIN ELEMENT PT FOOT S11 S22 33 12 13 S23 MISES NOTE 206 1 2 8192E 08 8 1398E 06 1 3867E 07 6 9975E 06 1 1688E 07 1 1556E 06 2 9392E 08 206 2 3 4766E 08 8 7629E 07 8 1158E 07 4 9896E 07 4 2710E 07 3 1290E 06 2 8690E 08 206 3 1 83411E 08 1 3272E 06 8 9091E 06 3 3674E 07 6 3447E 06 1 7790E 06 1 9661E 08 206 4 1 9471E 08 3 8981E 07 3 8422E 07 2 4493E 07 2 7244E 07 3 1046E 06 1 6851E 08 206 5 3 0367E 08 1 1909E 06 2 7817E 06 8 25811E 06 4 0589E 06 1 8407E 05 3 0608E 08 206 6 3 2968E 08 7 9725E 07 7 4055E 07 5 6416E 07 9 2002E 06 7 8331E 04 2 7153E 08 206 7 1 9944E 08 7 8575E 06 1 0716E 06 3 4469E 07 2 3479E 06 5 4628E 05 2 0512E 08 206 D a ice 3 3280E 07 3 2765E 07 3 0944E 07 5 6498E 06 7 4119E 04 1 5731E 08 Integration point at which results are given 1236 1 1 9946E 08 7 8863E 06 1 0719E 06 3 4403E 07 2 3479E 06 5 4545E 05 2 0510E 08 1236 2 1 8062E 08 3 3293E 07 3 2771E 07 3 0908E 07 5 6503E 06 7 4267E 04 1 5730E 08 1236 3 3 0367E 08 1 1878E 06 2 7818E 06 8 2327E 06 4 0583E 06 1 8502E 05 3 0607E 08 1236 4 3 2963E 08 7 9705E 07 7 4039E 07 5 6389E 07 9 1989E 06 7 8203E 04 2 7148E 08 1236 5 1 8343E 08 1 3529E 06 8 9107E 06 3 3606E 07 6 3449E 06 1 7770E 06 1 9658E 08 1236 6 1 9474E 08 3 8996E 07 3 8431E 07 2 4460E 07 2 7246E 07 3 1025E 06 1 68
115. method is to model the circuit board and packaging in an initial position very close to the surface with an initial velocity to simulate the 1 meter drop 4 43 m s 12 10 5 Reviewing the input file the model data We now review the model data required for this simulation including the model description the node and element definitions element and material properties boundary and initial conditions and surface definitions You can review these data by fetching and opening the input file circuit inp Model description The HEADING option in this example provides a suitable heading for your model SI units are used in this example HEADING Circuit board drop test 1 0 meter drop SI units kg m s N Nodal coordinates and element connectivity Use your preprocessor to generate the mesh in the local coordinate system Precede the nodal definitions with the SYSTEM option to transform the nodes into the tilted coordinate system as described previously In circuit inp the nodal definitions for the foam packaging and circuit board look like SYSTEM Dig Ung Oer 5y 707 225 5 07 5 NODE 1 0 005 0 010 0 012 EL 0 005 0 010 0 162 12 64 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST Reset coordinate system kk SYSTEM When you have finished defining the nodes in the rotated local coordinate system use the SYSTEM option again without any data lines so that additional node numbers will be given
116. model Element normals Use the undeformed shape plot to check the model definition Check that the element normals for the skew plate model were defined correctly and point in the positive 3 direction To display the element normals From the main menu bar select Options Common or use the 1234 tool in the toolbox The Common Plot Options dialog box appears Click the Normals tab Toggle on Show normals and accept the default setting of On elements Click OK to apply the settings and to close the dialog box The default view is isometric You can change the view using the options in the view menu or the view tools such as e from the View Manipulation toolbar To change the view 1 From the main menu bar select View Specify The Specify View dialog box appears From the list of available methods select Viewpoint Enter the X Y and Z coordinates of the viewpoint vector as 0 2 1 0 8 and the coordinates of the up vector as 0 0 1 Click OK Abaqus Viewer displays your model in the specified view as shown in Figure 5 13 5 21 5 EXAMPLE SKEW PLATE Figure 5 13 Shell element normals in the skew plate model Symbol plots Symbol plots display the specified variable as a vector originating from the node or element integration points You can produce symbol plots of most tensor and vector valued variables The exceptions are mainly nonmechanical output variables and eleme
117. must use second order elements in contact simulations do not use the quadratic triangular shell element STRI65 Use the 9 node quadrilateral shell element S9R5 instead e For very large models that will experience only geometrically linear behavior the linear thin shell element S4R5 will generally be more cost effective than the general purpose shell elements e The small membrane strain elements are effective for explicit dynamics problems involving small membrane strains and arbitrarily large rotations 5 5 Example skew plate You have been asked to model the plate shown in Figure 5 10 It is skewed 30 to the global 1 axis is built in at one end and is constrained to move on rails parallel to the plate axis at the other end You are to determine the midspan deflection when the plate carries a uniform pressure You are also to assess whether a linear analysis is valid for this problem You will perform an analysis using Abaqus Standard 5 5 1 Coordinate system The orientation of the structure in the global coordinate system and the suggested origin of the system are shown in Figure 5 10 The plate lies in the global 1 2 plane Will it be easy to interpret the results of the simulation if you use the default material directions for the shell elements in this model 5 5 2 Mesh design Figure 5 11 shows the suggested mesh for this simulation You must answer the following questions before selecting an element type I
118. nodes Since it is easy to offset beams with such cross sections from their nodes they can be used readily as stiffeners as shown in Figure 6 5 b If flange or web buckling of the stiffeners is important shells should be used to model the stiffeners The I beam shown in Figure 6 6 is attached to a shell 1 2 units thick The following input is used to orient the beam section as it is shown in the figure BEAM SECTION SECTION I ELSET lt element set name gt MATERIAL lt material gt 0 6 2 4 3 0 2 0 0 2 0 2 0 2 lt ni gt Sar lt n gt The first item on the first data line defines the offset of the beam node from the bottom of the I section The offset is one half of the shell thickness or 0 6 The remaining data items are the beam depth the width of the bottom and top flanges the thickness of the bottom and top flanges and the thickness of the web FORMULATION AND INTEGRATION Shell section thickness 1 2 Figure 6 6 I beam used as stiffener for a shell element You can give the location of the centroid and shear center if you specify the BEAM GENERAL SECTION option with the parameter SECTION GENERAL The SHEAR CENTER and CENTROID options allow these locations to be offset from the node enabling you to model stiffeners readily For example the input for the I beam attached to the shell as shown in Figure 6 6 is xBEAM GENERAL SECTION SECTION GENERAL ELSET lt element set name gt a oan
119. not suitable for nonlinear dynamic simulations Direct time integration DYNAMIC methods must be used in these situations The AMPLITUDE option allows any time variation of loads or prescribed boundary conditions to be defined Mode shapes and transient results can be animated in Abaqus Viewer This provides a useful way of understanding the response of dynamic and nonlinear static analyses 7 29 NONLINEARITY 8 Nonlinearity This chapter discusses nonlinear structural analysis in Abaqus The differences between linear and nonlinear analyses are summarized below Linear analysis All the analyses discussed so far have been linear there is a linear relationship between the applied loads and the response of the system For example if a linear spring extends statically by 1 m under a load of 10 N it will extend by 2 m when a load of 20 N is applied This means that in a linear Abaqus Standard analysis the flexibility of the structure need only be calculated once by assembling the stiffness matrix and inverting it The linear response of the structure to other load cases can be found by multiplying the new vector of loads by the inverted stiffness matrix Furthermore the structure s response to various load cases can be scaled by constants and or superimposed on one another to determine its response to a completely new load case provided that the new load case 1s the sum or multiple of previous ones This principle of superposition
120. of offshore structures to which fluid drag and buoyancy loads must be applied 3 17 SUMMARY 3 3 Two node rigid elements are available for plane strain plane stress and axisymmetric models A planar two node rigid beam element is also available in Abaqus Standard and is used mainly to model offshore structures in two dimensions Degrees of freedom Only the rigid body reference node has independent degrees of freedom For three dimensional elements the reference node has three translational and three rotational degrees of freedom for planar and axisymmetric elements the reference node has degrees of freedom 1 2 and 6 rotation about the 3 axis The nodes attached to rigid elements have only slave degrees of freedom The motion of these nodes is determined entirely by the motion of the rigid body reference node For planar and three dimensional rigid elements the only slave degrees of freedom are translations The rigid beam elements in Abaqus Standard have the same slave degrees of freedom as the corresponding deformable beam elements 1 6 for the three dimensional rigid beam and 1 2 and 6 for the planar rigid beam Physical properties All rigid elements must reference a RIGID BODY option For the planar and beam elements the cross sectional area can be defined on the data line For the axisymmetric and three dimensional elements the thickness can be defined on the data line these data are required only if you apply body fo
121. of an isotropic linear elastic material that has a Young s modulus of 30 0 GPa and a Poisson s ratio of 0 3 The following material option block specifies this material data MATERIAL NAME MAT1 ELASTIC 30 0E9 0 3 Local directions at the nodes While the ORIENTATION option defines a local coordinate system for elements you must use the TRANSFORM option to define a local coordinate system for nodes The two options are completely independent of each other If a node refers to a local coordinate system defined with TRANSFORM all data pertaining to the node such as boundary conditions concentrated loads or nodal output variables displacements velocities reaction forces etc are defined in the transformed coordinate system 5 16 EXAMPLE SKEW PLATE The TRANSFORM option has the following format TRANSFORM NSET lt node set name gt TYPE lt axis type gt lt x gt lt a gt lt x gt lt ri gt lt x3 gt lt x3 gt The data line specifies the coordinates of two points a and 6 in much the same way as the ORIENTATION option The coordinate system defined with TRANSFORM does not rotate as the body deforms it is fixed in the original directions defined at the beginning of the simulation Rectangular TYPE R cylindrical TYPE C and spherical TYPE S coordinate systems can be specified Use the NSET parameter to specify the node sets that use this local coordinate system As shown in Figure 5 10
122. of linear and nonlinear problems involving the static dynamic thermal electrical and electromagnetic response of components This product is discussed in detail in this guide Abaqus Standard solves a system of equations implicitly at each solution increment In contrast Abaqus Explicit marches a solution THE Abaqus PRODUCTS Associative CAD interfaces Abaqus CAE Systems Job control and Elysium direct monitoring translators Modeling Visualization _ Abaqus Viewer gt Third part Ana E irq y Translators gt Abaqus Standard Abaqus Explicit Abaqus Interface _ baqus CFD _ Abaqus Interface for Moldflow Abaqus Aqua for MSC ADAMS Moldflow Abaqus AMS Abaqus Design i Translators Third party postprocessors Figure 1 1 Abaqus products forward through time in small time increments without solving a coupled system of equations at each increment or even forming a global stiffness matrix Abaqus Explicit Abaqus Explicit is a special purpose analysis product that uses an explicit dynamic finite element formulation It is suitable for modeling brief transient dynamic events such as impact and blast problems and is also very efficient for highly nonlinear problems involving changing contact conditions such as forming simulations Abaqus Explicit is discussed in detail in this guide Abaqus CFD Abaqus CFD is a computational fluid dynamics analysis product It can solve a broad class of incompressibl
123. of load cases assumes that the same boundary conditions are used for all the load cases Abaqus Standard uses the principle of superposition of load cases in linear dynamics simulations which are discussed in Chapter 7 Linear Dynamics Nonlinear analysis A nonlinear structural problem is one in which the structure s stiffness changes as it deforms All physical structures exhibit nonlinear behavior Linear analysis is a convenient approximation that is often adequate for design purposes It is obviously inadequate for many structural simulations including manufacturing processes such as forging or stamping crash analyses and analyses of rubber components such as tires or engine mounts A simple example is a spring with a nonlinear stiffening response see Figure 8 1 Force Force Displacement Displacement Linear spring Nonlinear spring Stiffness is constant Stiffness is not constant Figure 8 1 Linear and nonlinear spring characteristics 5 SOURCES OF NONLINEARITY Since the stiffness is now dependent on the displacement the initial flexibility can no longer be multiplied by the applied load to calculate the spring s displacement for any load In a nonlinear implicit analysis the stiffness matrix of the structure has to be assembled and inverted many times during the course of the analysis making it much more expensive to solve than a linear implicit analysis In an explicit analysis the increased cost of a nonlinear
124. of the plate 1s approximately 30 ms so we need to increase the analysis period to allow enough time for the vibration to be damped out Therefore increase the analysis period to 150 ms The results of the damped analysis clearly show the effect of mass proportional damping Figure 10 34 shows the displacement history of the central node for both the damped and undamped analyses We have extended the analysis time to 150 ms for the undamped model to compare the data more effectively The peak response is also reduced due to damping By the end of the damped analysis the oscillation has decayed to a nearly static condition Rate dependence Some materials such as mild steel show an increase in the yield stress with increasing strain rate In this example the loading rate is high so strain rate dependence is likely to be important The RATE DEPENDENT option is used with the PLASTIC option to introduce strain rate dependence Add the following to the MATERIAL option block under the PLASTIC option 10 48 HYPERELASTICITY 50 00 40 00 30 00 20 00 Displacement mm Stet Undamped 10 00 0 00 0 05 0 10 0 15 Time s Figure 10 34 Damped and undamped displacement histories RATE DEPENDENT 40 0 5 0 With this definition of rate dependent behavior the ratio of the dynamic yield stress to the static yield stress R is given for an equivalent plastic strain rate D according to the equation D R 1
125. one end of the plate is constrained to move on rails that are parallel to the axis of the plate Since this boundary condition does not coincide with the global axes you must transform the nodes on this end of the plate into a local coordinate system that has an axis aligned with the plate The following TRANSFORM option achieves this transformation TRANSFORM NSET ENDB TYPE R 10 0E 2 5 77E 2 0 0 5 77E 2 10 0E 2 0 0 This option block defines the degrees of freedom for node set ENDB in a local coordinate system whose x axis is aligned with the long axis of the plate i e the local system is rotated 30 about the global 3 axis 5 5 5 Reviewing the input file the history data We now review the history definition portion of the input file A single step is needed to define this simulation Step definition The STEP definition specifies a linear static simulation STEP PERTURBATION Uniform pressure 20 0 kPa load STATIC The line following STEP PERTURBATION contains a clear description of the loading applied in this step Boundary conditions The nodes at the left hand end of the plate node set ENDA need to be constrained completely by the following boundary condition BOUNDARY ENDA ENCASTRE 5 17 5 EXAMPLE SKEW PLATE The nodes at the right hand end of the plate need to be constrained to model their rail boundary condition Since you have transformed the nodes at this end using TRANSFORM
126. online resources SIMULIA has a home page on the World Wide Web www simulia com containing a variety of useful information about the Abaqus suite of programs including e Frequently asked questions e Abaqus systems information and machine requirements e Benchmark timing documents e Error status reports e Abaqus documentation price list e Training course schedule e Newsletters Getting help You may want to read additional information about Abaqus Viewer features at various points during the tutorials The context sensitive help system allows you to locate relevant information quickly and easily Context sensitive help is available for every item in the main window and in all dialog boxes Note e On Windows platforms the help system uses your default web browser to display the online documentation e On UNIX and Linux platforms the help system searches the system path for Firefox If the help system cannot find Firefox an error is displayed The browser_type and browser_path variables can be set in the environment file to modify this behavior For more information see System customization parameters Section 4 1 4 of the Abaqus Installation and Licensing Guide GETTING HELP To obtain context sensitive help 1 From the main menu bar select Help On Context Tip You can also click the help tool i to access context sensitive help The cursor changes to a question mark 2 Click any part of the main window ex
127. option SHELL SECTION ELSET BOARD MATERIAL PCB ORIENTATION OR1 0 002 ORIENTATION NAME OR1 SYSTEM RECTANGULAR DEFINITION COORDINATES 0 5 0 707 0 25 0 5 0 707 0 5 2 90 0 The mass of each of the chips on the circuit board is defined to be 0 005 kg using the MASS option MASS ELSET CHIPS 0 005 12 65 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST Define the rigid body by referring to the element set FLOOR and the rigid body reference node on the RIGID BODY option The actual node number of the reference node must be specified not the node set name RIGID BODY ELSET FLOOR REF NODE lt reference node number gt Material properties We You now need to define the material properties for the circuit board and the foam packaging For the circuit board use a PCB elastic material with a Young s modulus of 45 GPa a Poisson s ratio of 0 3 and a density of 500 kg m MATERIAL NAME PCB ELASTIC 45 E9 0 3 DENSITY 500 The foam packaging material is modeled using the crushable foam plasticity model Use the ELASTIC option to define the Young s modulus as 3 MPa and the Poisson s ratio as 0 0 The material density is 100 kg m MATERIAL NAME FOAM ELASTIC 3 E6 0 0 DENSITY 100 The yield surface of a crushable foam in the p g pressure stress Mises equivalent stress plane is illustrated in Figure 12 54 The CRUSHABLE FOAM HARDENING VOLUMETRIC option uses two
128. pan the plot by selecting View Specify from the main menu bar You should have a plot similar to the one shown in Figure 10 54 in this and the images that follow the sweep and mirroring operations applied earlier have been suppressed Some elements in this corner of the model are becoming badly distorted because the mesh design in this area was inadequate for the type of deformation that occurs there Although the shape 10 74 EXAMPLE AXISYMMETRIC MOUNT Badly distorted mesh 2 5 Figure 10 54 Distortion at the left hand corner of the rubber mount model of the elements is fine at the start of the analysis they become badly distorted as the rubber bulges outward especially the element in the corner If the loading were increased further the element distortion may become so excessive that the analysis may abort Mesh design for large distortions Section 10 8 discusses how to improve the mesh design for this problem The keystoning pattern exhibited by the distorted elements in the bottom right hand corner of the model indicates that they are locking A contour plot of the hydrostatic pressure stress in these elements without averaging across elements sharing common nodes shows rapid variation in the pressure stress between adjacent elements This indicates that these elements are suffering from volumetric locking which was discusse
129. pipe vibration analysis Related Abaqus examples Summary Contact Overview of contact capabilities in Abaqus Interaction between surfaces Defining contact in Abaqus Standard Modeling issues for rigid surfaces in Abaqus Standard Abaqus Standard 2 D example forming a channel General contact in Abaqus Standard Abaqus Standard 3 D example shearing of a lap joint Defining contact in Abaqus Explicit Modeling considerations in Abaqus Explicit Abaqus Explicit example circuit board drop test Compatibility between Abaqus Standard and Abaqus Explicit Related Abaqus examples Suggested reading Summary CONTENTS 9 6 9 7 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 11 1 1 2 11 3 11 4 11 5 11 6 11 7 12 1 12 2 12 3 12 4 12 5 12 6 12 7 12 8 129 12 10 1211 12412 12 13 12 14 CONTENTS 13 Quasi Static Analysis with Abaqus Explicit Analogy for explicit dynamics 13 1 Loading rates 132 Mass scaling 13 3 Energy balance 13 4 Example forming a channel in Abaqus Explicit 13 5 Summary 13 6 A Example Files Overhead hoist frame A I Connecting lug A 2 Skew plate A 3 Cargo crane A 4 Cargo crane dynamic loading A 5 Nonlinear skew plate A 6 Stress wave propagation in a bar A 7 Connecting lug with plasticity A 8 Blast loading on a stiffened plate A 9 Axisymmetric mount A 10 Test fit of hyperelastic material data A 11 Vibration of a piping system A 12 Forming a channel with Abaqus S
130. point that corresponds to integration point 1 To create history curves of stress and direct strain along the lug in element 206 1 In the Results Tree click mouse button 3 on History Output for the output database named lug plas _hard odb From the menu that appears select Filter 2 In the filter field enter MISES to restrict the history output to just the Mises stress 3 Click mouse button 3 on the MISES stress at element 206 integration point 1 From the menu that appears select Save As Enter the name MISES and click OK 4 Filter the history output using E11 and save the E11 strain component at the same integration point Name the curve E11 10 24 EXAMPLE CONNECTING LUG WITH PLASTICITY Nodes on this face are constrained Figure 10 15 Location of integration point 1 in element 206 The MISES stress rather than the component of the true stress tensor is used because the plasticity model defines plastic yield in terms of Mises stress The E11 strain component is used because it is the largest component of the total strain tensor at this point using it clearly shows the elastic as well as the plastic behavior of the material at this integration point The curves appear in the XYData container Each of the curves is a history variable versus time plot You must combine the plots eliminating the time dependence to produce the desired stress strain plot To combine history curves to produce a stress strain p
131. positive normal direction is obtained using the right hand rule about the nodes of the element as shown in Figure 10 25 Since the magnitude of the load has been defined in the BLAST amplitude definition we need to apply only a unit pressure under DLOAD This pressure 1s applied so that it pushes against the top of the plate where the stiffeners are on the bottom of the plate Such a pressure load will place the outer fibers of the stiffeners in tension The full option is shown below DLOAD AMPLITUDE BLAST PLATE P 1 0 10 36 EXAMPLE BLAST LOADING ON A STIFFENED PLATE positive shell normal positive pressure load Figure 10 25 Definition of positive pressure load Output requests To check on the progress of the solution use the MONITOR option to monitor the deflection at the center node of the plate during the analysis In this example we monitor the out of plane displacement at the center node by adding the following command to the input file MONITOR NODE lt center node number gt DOF 2 For the input file shown in Blast loading on a stiffened plate Section A 9 the node number at the center of the plate is 411 Set the number of intervals during the step at which field data are written to the output database file ODB to 25 This ensures that the selected data outputs are written every 2 ms since the total time for the step is 50 ms In general you should try to limit the number of frames written during th
132. product line Abaqus Installation and Licensing Guide This manual describes how to install Abaqus and how to configure the installation for particular circumstances Some of this information of most relevance to users 1s also provided in the Abaqus Analysis User s Manual In addition to the documentation listed above the following manuals are available for Abaqus interfaces and custom programming techniques not discussed in this guide e Abaqus Interface for Moldflow User s Manual e Abaqus Interface for MSC ADAMS User s Manual e Abaqus Scripting User s Manual e Abaqus Scripting Reference Manual e Abaqus GUI Toolkit User s Manual e Abaqus GUI Toolkit Reference Manual SIMULIA also provides documentation for all of the geometry translators described in The Abaqus products Section 1 1 GETTING HELP 1 4 Additional publications available from SIMULIA Quality Assurance Plan This document describes the QA procedures followed by SIMULIA It is a controlled document provided to customers who subscribe to either the Nuclear QA Program or the Quality Monitoring Service Lecture Notes These notes are available on many topics to which Abaqus is applied They are used in the technical seminars that are presented to help users improve their understanding and usage of Abaqus While not intended as stand alone tutorial material they are sufficiently comprehensive that they can usually be used in that mode Abaqus
133. reading 6 6 Summary 6 7 7 Linear Dynamics Introduction 7 1 Damping IZ Element selection 7 3 Mesh design for dynamics 7 4 Example cargo crane under dynamic loading es Effect of the number of modes 7 6 Effect of damping Tad Comparison with direct time integration 7 8 Other dynamic procedures 7 9 Related Abaqus examples 7 10 Suggested reading 7 11 Summary The 8 Nonlinearity Sources of nonlinearity 8 1 The solution of nonlinear problems 8 2 Including nonlinearity in an Abaqus analysis 8 3 Example nonlinear skew plate 8 4 Related Abaqus examples 8 5 Suggested reading 8 6 Summary 8 7 9 Nonlinear Explicit Dynamics Types of problems suited for Abaqus Explicit 9 1 Explicit dynamic finite element methods 9 2 Automatic time incrementation and stability 9 3 Example stress wave propagation in a bar 9 4 Damping of dynamic oscillations 9 5 10 11 12 Energy balance Summary Materials Defining materials in Abaqus Plasticity in ductile metals Selecting elements for elastic plastic problems Example connecting lug with plasticity Example blast loading on a stiffened plate Hyperelasticity Example axisymmetric mount Mesh design for large distortions Techniques for reducing volumetric locking Related Abaqus examples Suggested reading Summary Multiple Step Analysis General analysis procedures Linear perturbation analysis Example vibration of a piping system Restart analysis Example restarting the
134. requests boundary conditions and concentrated loads ELEMENT PRINT THE FOLLOWING TABLE IS PRINTED AT EVERY 1 INCREMENT FOR ALL ELEMENTS OF TYPE T2D2 OUTPUT IS AT THE INTEGRATION POINTS SUMMARIES WILL BE PRINTED WHERE APPLICABLE TABLE 1 sil ELEMENT FILE OUTPUT THE FOLLOWING TABLE IS OUTPUT AT EVERY 1 INCREMENT FOR ALL ELEMENTS OF TYPE T2D2 OUTPUT IS AT THE INTEGRATION POINTS S NODE PRINT THE FOLLOWING TABLE IS PRINTED FOR ALL NODES AT EVERY 1 INCREMENT SUMMARIES WILL BE PRINTED TABLE 1 U1 U2 THE FOLLOWING TABLE IS PRINTED FOR ALL NODES AT EVERY 1 INCREMENT SUMMARIES WILL BE PRINTED TABLE 2 RF1 RF2 NODE FILE OUTPUT THE FOLLOWING TABLE IS OUTPUT FOR ALL NODES AT EVERY 1 INCREMENT U RF 2 24 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST BOUNDARY CONDITIONS NODE DOF AMP MAGNITUDE NODE DOF AMP MAGNITUDE REF REF 103 2 RAMP 0 0000 RAMP OR STEP INDICATE USE OF DEFAULT AMPLITUDES ASSOCIATED WITH THE STEP BOUNDARY CONDITIONS NODE TYPE NODE TYPE NODE TYPE NODE TYPE NODE TYPE 101 ENCASTRE CONCENTRATED LOADS NODE DOF AMP AMPLITUDE NODE DOF AMP AMPLITUDE NODE DOF AMP AMPLITUDE REF REF REF 102 2 10000 Remaining items in the data file If there are any error messages the number of such messages produced during the datacheck analysis 1s listed at the end of the data file If there are only warning messages the number of these messages is listed at the bottom of the data file
135. seen in the simulation Look closely at the information in the plot s title for an explanation The deformation scale factor used in this plot is 0 02 1 e the displacements are scaled to 2 of their actual values Your deformation scale factor may be different Abaqus Viewer always scales the displacements in a geometrically linear simulation such that the deformed shape of the model fits into the viewport This is in contrast to a geometrically nonlinear simulation where Abaqus Viewer does not scale the displacements and instead adjusts the view by zooming in or out to fit the deformed shape in the plot To plot the actual displacements 10 18 EXAMPLE CONNECTING LUG WITH PLASTICITY set the deformation scale factor to 1 0 This will produce a plot of the model in which the lug has deformed until it is almost parallel to the vertical global Y axis The applied load of 60 kN exceeds the limit load of the lug and the lug collapses when the material yields at all the integration points through its thickness The lug then has no stiffness to resist further deformation because of the perfectly plastic post yield behavior of the steel This 1s consistent with the pattern observed earlier concerning the locations of the large strain increments and maximum displacement corrections 10 4 5 Adding hardening to the material model The connecting lug simulation with perfectly plastic material behavior predicts that the lug will suffer catastr
136. set the selection method to individually and select the nodes at the bottom of the hole in the lug as indicated in Figure 4 35 Click Done when all the nodes on the bottom of the hole are highlighted in the viewport In the Create Display Group dialog box click Save Selection As Save the display group asnodes at hole bottom Now generate the reports To generate field data reports 1 In the Results Tree click mouse button 3 on built in elements underneath the Display Groups container In the menu that appears select Plot to make it the current display group 2 From the main menu bar select Report Field Output 3 Inthe Variable tabbed page of the Report Field Output dialog box accept the default position labeled Integration Point Click the triangle next to S Stress components to expand the list of available variables From this list select Mises and the six individual stress components 11 22 S33 S12 13 and S23 In the Setup tabbed page name the report Lug rpt In the Data region at the bottom of the page toggle off Column totals 4 36 EXAMPLE CONNECTING LUG Select these nodes Y p Figure 4 35 Nodes in display group nodes at hole bottom 5 Click Apply 6 In the Results Tree click mouse button 3 on built in nodes underneath the Display Groups container In the menu that appears select Plot to make it the current display group To see the nodes toggle on Show node sy
137. shown in Figure 12 35 unless the mesh on the slave surface 1s adequately refined 12 47 5 DEFINING CONTACT IN Abaqus Explicit master surface slave surface Figure 12 35 Penetration of master nodes into slave surface with pure master slave contact Balanced master slave contact simply applies the pure master slave approach twice reversing the surfaces on the second pass One set of contact constraints is obtained with surface 1 as the slave and another set of constraints is obtained with surface 2 as the slave The acceleration corrections or forces are obtained by taking a weighted average of the two calculations For kinematic balanced master slave contact a second correction is made to resolve any remaining penetrations as described in Contact formulations for contact pairs in Abaqus Explicit Section 37 2 2 of the Abaqus Analysis User s Manual The balanced master slave contact constraint when kinematic compliance is used is illustrated in Figure 12 36 Figure 12 36 Balanced master slave contact constraint with kinematic compliance The balanced approach minimizes the penetration of the contacting bodies and thus provides more accurate results in most cases The general contact algorithm uses balanced master slave weighting whenever possible pure master slave weighting is used for general contact interactions involving node based surfaces which can act only as pure slave surfaces For the contact pair alg
138. states that the nodal mass matrix M times the nodal accelerations u equals the net nodal forces the difference between the external applied forces P and internal element forces I Mu P I The accelerations at the beginning of the current increment time are calculated as la M gt P D o Since the explicit procedure always uses a diagonal or lumped mass matrix solving for the accelerations is trivial there are no simultaneous equations to solve The acceleration of any node is determined completely by its mass and the net force acting on it making the nodal calculations very inexpensive The accelerations are integrated through time using the central difference rule which calculates the change in velocity assuming that the acceleration is constant This change in velocity is added to the velocity from the middle of the previous increment to determine the velocities at the middle of the current increment Atl Han Atlee z la egy t ilo The velocities are integrated through time and added to the displacements at the beginning of the increment to determine the displacements at the end of the increment Ul At ula Atle an l aa Thus satisfying dynamic equilibrium at the beginning of the increment provides the accelerations Knowing the accelerations the velocities and displacements are advanced explicitly through time The term explicit refers to the fact that the state at
139. step and increment specified on the RESTART option and all previously defined history data should be ignored The simulation may then continue with the new steps defined after the RESTART option For example ifa step allowed only a maximum of 20 increments which was less than the number of increments necessary to complete the step the following restart input file would allow Abaqus to restart the simulation and finish the applied load HEADING Continue an analysis that exceeded the maximum number of increments 11 18 EXAMPLE RESTARTING THE PIPE VIBRATION ANALYSIS RESTART READ STEP lt step gt INC 20 END STEP STEP INC 100 repeat step definition END STEP In this situation the entire step definition including applied loads and boundary conditions should be identical to that specified in the original run with the following exceptions e The number of increments should be increased e The total time of the new step should be the total time of the original step less the time completed in the step in the first run For example if the time of the step as originally specified was 100 seconds and the analysis ran out of increments at a step time of 20 seconds the duration of the step in the restart analysis should be 80 seconds e Any amplitude definitions specified in terms of step time need to be respecified to reflect the new time scale of the step Amplitude definitions specified in terms of total time do not need
140. stress displacement elements Continuum stress displacement elements in Abaqus have names that begin with the letter C The next two letters indicate the dimensionality and usually but not always the active degrees of freedom FINITE ELEMENTS in the element The letters 3D indicate a three dimensional element AX an axisymmetric element PE a plane strain element and PS a plane stress element The use of continuum elements is discussed further in Chapter 4 Using Continuum Elements Three dimensional continuum element library Three dimensional continuum elements can be hexahedra bricks wedges or tetrahedra The full inventory of three dimensional continuum elements and the nodal connectivity for each type can be found in Three dimensional solid element library Section 28 1 4 of the Abaqus Analysis User s Manual Whenever possible hexahedral elements or second order tetrahedral elements should be used in Abaqus First order tetrahedra C3D4 have a simple constant strain formulation and very fine meshes are required for an accurate solution Two dimensional continuum element library Abaqus has several classes of two dimensional continuum elements that differ from each other in their out of plane behavior Two dimensional elements can be quadrilateral or triangular Figure 3 3 shows the three classes that are used most commonly ae 2 z Peg I ay SES oe 2 1 7 TOSIN
141. structure during the analysis Geometric nonlinearity occurs whenever the magnitude of the displacements affects the response of the structure This may be caused by e Large deflections or rotations e Snap through e Initial stresses or load stiffening For example consider a cantilever beam loaded vertically at the tip see Figure 8 5 N Figure 8 5 Large deflection of a cantilever beam If the tip deflection is small the analysis can be considered as being approximately linear However if the tip deflections are large the shape of the structure and hence its stiffness changes In addition if the load does not remain perpendicular to the beam the action of the load on the structure changes significantly As the cantilever beam deflects the load can be resolved into a component perpendicular to the beam and a component acting along the length of the beam Both of these effects contribute to the nonlinear response of the cantilever beam 1 e the changing of the beam s stiffness as the load it carries increases One would expect large deflections and rotations to have a significant effect on the way that structures carry loads However displacements do not necessarily have to be large relative to the 8 4 THE SOLUTION OF NONLINEAR PROBLEMS dimensions of the structure for geometric nonlinearity to be important Consider the snap through under applied pressure of a large panel with a shallow curve as sho
142. subsequent step Abaqus will issue a warning stating that they are being included in the step anyway Other geometrically nonlinear effects The large deformations in a model are not the only important effects that are considered when geometric nonlinearity is activated Abaqus Standard also includes terms in the element stiffness calculations that are caused by the applied loads the so called load stiffness These terms improve convergence behavior In addition the membrane loads in shells and the axial loads in cables and beams contribute much of the stiffness of these structures in response to transverse loads By including geometric nonlinearity the membrane stiffness in response to transverse loads is considered as well 8 3 2 Material nonlinearity The addition of material nonlinearity to an Abaqus model is discussed in Chapter 10 Materials 8 3 3 Boundary nonlinearity The introduction of boundary nonlinearity is discussed in Chapter 12 Contact 8 4 Example nonlinear skew plate This example is a continuation of the linear skew plate simulation described in Chapter 5 Using Shell Elements and shown in Figure 8 11 You will now reanalyze the plate in Abaqus Standard to include the effects of geometric nonlinearity The results from this analysis will allow you to determine the importance of geometrically nonlinear effects and therefore the validity of the linear analysis You only need to modify the history d
143. surface are constrained not to penetrate into the master surface The nodes of the master surface can in principle penetrate into the slave surface Abaqus Explicit includes this formulation but typically uses a balanced 12 91 SUGGESTED READING master slave weighting by default see Contact formulations for contact pairs in Abaqus Explicit Section 37 2 2 of the Abaqus Analysis User s Manual e The contact formulations in Abaqus Standard and Abaqus Explicit differ in many respects For example Abaqus Standard provides a surface to surface formulation while Abaqus Explicit provides an edge to edge formulation e The constraint enforcement methods in Abaqus Standard and Abaqus Explicit differ in some respects For example both Abaqus Standard and Abaqus Explicit provide penalty constraint methods but the default penalty stiffnesses differ e Abaqus Standard and Abaqus Explicit both provide a small sliding contact formulation see Contact formulations in Abaqus Standard Section 37 1 1 of the Abaqus Analysis User s Manual and Contact formulations for contact pairs in Abaqus Explicit Section 37 2 2 of the Abaqus Analysis User s Manual However the small sliding contact formulation in Abaqus Standard transfers the load to the master nodes according to the current position of the slave node Abaqus Explicit always transfers the load through the anchor point As a result of these differences contact definitions spec
144. surface must be the master surface in each of these contact pairs Each contact pair must refer to a SURFACE INTERACTION option that defines a surface interaction model governing how the surfaces of the contact pair interact with each other Multiple contact pairs can refer to the same SURFACE INTERACTION option In this example we assume that the friction coefficient 1s zero between the blank and the punch The friction coefficient between the blank and the other two tools is assumed to be 0 1 Therefore two SURFACE INTERACTION options must be used in the model one with friction and one without Frictionless contact is the default in Abaqus so no FRICTION option is needed in the surface interaction definition for the contact pair The option blocks to define the contact pairs and surface interactions in your model will look like 12 24 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL CONTACT PAIR INTERACTION FRIC TYPE SURFACE TO SURFACE BLANK B DIE BLANK T HOLDER CONTACT PAIR INTERACTION NOFRIC TYPE SURFACE TO SURFACE BLANK T PUNCH SURFACE INTERACTION NAME FRIC FRICTION 0 1 SURFACE INTERACTION NAME NOFRIC For each contact pair the surface to surface contact discretization technique has been used which controls the location where contact constraints will be generated and enforced 12 5 6 Reviewing the input file the history data There are two major sources of difficulty in Abaqus Standard contact analyses r
145. that Abaqus terminated the analysis early because these numerical problems forced it to cut back the time increment until 1t was below the minimum allowable time increment In the third column of the status file you will see the number of attempts Abaqus made to solve an increment In the sixth column the number of iterations needed for the last attempt at an increment is printed Now you should look at the results in Abaqus Viewer to understand what caused this excessive plasticity 10 17 5 EXAMPLE CONNECTING LUG WITH PLASTICITY 10 4 4 Postprocessing the results Look at the results in Abaqus Viewer to understand what caused the excessive plasticity Run Abaqus Viewer by entering the following command at the operating system prompt abaqus viewer odb lug plas Plotting the deformed model shape Create a plot of the model s deformed shape and check that this shape is realistic The default view is isometric You can set the view shown in Figure 10 10 by using the options in the View menu or the tools in the View Manipulation toolbar in this figure perspective is also turned off Step Step 1 Increment 23 Step Time 0 9529 Deformed Var U Deformation Scale Factor 2 000e 02 Figure 10 10 Deformed model shape using results for the simulation without hardening The displacements and particularly the rotations of the lug shown in the plot are large but do not seem large enough to have caused all of the numerical problems
146. that from rotating machinery you must perform a dynamic analysis This chapter discusses linear dynamic analysis in Abaqus Standard see Chapter 9 Nonlinear Explicit Dynamics for a discussion of nonlinear dynamic analysis in Abaqus Explicit 7 1 Introduction A dynamic simulation is one in which inertia forces are included in the dynamic equation of equilibrium M I P 0 where M is the mass of the structure u is the acceleration of the structure I are the internal forces in the structure and P are the applied external forces The expression in the equation shown above is nothing more than Newton s second law of motion F ma The inclusion of the inertial forces M in the equation of equilibrium is the major difference between static and dynamic analyses Another difference between the two types of simulations is in the definition of the internal forces I In a static analysis the internal forces arise only from the deformation of the structure in a dynamic analysis the internal forces contain contributions created by both the motion i e damping and the deformation of the structure 7 1 1 Natural frequencies and mode shapes The simplest dynamic problem is that of a mass oscillating on a spring as shown in Figure 7 1 The internal force in the spring is given by ku so that its dynamic equation of motion is mu ku p 0 INTRODUCTION Stiffness k Displacement u Force p Mass m F
147. that predicted from the linear analysis Including the nonlinear geometric effects in the simulation reduces the vertical deflection U3 of the midspan of the plate Another difference between the two analyses is that in the nonlinear simulation there are nonzero deflections in the 1 and 2 directions What effects make the in plane displacements U1 and U2 nonzero in the nonlinear analysis Why is the vertical deflection of the plate less in the nonlinear analysis The plate deforms into a curved shape a geometry change that is taken into account in the nonlinear simulation As a consequence membrane effects cause some of the load to be carried by membrane action rather than by bending alone This makes the plate stiffer In addition the pressure loading which is always normal to the plate s surface starts to have a component in the 1 and 2 directions as the plate deforms The nonlinear analysis includes the effects of this stiffening and the changing direction of the pressure Neither of these effects is included in the linear simulation The differences between the linear and nonlinear simulations are sufficiently large to indicate that a linear simulation 1s not adequate for this plate under this particular loading condition For five degree of freedom shells such as the S8R5 element used in this analysis Abaqus does not output total rotations at the nodes 8 22 EXAMPLE NONLINEAR SKEW PLATE 8 4 4 Postprocessing When you ar
148. that they are behind surfaces 1 and 2 Figure 12 43 shows an adequate surface definition for this connection The surfaces are continuous and describe the entire geometry of the contacting bodies CONTACT PAIR SURFACE 4 SURFACE 5 Figure 12 43 Correct surface definition Consistent surface normals Single sided surfaces on shell membrane or rigid elements must be defined so that the normal directions do not flip as the surface is traversed Figure 12 44 shows a mesh of SAX1 elements whose normals are not continuous from one element to the next The face identifier SPOS indicates that the surface is on the face with the positive outward normal and the face identifier SNEG indicates the reverse If a surface was defined using the SPOS face for all the elements Abaqus Explicit would issue a warning message stating that the surface is not valid A valid surface could be defined with this mesh if the surface definition shown in the figure which uses both SPOS and SNEG face identifiers to accommodate the inconsistent element normals 1s used It is not necessary for the normals of all the underlying shell membrane or rigid elements to have a consistent positive orientation for a double sided surface if possible Abaqus Explicit will define the surface such that its facets have consistent normals even if the underlying elements do not have consistent normals The facet normals will be the same as the element normals if the elem
149. the SECTION POINTS option which must follow the BEAM GENERAL SECTION option to specify the location of the section points SECTION POINTS 5 BEAM CROSS SECTION GEOMETRY The x and z2 coordinates are given in the local 1 2 coordinate system of the beam cross section For example if we require stresses at the corners of an element with the rectangular beam cross section shown in Figure 6 3 we would use the following option block SECTION POINTS 0 01 0 005 0 01 0 005 0 01 0 005 0 01 0 005 Figure 6 3 Section points at the corners of a rectangular beam The points you specify are assigned identifying numbers based on the order they are given 1 e the first point is section point 1 the second is section point 2 etc 6 1 2 Cross section orientation You must define the orientation of a beam s cross section in global Cartesian space The local tangent along the beam element t is defined as the vector along the element axis pointing from the first node of the element to the next node The beam cross section 1s perpendicular to this local tangent The local 1 2 beam section axes are represented by the vectors n and ng The three vectors t n and ny form a local right handed coordinate system see Figure 6 4 The n direction is always 0 0 0 0 1 0 for two dimensional beam elements For three dimensional beam elements there are several ways to define the orientation of the local beam section axe
150. the Y value type to strain 12 88 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST 8 In the XYData container of the Results Tree click mouse button 3 on LEP Max and select Edit from the menu that appears 9 In the Edit XY Data dialog box choose Strain as the Y value type 10 Similarly edit LEP Min and select Strain as the Y value type 11 Using the Results Tree plot LEP Man and LEP Min along with the principal strains recorded during the analysis LEP1 and LEP2 for the element in set BOTPART 12 As before customize the plot appearance to obtain a plot similar to Figure 12 66 LEP Max LEP Min LEP2_ ANTIALIASING ELSET BOTPART LEP1_ANTIALIASING ELSET BOTPART x1 E 3 0 10 Strain Q D 10 15 20 x1 E 3 Time s Figure 12 66 Principal logarithmic strain values versus time In Figure 12 66 we see that the filtered principal logarithmic strain curves recorded during the analysis are indistinguishable from the principal logarithmic strain curves calculated from the filtered strain components Therefore the anti aliasing filter cutoff frequency 2 4 kHz did not remove any of the frequency content introduced by the nonlinear operation to calculate principal strains form the original strain data Next filter the strain data with a lower cutoff frequency of 500 Hz To filter principal logarithmic strains with a cutoff frequency of 500 Hz 1 In the Results Tree double click XYData then select
151. the default isometric view using the whe tool in the Views toolbar Tip If the Views toolbar is not visible select View Toolbars Views from the main menu bar Figure 10 32 shows a contour plot of the von Mises stress at the end of the analysis 7 Similarly contour the equivalent plastic strain Select Primary from the list of variable types on the left side of the Field Output toolbar and select PEEQ from the list of output variables next to it Figure 10 33 shows a contour plot of the equivalent plastic strain at the end of the analysis 10 46 EXAMPLE BLAST LOADING ON A STIFFENED PLATE Figure 10 32 Contour plot of von Mises stress at 50 ms om 0 H EE stl qaqa SS ANANN NNN MMMMMMO pop eee eoleje ee eleterexe CALETA totot ORB ORO RO ROR OR OR OR ORO ORO Coe OR MSNHARNOHMO wun QMEAWMANAROtTMAO SHS RR ADFOSNAOOTANWO on AAA ONwOWOHTMHO N aunmrttttt ttttet MeO 5 ba ann Figure 10 33 Contour plot of equivalent plastic strain at 50 ms 10 47 5 EXAMPLE BLAST LOADING ON A STIFFENED PLATE 10 5 8 Reviewing the analysis The objective of this analysis is to study the deformation of the plate and the stress in various parts of the structure when it is subjected to a blast load To judge the accuracy of the analysis you will need to consider the assumptions and approximations made and identify some of the limitations of the model Damping Undamped struc
152. the face numbers are shown in Figure 4 20 Face 4 Face 1 1 2 3 4 face Face 2 5 8 7 6 face Face 3 1 5 6 2 face Face 4 2 6 7 3 face Face 5 3 7 8 4 face Face 6 4 8 5 1 face Figure 4 20 Face numbers on hexahedral elements In the model as defined in Connecting lug Section A 2 the pressure is applied to face 6 of the elements around the bottom of the hole so the load ID is P6 For meshes generated with a preprocessor the face numbers and hence the load IDs will depend on how the mesh is generated Some preprocessors such as Abaqus CAE can determine the correct load ID automatically this makes it very easy to specify pressure loads on complicated meshes However this method tends to produce long lists of data lines in the input file In models where the same load ID and load magnitude are used for each element you can use an element set which is more efficient to apply the pressure loads For example in this model the DLOAD option block may appear as DLOAD PRESS P6 5 E 07 where we have made use of the element set PRESS whose members are shown in Figure 4 16 Output requests By default many preprocessors create an Abaqus input file that has a large number of output request options These requests are in addition to the output database file request that is generated automatically by Abaqus If when you edit your input file you find that these additional output options were created delete them because t
153. the internal and external forces into balance This second iteration uses the stiffness Ka calculated at the end of the previous iteration together with Ra to determine another displacement correction cp that brings the system closer to equilibrium point b in Figure 8 10 Ua Up Displacement Figure 8 10 Second iteration 5 THE SOLUTION OF NONLINEAR PROBLEMS Abaqus Standard calculates a new force residual R using the internal forces from the structure s new configuration up Again the largest force residual at any degree of freedom Ry is compared against the force residual tolerance and the displacement correction for the second iteration cy is compared to the increment of displacement Aup up uo If necessary Abaqus Standard performs further iterations For each iteration in a nonlinear analysis Abaqus Standard forms the model s stiffness matrix and solves a system of equations This means that each iteration is equivalent in computational cost to conducting a complete linear analysis It should now be clear that the computational expense of a nonlinear analysis in Abaqus Standard can be many times greater than for a linear one It is possible with Abaqus Standard to save results at each converged increment Thus the amount of output data available from a nonlinear simulation is many times that available from a linear analysis of the same geometry Consider both of these factors and the types of nonlinear s
154. the node and element numbers in your model and not those shown in the figure Section properties Look up the C3D20R element in Chapter 28 Continuum Elements of the Abaqus Analysis User s Manual to determine the correct element section option and the required data that must be specified for this element You will discover that the C3D20R element uses the SOLID SECTION option to define the element s section properties Because this 1s a three dimensional element Abaqus needs no additional geometric data for the element section Element set LUG contains all the elements so that element set is suitable for this example The following element section option statement is used for this example SOLID SECTION ELSET LUG MATERIAL STEEL 4 17 5 EXAMPLE CONNECTING LUG If you did not define an element set with the name LUG use the name of whatever element set contains all the elements in your model as the value of the ELSET parameter The material property definition in the model will have the name STEEL Materials The connecting lug is made of a mild steel and thus has isotropic linear elastic material behavior under the loads being applied Assume that amp 200 GPa and that v 0 3 These are given on the data line of the ELASTIC option remember the overhead hoist example in Chapter 2 Abaqus Basics The following material property definition specifies these properties in the input file MATERIA
155. the output requests so as to not break up the block of suboptions associated with the OUTPUT option 10 4 3 Running the analysis Save these changes to your model and run the analysis with the following command abaqus job lug plas Status file Monitor the simulation while it is running by looking at the status file lug plas sta When Abaaus has finished the simulation your status file will contain information similar to the following SUMMARY OF JOB INFORMATION STEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC OF DOF IF DISCON ITERS ITERS TIME TIME LPF TIME LPF MONITOR RIKS ITERS FREQ 1 1 1 0 I 1 0 200 0 200 0 2000 1 2 1 0 1 1 0 400 0 400 0 2000 1 3 1 0 3 3 0 700 0 700 0 3000 1 4 1U 0 4 4 0 700 0 700 0 3000 1 4 2 0 2 2 0 775 0 775 0 07500 1 5 1 0 4 4 0 887 0 887 0 1125 1 6 1U 0 4 4 0 887 0 887 0 1125 1 6 2 0 3 3 0 916 0 916 0 02813 1 7 1U 0 5 5 0 916 0 916 0 04219 1 7 2 0 2 2 0 926 0 926 0 01055 1 8 1 0 4 4 0 942 0 942 0 01582 1 9 1U 0 3 3 0 942 0 942 0 02373 1 9 2 0 5 5 0 948 0 948 0 005933 1 10 1U 0 4 4 0 948 0 948 0 005933 1 10 2 0 4 4 0 949 0 949 0 001483 1 11 1 0 4 4 0 951 0 951 0 001483 1 12 1U 0 3 3 0 951 0 951 0 002225 1 12 2 0 3 3 0 951 0 951 0 0005562 1 13 1 0 4 4 0 952 0 952 0 0008343 1 14 1U 0 2 2 0 952 0 952 0 001251 1 14 2 0 4 4 0 953 0 953 0 0003129 1 15 1U 0 2 2 0 953 0 953 0 0004693 1 15 2 0 3 3 0 953 0 953 0 0001173 1 16 1U 0 3 3 0 953 0 953 0 0001760 1 16 2 0 3 3 0 953 0 953 4 399e 005
156. this force residual tolerance Abaqus Standard accepts the structure s updated configuration THE SOLUTION OF NONLINEAR PROBLEMS as the equilibrium solution By default this tolerance value is set to 0 5 of an average force in the structure averaged over time Abaqus Standard automatically calculates this spatially and time averaged force throughout the simulation If Ra is less than the current tolerance value P and J are in equilibrium and ua is a valid equilibrium configuration for the structure under the applied load However before Abaqus Standard accepts the solution it also checks that the displacement correction c is small relative to the total incremental displacement Au Ua ug If cg is greater than 1 of the incremental displacement Abaqus Standard performs another iteration Both convergence checks must be satisfied before a solution is said to have converged for that load increment The exception to this rule is the case of a linear increment which is defined as any increment in which the largest force residual is less than 10 times the time averaged force Any case that passes such a stringent comparison of the largest force residual with the time averaged force is considered linear and does not require further iteration The solution is accepted without any check on the size of the displacement correction If the solution from an iteration is not converged Abaqus Standard performs another iteration to try to bring
157. to be changed provided the modifications given above are used The magnitudes of any loads or prescribed boundary conditions remain unchanged since they are always total values in general analysis steps 11 5 Example restarting the pipe vibration analysis To demonstrate how to restart an analysis take the pipe section example in Example vibration of a piping system Section 11 3 and restart the simulation adding two additional steps of load history The first simulation predicted that the piping section would be vulnerable to resonance when extended axially you must now determine how much additional axial load will increase the pipe s lowest vibrational frequency to an acceptable level Step 3 will be a general step that increases the axial load on the pipe to 8 MN and Step 4 will calculate the eigenmodes and eigenfrequencies again Create a new input file called pipe 2 inp and add the option blocks discussed below If you wish to create the entire model using Abaqus CAE refer to Example restarting the pipe vibration analysis Section 11 5 of Getting Started with Abaqus Interactive Edition 11 5 1 Reviewing the input file the model data The only model data required are the HEADING option and a RESTART option to read the restart data from the end of the previous analysis Abaqus reads all other model data such as node and element definitions directly from the restart file Add the following option blocks to your ne
158. tools for solving many different problems The elements available in Abaqus Explicit are with a few exceptions a subset of those available in Abaqus Standard This section introduces you to the five aspects of an element that influence how it behaves 3 1 1 Characterizing elements Each element is characterized by the following e Family e Degrees of freedom directly related to the element family e Number of nodes e Formulation e Integration Each element in Abaqus has a unique name such as T2D2 S4R or C3D8I The element name as you saw in the overhead hoist example in Chapter 2 Abaqus Basics is used as the value of the TYPE parameter on the ELEMENT option in the input file The element name identifies each of the five aspects of an element The naming convention 1s explained in this chapter FINITE ELEMENTS Family Figure 3 1 shows the element families most commonly used in a stress analysis One of the major distinctions between different element families is the geometry type that each family assumes lt gt Continuum Shell Beam Rigid solid elements elements elements elements Wa Membrane Infinite Springs and dashpots Truss elements elements elements Figure 3 1 Commonly used element families The element families that you will use in this guide continuum shell beam truss and rigid elements are discussed in detail in other chapters The other element families are not covered in this guide
159. use a reduced integration scheme all wedge tetrahedral and triangular solid elements use full integration although they can be used in the same mesh with reduced integration hexahedral or quadrilateral elements Reduced integration elements use one fewer integration point in each direction than the fully integrated elements Reduced integration linear elements have just a single integration point located at the element s centroid Actually these first order elements in Abaqus use the more accurate uniform strain formulation where average values of the strain components are computed for the element This distinction is not important for this discussion The locations of the integration points for reduced integration quadrilateral elements are shown in Figure 4 7 5 ELEMENT FORMULATION AND INTEGRATION 4 3 xl 2 Linear element Quadratic element e g CPS4R e g CPS8R Figure 4 7 Integration points in two dimensional elements with reduced integration Abaqus simulations of the cantilever beam problem were performed using the reduced integration versions of the same four elements utilized previously and using the four finite element meshes shown in Figure 4 3 The results from these simulations are presented in Table 4 2 Table 4 2 Normalized tip displacements with reduced integration elements Mesh Size Depth x Length CPS8R 1 000 1 000 1 000 1 000 C3D8R 1 323 1 063 1 015 C3D20R 0 999 1 000 1 000 1 000
160. use the Results Tree to query the components of the model The Results Tree allows easy access to the history output contained in an output database file for the purpose of creating X Y plots and also to groups of elements nodes and surfaces based on set names material and section assignment etc for the purposes of verifying the model and also controlling the viewport display To query the model 1 All output database files that are open in a given postprocessing session are listed underneath the Output Databases container Expand this container and then expand the container for the output database named frame odb 2 Expand the Materials container and click the material named STEEL All elements are highlighted in the viewport because only one material assignment was used in this analysis The Results Tree will be used more extensively in later examples to illustrate the X Y plotting capability and manipulating the display using display groups Customizing an undeformed shape plot You will now use the plot options to enable the display of node and element numbering Plot options that are common to all plot types undeformed deformed contour symbol and material orientation are set in a single dialog box The contour symbol and material orientation plot types have additional options each specific to the given plot type To display node numbers 2 3 1 From the main menu bar select Options Common or use the 1234 to
161. using 0 0 1 as the X Y and Z coordinates of the viewpoint vector and 0 1 0 as the X Y and Z coordinates of the up vector Y oe een X Tip You can also display the model using this view by clicking Cx from the Views toolbar The undeformed shape of the crane superimposed upon the deformed shape is shown in Figure 6 18 Figure 6 18 Deformed shape of cargo crane Using display groups to plot element and node sets You can use display groups to plot existing node and element sets you can also create display groups by selecting nodes or elements directly from the viewport You will create a display group containing only the elements associated with the main members in truss structure A 6 24 EXAMPLE CARGO CRANE To create and plot a display group 1 In the Results Tree expand the Sections container underneath the output database file named crane odb y To facilitate your selection change the view back to the default isometric view using the he tool in the Views toolbar Tip If the Views toolbar is not visible select View Toolbars Views from the main menu bar In succession click the items in the container until the elements associated with the main members in truss A are highlighted in the viewport Click mouse button 3 on this item and select Replace from the menu that appears Abaqus Viewer now displays only this group of elements EE To save this group double click Displ
162. want to let the mount deform radially in this analysis do not apply any boundary conditions again Abaqus will prevent rigid body motions automatically Loading The mount must carry a maximum axial load of 5 5 kN spread uniformly over the steel plates A distributed load is therefore applied to the bottom of the steel plate The magnitude of the pressure is given by p 5500 7 0 06 0 01 0 50MPa If you generated the pressure loading using a preprocessor a DLOAD option block with many data lines may be present in the input file DLOAD 1 Pl 0 50E6 10 66 EXAMPLE AXISYMMETRIC MOUNT 2 Pl 0 50E6 29 P1 0 50E6 30 P1 0 50E6 For the element and node numbering discussed here the pressure is applied to face 1 of all the elements in element set PLATE This allows us to use a much more compact format for the data lines of the DLOAD option block DLOAD PLATE P1 0 50E6 Output requests Write the preselected variables and nominal strains as field output to the output database file In addition write the displacement of one of the nodes on the bottom of the steel plate to the output database file so that the stiffness of the mount can be calculated You will need to create a node set containing the node The output option blocks in your model should be similar to the following NSET NSET OUT 1 OUTPUT FIELD VARIABLE PRESELECT ELEMENT OUTPUT NE OUTPUT HISTORY NODE OUTPUT NSET OUT U
163. will calculate the principal logarithmic strains using the filtered strain components and compare the result to the filtered principal logarithmic strains To calculate the principal logarithmic strains 1 In the Results Tree filter the History Output according to LE select the logarithmic strain component LE11 on the SPOS surface of the element in set BOTPART and save the data as LE11 2 Similarly save the LE12 and LE22 strain components for the same element as LE12 and LE22 respectively 3 In the Results Tree double click XYData then select Operate on XY data in the Create XY Data dialog box Click Continue 4 In the Operate on XY Data dialog box use the saved logarithmic strain components to calculate the maximum principal logarithmic strain The expression at the top of the dialog box should appear as LE11 LE22 2 sqrt power LE11 LE22 2 2 power LE12 2 2 5 Click Save As to save calculated maximum principal logarithmic strain as LEP Max 6 Edit the expression in the Operate on XY Data dialog box to calculate the minimum principal logarithmic strain The modified expression should appear as LE11 LE22 2 sqrt power LE11 LE22 2 2 power LE12 2 2 7 Click Save As to save calculated minimum principal logarithmic strain as LEP Min In order to plot the calculated principal logarithmic strains with the same Y axis as the strains recorded during the analysis change
164. you must apply the boundary conditions in the local coordinate system To allow these nodes to move in the local 1 direction along the axis of the plate only all other degrees of freedom must be constrained as follows ENDB 2 6 Had you not defined node sets ENDA and ENDB you would have had to create a data line for each node Loading A distributed pressure load of 20 0 kPa is applied to the plate in this simulation As shown in Figure 5 10 the pressure acts in the negative global 3 direction Pressure loads are applied to the faces of elements with the DLOAD option DLOAD is described in Chapter 4 Using Continuum Elements for the lug model example Shell elements have only one face therefore the load identifier for pressure is just P A positive pressure on a shell acts in the direction of the positive element normal The shell elements in the input file from Skew plate Section A 3 have normals that align with the positive global 3 axis Thus the following input defines the correct pressure loading in that model DLOAD PLATE P 20000 0 Since element set PLATE contains all elements in the model this option block applies a pressure load to all elements in the model Output requests If the preprocessor has generated default output request options you should delete them To create an output database odb file for use with Abaqus Viewer and printed tables of the element stresses nodal reaction for
165. your model changing the node numbers to correspond to those in your model If all of the nodes on the two truss structures had been grouped into a node set called TRUSNODE and all of the nodes on the cross bracing had been grouped into a node set called CROSNODE the option block could have been shortened to the following NSET NSET TRUSNODE UNSORTED 101 102 103 105 106 201 202 203 205 206 NSET NSET CROSNODE UNSORTED 301 302 303 305 306 401 402 403 405 406 MPC PIN TRUSNODE CROSNODE 6 21 5 EXAMPLE CARGO CRANE If a node set is provided as the first item after the MPC type the second item can be either another node set or a single node When the data line of an MPC option contains a node set and then a single node as shown below Abaqus creates an MPC constraint between each node in the set and the individual node specified For example the following option block would create a pinned joint between node 301 and each node in node set TRUSNODE xMPC PIN TRUSNODE 301 Constraint equations Constraints between nodal degrees of freedom can also be specified with linear equations by using the EQUATION option The form of each equation is Aui Aoue a hem AnUn 0 where A is the coefficient associated with degree of freedom u Each linear constraint equation requires at least two data lines The number of terms n involved in the equation is given on the first data line beneath the EQUATION option On the subsequent dat
166. 1 000 Loc 1 Nodal values from source 1 Output sorted by column Node Label Field Output reported at nodes for part PART 1 1 Node U U1 U U2 U U3 Label Loc 1 Loc 1 Loc 1 601 2 68589E 03 746 369E 06 49 4577E 03 602 2 62498E 03 749 228E 06 48 9958E 03 603 2 57304E 03 758 277E 06 48 5853E 03 604 2 53788E 03 761 475E 06 48 1742E 03 605 2 48991E 03 774 13E 06 47 6904E 03 606 2 45666E 03 777 171E 06 47 1307E 03 607 2 40294E 03 792 3E 06 46 52E 03 608 2 36145E 03 793 014E 06 45 9489E 03 609 2 27792E 03 805 258E 06 45 4701E 03 8 26 SUGGESTED READING Minimum 2 68589E 03 805 258E 06 49 4577E 03 At Node 601 609 601 Maximum 2 27792E 03 746 369E 06 45 4701E 03 At Node 609 601 609 8 4 5 Running the analysis in Abaqus Explicit As an optional exercise you can modify the model and run a dynamic analysis of the skew plate in Abaqus Explicit To do so you must add a density of 7800 kg m to the material definition and change the element type to S4R with appropriate modifications to the element connectivity list After making the appropriate model changes you can create and run a new job to examine the transient dynamic effects in the plate under a suddenly applied load 8 5 Related Abaqus examples e Elastic plastic collapse of a thin walled elbow under in plane bending and internal pressure Section 1 1 2 of the Abaqus Example Problems Manual e Laminated composite shells buckling of a cy
167. 1 General analysis procedures The starting point for each general step is the deformed state at the end of the last general step Therefore the state of the model evolves in a sequence of general steps as it responds to the loads defined in each 5 GENERAL ANALYSIS PROCEDURES step Any initial conditions specified using the INITIAL CONDITIONS option define the starting point for the first general step in the simulation All general analysis procedures share the same concepts for applying loads and defining time 11 1 1 Time in general analysis steps Abaqus has two measures of time in a simulation The total time increases throughout all general steps and is the accumulation of the total step time from each general step Each step also has its own time scale known as the step time which begins at zero for each step Time varying loads and boundary conditions can be specified in terms of either time scale The time scales for an analysis whose history is divided into three steps each 100 seconds long are shown in Figure 11 1 Total Step Jos 100s Os 100s Os 100s time Figure 11 1 Step and total time for a simulation 11 1 2 Specifying loads in general steps In general steps the loads must be specified as total values not incremental values For example if a concentrated load has a value of 1000 N in the first step and it is increased to 3000 N in the second general step the magnitude given on the CLOAD option in the tw
168. 10 mesh Create this mesh in your preprocessor Use the coordinate system shown in Figure 9 3 Node and element sets 9 4 1 This example defines node and element sets to apply the loads and boundary conditions and to visualize output The node sets are defined on their respective faces as shown in Figure 9 4 9 11 5 EXAMPLE STRESS WAVE PROPAGATION IN A BAR NTOP NFIX NBACK NFRONT NBOT Figure 9 4 Node sets The element sets are defined as shown in Figure 9 5 ELOAD entire model in element set BAR Figure 9 5 Element sets for modeling In addition this example defined an element set containing three elements in the center of the bar You can define this element set manually by selecting these elements such that their faces nearest to the free end are at distances 0 25 m 0 5 m and 0 75 m from the free end as shown in Figure 9 6 These elements will be used for postprocessing 9 12 EXAMPLE STRESS WAVE PROPAGATION IN A BAR Figure 9 6 Element sets for postprocessing 9 4 2 Reviewing the input file the model data In this section you will review your input file and include additional information Model description The following would be a suitable description in the HEADING option for this simulation HEADING Stress wave propagation in a bar 50x10x10 elements SI units kg m s N Element connectivity If you create input files using a preprocessor check to make sure that you ar
169. 19 8 1 819458E 06 1 000000E 00 601 9 1 819458E 06 1 000000E 00 619 10 1 819458E 06 1 000000E 00 9 16 EXAMPLE STRESS WAVE PROPAGATION IN A BAR The status file continues with information about the progress of the solution STEP 1 ORIGIN 0 0000 Total memory used for step 1 is approximately 6 9 megabytes Global time estimation algorithm will be used Scaling factor 1 0000 Variable mass scaling factor at zero increment 1 0000 STEP TOTAL CPU STABLE CRITICAL KINETIC INCREMENT TIME TIME TIME INCREMENT ELEMENT ENERGY O 0 000E 00 0 000E 00 00 00 00 1 819E 06 1 0 000E 00 Results number 0 at increment zero TOTAL ENERGY 0 000E 00 ODB Field Frame Number 0 of ODB Field Frame Number 0 of 4 requested intervals at increment zero 2 requested intervals at increment zero 1 6 1 092E 05 1 092E 05 00 00 00 1 819E 06 4 432E 05 1 134E 06 12 2 183E 05 2 183E 05 00 00 00 1 819E 06 201 9 043E 05 1 437E 06 17 3 318E 05 3 318E 05 00 00 00 2 896E 06 1 1 376E 04 1 201E 06 21 4 474E 05 4 474E 05 00 00 00 2 882E 06 1 1 547E 04 1 875E 06 23 5 050E 05 5 050E 05 00 00 00 2 877E 06 1 1 533E 04 2 685E 06 ODB Field Frame Number 1 of 4 requested intervals at 5 049687E 05 27 6 199E 05 6 199E 05 00 00 00 2 870E 06 1 1 517E 04 9 508E 07 9 4 5 Postprocessing Start Abaqus Viewer by typing the following command at the operating system prompt abaqus viewer odb wave_50x10x10 Plotting the stress along a path We are interested in looking at how the str
170. 2 7 4 DAMPING Static Equilibrium Underdamped Re OP ONSE 0 40 Critically damped 0 20 0 00 0 00 0 50 1 00 1 50 2 00 2 50 53 00 53 50 4 00 4 50 5 00 TIME x10 Figure 7 2 Damped motion patterns for various values of 7 2 1 Definition of damping in Abaqus Standard In Abaqus Standard a number of different types of damping can be defined for a transient modal analysis direct modal damping Rayleigh damping and composite modal damping Damping is defined for modal dynamic procedures by using the MODAL DAMPING option This option is part of the step definition and allows different amounts of damping to be defined for each mode Direct Rayleigh and composite damping can all be defined this way Direct modal damping The fraction of critical damping associated with each mode can be defined using direct modal damping Typically values in the range of 1 to 10 of critical damping are used Direct modal damping allows you to define precisely the damping of each mode of the system The MODAL DIRECT parameter on the MODAL DAMPING option indicates that direct modal damping is being specified For example to define 4 of critical modal damping for the first 10 modes and 5 for modes 11 20 include the following in the step definition MODAL DAMPING MODAL DIRECT 1 a be 10 0 04 20 0 05 DAMPING Rayleigh damping In Rayleigh damping the assumption is made that the damping matrix is a linear co
171. 2 This example uses the mesh the node and element sets shown in Figure 4 16 and the pressure load and boundary conditions shown in Figure 4 14 ie ee l Node set LHEND Element set BUILTIN Element set PRESS Node set HOLEBOT Figure 4 16 Useful node and element sets for the connecting lug simulation Subsequent steps will add the additional data needed for the model to describe the format of an Abaqus input file If you would prefer to adjust the mesh and you do not have a preprocessor use the Abaqus mesh generation options in Connecting lug Section A 2 If you wish to create the entire model using Abaqus CAE refer to Example connecting lug Section 4 3 of Getting Started with Abaqus Interactive Edition In the description of this simulation that follows the node and element numbers used are from the model found in Connecting lug Section A 2 These node and element numbers are shown in Figure 4 17 and Figure 4 18 If you use a preprocessor the node and element numbering in your model will almost certainly differ from that shown here As you make modifications to your input file remember to use the node and element numbers in your model and not those given here 4 14 EXAMPLE CONNECTING LUG Additional planes of nodes in the z direction are incremented by 5000 Figure 4 17 Node numbers in the plane z 0 Additional p
172. 3 2 765 1 936 4 8241 1 2520E 04 3365 150 5 8245 1 11681E 04 1683 221 0 8249 0 7131 761 5 1 5664E 02 8253 1 1682E 04 1681 220 9 8257 1 2518E 04 3364 150 4 13241 2632 1467 1 2818E 11 13243 1 8432E 04 256 3 5 4115E 10 13245 6063 273 5 1 1869E 10 13247 5943 946 3 1 0687E 10 13249 0 4196 470 0 1 4521E 10 13251 5944 944 6 1 1846E 10 13253 6063 273 8 1 7849E 10 13255 1 8431E 04 255 3 4 3929E 10 13257 2632 1467 8 8306E 11 18241 1 2520E 04 3365 150 5 18245 1 1681E 04 1683 221 0 18249 0 7131 761 5 1 5664E 02 18253 1 1682E 04 1681 220 9 18257 1 2518E 04 3364 150 4 23241 872 9 765 2 936 5 23243 1 0792E 04 139 6 2692 23245 2544 29 24 636 7 ee ay Ee Fee The totals of the reaction forces 23251 3473 247 2 879 7 make it easy to check that the sum 23253 2543 29 40 636 9 i 23255 1 0792E 04 140 0 2692 of the forces acting on the model K Sree a es applied loads plus the reaction TOTAL 1 7806E 09 3 0000E 04 1 6445E 09 forces is equal to zero Figure 4 23 Table of reaction forces in the data file e Click the label for any of the axes on the 3D compass to select a predefined view the selected axis is perpendicular to the plane of the viewport e Double click anywhere on the 3D compass to specify a view Most of the views in this manual are specified directly This is to allow you to confirm the state of your model by checking against the images in the manual You are encouraged ho
173. 385 kg The effective mass in the x y and z directions is 6 98 and 97 respectively of the mass that can move The total effective mass in the 2 and 3 directions is well above the 90 recommended earlier the total effective mass in the direction is much lower However since the loading is applied in the 2 direction the response in the direction is not significant The data file does not contain any results for the modal dynamics step because all of the data file output requests were turned off 7 9 9 When you are in the directory containing the output database file dynamics odb type the following command at the operating system prompt Postprocessing 7 16 EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING abaqus viewer odb dynamics Plotting mode shapes You can visualize the deformation mode associated with a given natural frequency by plotting the mode shape associated with that frequency To select a mode and plot the corresponding mode shape 1 In the context bar click the frame selector tool h The Frame Selector dialog box appears Drag the bottom corner of the dialog box to enlarge it so that both step names are clearly visible 2 Drag the frame slider to select frame 1 in Step 1 This is the first eigenmode 3 From the main menu bar select Plot Deformed Shape or use the ik tool in the toolbox Abaqus Viewer displays the deformed model shape associated with the first vibration mode as shown in F
174. 4 7861E 06 14 7861E 06 114 2 73 2731E 06 73 2731E 06 28 832E 06 28 832E 06 21 4032E 06 21 4032E 06 114 3 74 7242E 06 74 7242E 06 2 78322E 06 2 78322E 06 10 5987E 06 10 5987E 06 114 4 42 7593E 06 42 7593E 06 9 30515E 06 9 30515E 06 6 75836E 06 6 75836E 06 Minimum 238 256E 06 90 2214E 06 103 26E 06 10 5215E 06 18 8595E 06 70 0247E 06 At Element 4 54 4 63 81 111 Int Pt 3 3 1 1 2 2 Maximum 90 2214E 06 238 256E 06 10 5215E 06 103 26E 06 70 0247E 06 18 8595E 06 At Element 54 4 63 4 111 81 Int Pt 3 3 1 1 2 2 The reaction forces and moments are listed in the following table Field Output Report Source 1 ODB skew odb Step Step 1 Frame Increment 1 Step Time 2 2200E 16 Loc 1 Nodal values from source 1 Output sorted by column Node Label Field Output reported at nodes for part PART 1 1 Node RF RF1 RF RF2 RF RF3 RM RM1 RM RM2 RM RM3 Label Loc 1 Loc 1 Loc 1 Loc 1 Loc 1 Loc 1 1 0 0 109 912 1 77484 328 266E 03 0 2 0 0 6 44824 7 59742 36 4615 0 3 0 0 239 923 6 5683 35 4597 0 4 0 0 455 379 6 80581 88 2614 0 5 0 0 260 543 6 94783 51 1276 0 6 0 0 750 833 8 30465 126 458 0 7 0 0 73 904 8 74902 62 2273 0 8 0 0 2 28569E 03 31 0634 205 759 0 9 0 0 37 1932 1 6098 76 4492 0 1201 0 0 37 1932 1 6098 76 4492 0 1202 0 0 2 28569E 03 31 0634 205 759 0 1203 0 0 73 904 8 74902 62 2273 0 1204 0 0 750 833 8 30465 126 458 0 1205 0 0 260 543 6 94783 51 1276 0 1206 0 0 455 379 6 80581 8
175. 5 196 584E 06 183 433E 06 1 35291E 06 8 91071E 06 33 6059E 06 6 34491E 06 1 77698E 06 1236 6 168 507E 06 194 738E 06 38 996E 06 38 4311E 06 24 4598E 06 27 2461E 06 3 10252E 06 1236 7 293 927E 06 281 931E 06 8 13693E 06 13 8641E 06 6 97109E 06 11 6862E 06 1 15429E 06 1236 8 286 857E 06 347 614E 06 87 6102E 06 81 1438E 06 49 8721E 06 42 7034E 06 3 12746E 06 Minimum 35 7223E 06 347 614E 06 87 6102E 06 81 1438E 06 56 4163E 06 42 7097E 06 3 12903E 06 4 38 EXAMPLE CONNECTING LUG At Element 226 236 236 1236 1206 1206 1206 Int Pt 2 4 4 8 2 6 6 Maximum 306 077E 06 347 661E 06 87 6292E 06 81 1577E 06 6 97109E 06 42 7097E 06 3 12903E 06 At Element 206 1206 1206 206 1236 206 206 Int Pt 5 6 6 2 7 2 2 How does the maximum value of Mises stress compare to the value reported in the contour plot generated earlier Do the two maximum values correspond to the same point in the model The Mises stresses shown in the contour plot have been extrapolated to the nodes whereas the stresses written to the report file for this problem correspond to the element integration points Therefore the location of the maximum Mises stress in the report file is not exactly the same as the location of the maximum Mises stress in the contour plot This difference can be resolved by requesting that stress output at the nodes extrapolated from the element integration points and averaged over all elements containing a given node be
176. 51E 08 1236 7 2 8193E 08 8 1369E 06 1 3864E 07 6 9711E 06 1 1686E 07 1 1543E 06 2 9393E 08 1236 8 3 4761E 08 8 7610E 07 8 1144E 07 4 9872E 07 4 2703E 07 3 1275E 06 2 8686E 08 MAXIMUM 3 4766E 08 8 7629E 07 8 1158E 07 6 9711E 06 4 2710E 07 3 1290E 06 3 0608E 08 ELEMENT 206 206 206 236 206 206 206 MINIMUM 3 4761E 08 8 7610E 07 8 1144E 07 5 6416E 07 4 2710E 07 3 1290E 06 3 5722E 07 ELEMENT 236 236 236 206 1206 1206 226 Figure 4 21 Table of element stresses in the data file The tables showing the displacements of the nodes along the bottom of the hole and the reaction forces at the constrained nodes are shown in Figure 4 22 and Figure 4 23 respectively 4 22 EXAMPLE CONNECTING LUG THE FOLLOWING TABLE IS PRINTED FOR NODES BELONGING TO NODE SET HOLEBOT NODE FOOT U2 NOTE 1 3 1342E 04 5001 3 1348E 04 10001 3 1349E 04 15001 3 1348E 04 20001 3 1342E 04 MAXIMUM 3 1342E 04 AT NODE 20001 MINIMUM 3 1349E 04 AT NODE 10001 Figure 4 22 Table of nodal displacements in the data file The bottom of the hole in the lug has displaced about 0 3 mm The total reaction force in the 2 direction at the constrained nodes is equal and opposite to the applied load in that direction of 30 kN 4 3 8 Postprocessing visualizing the results Once you have looked at the results in the data file start Abaqus Viewer by typing the following command at the operating system prompt abaqus viewer odb lug Plotting the
177. 585E 03 AT NODE 651 DOF 3 LARGEST CORRECTION TO DISP 1 846E 04 AT NODE 509 DOF 3 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE AVERAGE MOMENT 2 27 TIME AVG MOMENT 1 70 LARGEST RESIDUAL MOMENT 1 226E 02 AT NODE 208 DOF 4 LARGEST INCREMENT OF ROTATION 1 586E 02 AT NODE 1051 DOF 4 8 20 EXAMPLE NONLINEAR SKEW PLATE LARGEST CORRECTION TO ROTATION 7 332E 04 AT NODE 409 DOF 5 MOMENT EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 2 AVERAGE FORCE 10 2 TIME AVG FORCE 6 33 LARGEST RESIDUAL FORCE 5 316E 04 AT NODE 359 DOF 2 LARGEST INCREMENT OF DISP 5 587E 03 AT NODE 651 DOF 3 LARGEST CORRECTION TO DISP 2 954E 06 AT NODE 459 DOF 3 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED AVERAGE MOMENT 2 67 TIME AVG MOMENT 1 90 LARGEST RESIDUAL MOMENT 4 569E 07 AT NODE 208 DOF 4 LARGEST INCREMENT OF ROTATION 1 586E 02 AT NODE 1051 DOF 4 LARGEST CORRECTION TO ROTATION 1 028E 05 AT NODE 209 DOF 4 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED TIME INCREMENT MAY NOW INCREASE TO 0 150 ITERATION SUMMARY FOR THE INCREMENT 2 TOTAL ITERATIONS OF WHICH 0 ARE SEVERE DISCONTINUITY ITERATIONS AND 2 ARE EQUILIBRIUM ITERATIONS TIME INCREMENT COMPLETED 0 100 FRACTION OF STEP COMPLETED 0 200 STEP TIME COMPLETED 0 200 TOTAL TIME COMPLETED 0 200 Abaqus continues this process of applying an increment of load then iterating to find a solution until it completes the whole analysis or reaches the increment specified a
178. 8 2614 0 1207 0 0 239 923 6 5683 35 4597 0 1208 0 0 6 44824 7 59742 36 4615 0 1209 0 0 109 912 1 77484 328 266E 03 0 Minimum 0 0 109 912 31 0634 205 759 0 At Node 1209 1209 1 1202 8 1209 Maximum 0 0 2 28569E 03 31 0634 205 759 0 At Node 1209 1209 8 8 1202 1209 Total 0 0 8 00000E 03 0 0 0 5 27 SUGGESTED READING 5 6 5 7 Related Abaqus examples e Pressurized fuel tank with variable shell thickness Section 2 1 6 of the Abaqus Example Problems Manual e Analysis of an anisotropic layered plate Section 1 1 2 of the Abaqus Benchmarks Manual e Buckling of a simply supported square plate Section 1 2 4 of the Abaqus Benchmarks Manual e The barrel vault roof problem Section 2 3 1 of the Abaqus Benchmarks Manual Suggested reading The following references provide a more in depth treatment of the theoretical and computational aspects of shell theory Basic shell theory e Timoshenko S Strength of Materials Part II Krieger Publishing Co 1958 e Timoshenko S and S W Krieger Theory of Plates and Shells McGraw Hill Inc 1959 e Ugural A C Stresses in Plates and Shells McGraw Hill Inc 1981 Basic computational shell theory e Cook R D D S Malkus and M E Plesha Concepts and Applications of Finite Element Analysis John Wiley amp Sons 1989 e Hughes T J R The Finite Element Method Prentice Hall Inc 1987 Advanced shell theory e Budiansky B
179. 8948E 03 I ZZ 2 712609E 02 1 109771E 03 I XY 8 881784E 16 2 925000E 00 I YZ 8 881784E 16 2 925000E 00 I ZX 2 273737E 13 8 385000E 02 STABLE TIME INCREMENT INFORMATION 10 38 EXAMPLE BLAST LOADING ON A STIFFENED PLATE The stable time increment estimate for each element is based on linearization about the initial state Initial time increment 8 18646E 06 Statistics for all elements Mean 1 30938E 05 Standard deviation 2 69043E 06 Most critical elements Element number Rank Time increment Increment ratio 1022 1 8 186462E 06 1 000000E 00 1024 2 8 186462E 06 1 000000E 00 1027 3 8 186462E 06 1 000000E 00 1029 4 8 186462E 06 1 000000E 00 1033 5 8 186462E 06 1 000000E 00 1038 6 8 186462E 06 1 000000E 00 2022 7 8 186462E 06 1 000000E 00 2024 8 8 186462E 06 1 000000E 00 2027 9 8 186462E 06 1 000000E 00 2029 10 8 186462E 06 1 000000E 00 During the analysis the status file can be viewed to monitor the progress of the analysis Shown below is the beginning of the solution progress portion of the status file Many more increments have been carried out than you would expect from an Abaqus Standard analysis and that the output database file is being written at intervals of 2 ms STEP 1 ORIGIN 0 0000 Total memory used for step 1 is approximately 1 7 megabytes Global time estimation algorithm will be used Scaling factor 1 0000 Variable mass scaling factor at zero increment 1 0000 STEP TOTAL CPU STABLE CRITICAL
180. AMIC FINITE ELEMENT METHODS which is an expensive procedure for large models The effective stiffness matrix K is a linear combination of the tangent stiffness matrix and the mass matrix for the iteration The iterations continue until several quantities force residual displacement correction etc are within the prescribed tolerances For a smooth nonlinear response Newton s method has a quadratic rate of convergence as illustrated below Iteration Relative Error l l 2 10 3 10 However if the model contains highly discontinuous processes such as contact and frictional sliding quadratic convergence may be lost and a large number of iterations may be required Cutbacks in the time increment size may become necessary to satisfy equilibrium In extreme cases the resulting time increment size in the implicit analysis may be on the same order as a typical stable time increment for an explicit analysis while still carrying the high solution cost of implicit iteration In some cases convergence may not be possible using the implicit method Each iteration in an implicit analysis requires solving a large system of linear equations a procedure that requires considerable computation disk space and memory For large problems these equation solver requirements are dominant over the requirements of the element and material calculations which are similar for an analysis in Abaqus Explicit As the problem size increases the equation solver req
181. AMPLE RESTARTING THE PIPE VIBRATION ANALYSIS 11 5 3 Running the analysis When running a simulation that will need to read data from a restart file you must specify the root name of the restart file without the res extension with the oldjob parameter on the Abaqus command line Thus use the following command to run this restart analysis abaqus job pipe 2 oldjob pipe 11 5 4 Status file Again check the status file as the job is running When the analysis completes the contents of the status file will look like SUMMARY OF JOB INFORMATION STEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC OF DOF IF DISCON ITERS ITERS TIME TIME LPF TIME LPF MONITOR RIKS ITERS FREQ 3 1 1 0 1 1 1 10 0 100 0 1000 3 2 1 0 1 1 1 20 0 200 0 1000 3 3 1 0 1 1 1 35 0 350 0 1500 3 4 1 0 1 1 1 58 0 575 0 2250 3 5 1 0 1 1 1 91 0 913 0 3375 3 6 1 0 1 1 2 00 1 00 0 08750 4 1 1 0 6 0 2 00 1 00e 36 1 000e 36 This analysis starts at Step 3 since Steps 1 and 2 were completed in the previous analysis There are now two output database odb files associated with this simulation Data for Steps 1 and 2 are in the file pipe odb data for Steps 3 and 4 are in the file pipe 2 odb When plotting results in Abaqus Viewer you need to remember which results are stored in each file and you need to ensure that Abaqus Viewer is using the correct output database file 11 5 5 Postprocessing the restart analysis results Start Abaqus Viewer and specify that the output
182. ART 1 1 PUNCH Click mouse button 3 and select Replace from the menu that appears Using the Common Plot Options dialog box turn on the display of the normal vectors On surfaces and set the length of the vector arrows to Short Use the tool if necessary to zoom into any region of interest as shown in Figure 12 25 To contour the contact pressure 1 2 Plot the contours of plastic strain again From the list of variable types on the left side of the Field Output toolbar select Primary if it is not already selected From the list of output variables in the center of the toolbar select CPRESS Remove the PART 1 1 PUNCH surface from your display group To visualize contours of surface based variables better in two dimensional models you can extrude the plane strain elements to construct the equivalent three dimensional view You can sweep axisymmetric elements in a similar fashion From the main menu bar select View ODB Display Options The ODB Display Options dialog box appears Select the Sweep Extrude tab to access the Sweep Extrude options In the Extrude region of the dialog box toggle on Extrude elements and set the Depth to 0 05 to extrude the model for the purpose of displaying contours Click OK to apply these settings Rotate the model using the C tool to display the model from a suitable view such as the one shown in Figure 12 26 12 33 Abaqus Standard 3 D EXAM
183. ATION THICK OR THIN Mid surface a OFFSET 0 b OFFSET 0 5 SNEG c OFFSET 0 5 SPOS Reference surface and Reference surface is Reference surface is midsurface are coincident the bottom surface the top surface Figure 5 4 Schematic of shell offsets for offset values of 0 0 5 and 0 5 The degrees of freedom for the shell are associated with the reference surface All kinematic quantities including the element s area are calculated there Large offset values for curved shells may lead to a surface integration error affecting the stiffness mass and rotary inertia for the shell section For stability purposes Abaqus Explicit also automatically augments the rotary inertia used for shell elements on the order of the offset squared which may result in errors in the dynamics for large offsets When large offsets from the shell s midsurface are necessary use multi point constraints or rigid body constraints instead 5 2 Shell formulation thick or thin Shell problems generally fall into one of two categories thin shell problems and thick shell problems Thick shell problems assume that the effects of transverse shear deformation are important to the solution Thin shell problems on the other hand assume that transverse shear deformation is small enough to be neglected Figure 5 S a illustrates the transverse shear behavior of thin shells material lines that are initially normal to the shell surface remain straight
184. Abaqus Explicit and Abaqus CFD are given at the top of the data dat file SUPPORT The release numbers for the Abaqus Interface for Moldflow and the Abaqus Interface for MSC ADAMS are output to the screen e The type of computer on which you are running Abaqus e The symptoms of any problems including the exact error messages if any e Workarounds or tests that you have already tried For support about a specific problem any available Abaqus output files may be helpful in answering questions that the support engineer may ask you The support engineer will try to diagnose your problem from the model description and a description of the difficulties you are having Frequently the support engineer will need model sketches which can be e mailed faxed or sent in the mail Plots of the final results or the results near the point that the analysis terminated may also be needed to understand what may have caused the problem If the support engineer cannot diagnose your problem from this information you may be asked to supply the input data The data can be attached to a support incident in the online system It can also be sent by means of e mail ftp CD or DVD Please check the Support Overview page at www simulia com for the media formats that are currently accepted All support incidents are tracked This tracking enables you as well as the support engineer to monitor the progress of a particular problem and to check that we are
185. All of the other examples in this guide assume that you will be using a preprocessor such as Abaqus CAE to generate the mesh if you are going to create the model from scratch Input files for all the examples are available See Appendix A Example Files for instructions on how to retrieve these input files However since the purpose of this example is to help you understand the structure and format of the Abaqus input file you should type this input file in directly rather than use a preprocessor or copy the input file that 1s provided If you wish to create the entire model using Abaqus CAE refer to Example creating a model of an overhead hoist Section 2 3 of Getting Started with Abaqus Interactive Edition 1 Units Before starting to define this or any model you need to decide which system of units you will use Abaqus has no built in system of units Do not include unit names or labels when entering data in Abaqus All input data must be specified in consistent units Some common systems of consistent units are shown in Table 2 1 Table 2 1 Consistent units Quantity si Si mm US Unit ft US Unit inch mm ft in Length m Force N lbf lbf Mass tonne 10 kg slug lbf s in Time S S S Stress Pa N m MPa N mm Ibf ft psi lbf in Energy J mJ 10 J ft lbf in lbf Density kg m tonne mm slug ft lbf s in 2 8 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST The SI system of units
186. Another thing to consider when designing a mesh is what type of results you want from the simulation The mesh in Figure 4 15 is rather coarse and therefore unlikely to yield accurate stresses Four quadratic elements per 90 is the minimum number that should be considered for a problem like this one using twice that many is recommended to obtain reasonably accurate stress results However this mesh should be adequate to predict the overall level of deformation in the lug under the applied loads which is what you were asked to determine The influence of increasing the mesh density used in this simulation is discussed in Mesh convergence Section 4 4 You need to decide what system of units to use in your model The SI system of meters seconds and kilograms is recommended but use another system if you prefer 4 3 3 Preprocessing creating the model The model for the overhead hoist in Chapter 2 Abaqus Basics was simple enough that the Abaqus input file could be created by typing the input directly into a text editor This approach clearly is impractical for most real problems instead this example and all subsequent examples in the book point 4 13 5 EXAMPLE CONNECTING LUG you to the completed input file for the example and the steps in the examples illustrate the syntax of model and history data in the Abaqus input file The complete input file for this example lug inp is available in Connecting lug Section A
187. CARGO CRANE UNDER DYNAMIC LOADING To create a time history animation of the transient results 1 From the main menu bar select Result Active Steps Frames to select which frames will be active in the history animation Abaqus Viewer displays the Active Steps Frames dialog box 2 Toggle the step names so that only the second step Step 2 is selected 3 Click OK to accept the selection and to close the dialog box From the main menu bar select Animate Time History or use the Ey tool from the toolbox Abaqus Viewer steps through each available frame of the second step The state block indicates the current step and increment throughout the animation After the last increment of this step is reached the animation process repeats itself You can customize the deformed shape plot while the animation is running a Display the Common Plot Options dialog box b Choose Uniform from the Deformation Scale Factor field c Enter 15 0 as the deformation scale factor value d Click Apply to apply your change Abaqus Viewer now steps through the frames in the second step with a deformation scale factor of 15 0 e Choose Auto compute from the Deformation Scale Factor field f Click OK to apply your change and to close the Common Plot Options dialog box Abaqus Viewer now steps through the frames in the second step with a default deformation scale factor of 0 8 Determining the peak pull out force To find the peak p
188. Cai a oe I p Se a 1 I gt I 7 a Se a I a l 1 r i P N Py ey i s I 3 0 z S E n y ae oa _ Axisymmetric I x _7 E we So SG ate be 7 element CAX4 I j 1 ee Plane strain Plane stress element CPE4 element CPS4 Figure 3 3 Plane strain plane stress and axisymmetric elements without twist FINITE ELEMENTS Plane strain elements assume that the out of plane strain 33 1s zero they can be used to model thick structures Plane stress elements assume that the out of plane stress o33 is zero they are suitable for modeling thin structures Axisymmetric elements without twist the CAX class of elements model a 360 ring they are suitable for analyzing structures with axisymmetric geometry subjected to axisymmetric loading Abaqus Standard also provides generalized plane strain elements axisymmetric elements with twist and axisymmetric elements with asymmetric deformation e Generalized plane strain elements include the additional generalization that the out of plane strain may vary linearly with position in the plane of the model This formulation is particularly suited for the thermal stress analysis of thick sections e Axisymmetric elements with twist model an initially axisymmetric geometry that can twist about the axis of symmetry These elements are useful for modeling the torsion of cylindrical structures such as axisymmetric rub
189. E 07 9 999993E 01 69 8 8 803926E 07 9 999993E 01 77 9 8 803926E 07 9 999993E 01 86 10 8 803926E 07 9 999993E 01 12 70 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST STEP 1 ORIGIN 0 0000 Total memory used for step 1 is approximately 3 7 megabytes Global time estimation algorithm will be used Scaling factor 1 0000 Variable mass scaling factor at zero increment 1 0000 STEP TOTAL CPU STABLE CRITICAL KINETIC INCREMENT TIME TIME TIME INCREMENT ELEMENT ENERGY 0 0 000E 00 0 000E 00 00 00 00 8 394E 07 98 3 430E 01 Results number 0 at increment zero ODB Field Frame Number 0 of 5 requested intervals at increment zero 1188 1 000E 03 1 000E 03 00 00 03 8 394E 07 91 3 123E 01 12 10 8 Postprocessing Start Abaqus Viewer by typing the following abaqus viewer odb circuit at the operating system prompt Checking material directions The material directions obtained from this orientation definition can be checked with Abaqus Viewer To plot the material orientation 1 First change the view to a more convenient setting If it is not visible display the Views toolbar by selecting View Toolbars Views from the main menu bar In the Views toolbar select the X Z setting 2 From the main menu bar select Plot Material Orientations On Deformed Shape The orientations of the material directions for the circuit board at the end of the simulation are shown The material directions are drawn in different colors The material 1
190. ELEMENT option block in your input file It will look similar to ELEMENT TYPE C3D20R ELSET LUG 1 L 401 405 5 10001 10401 10405 10005 201 403 205 3 10201 10403 10205 10003 5001 5401 5405 5005 2 5 405 409 9 10005 10405 10409 10009 205 407 209 7 10205 10407 10209 10007 5005 5405 5409 5009 Here three data lines are used to define the connectivity of one C3D20R element completely a minimum of two is required If a data line in an ELEMENT option block ends with a comma it indicates that the next data line contains more nodes defining the current element The parameter ELSET LUG indicates that all the elements defined in the following data lines will be stored in an element set called LUG If your model does not have a descriptive element set name in the ELEMENT option change it to LUG Node and element sets The node and element sets are important components of an Abaqus input file because they allow you to assign loads boundary conditions and material properties efficiently They also offer great flexibility in defining the output that your simulation will produce and make it much easier to understand the input file 4 16 EXAMPLE CONNECTING LUG Some preprocessors such as Abaqus CAE will allow you to select and name groups of entities such as nodes and elements as you build the model when the Abaqus input file 1s created node and element sets are generated from these groups You de
191. ES for the elements at the constrained end element set BUILTIN EL PRINT ELSET BUILTIN S MISES You will use the NFORC output variable to create and display free body cuts in Postprocessing visualizing the results Section 4 3 8 The following options write the nodal forces due to the element stresses to the output database while also writing the default output OUTPUT FIELD VARIABLE PRESELECT ELEMENT OUTPUT NFORC OUTPUT HISTORY VARIABLE PRESELECT The end of a step is indicated with the option END STEP This input option must be the last option in your model 4 21 5 EXAMPLE CONNECTING LUG 4 3 6 Running the analysis If you modified any input data store the input in a file called lug inp an example file is listed in Connecting lug Section A 2 Then run the simulation using the command abaqus job lug interactive When the job has completed check the data file lug dat for any errors or warnings If there are any errors correct the input file and run the simulation again If you have problems correcting any errors try comparing your input file to the one given in Connecting lug Section A 2 Check that you have the correct parameters for each input option 4 3 7 Results When the job has completed successfully look at the three tables of output that you requested They will be found at the end of the data file A portion of the table of element stresses is shown in Figure 4 21 The
192. In this case the load 1s applied directly to the node set defined earlier Use the node set name from your model or the node number in the CLOAD option in your input file Output requests Write data to the restart file every 10 increments In addition write the preselected field data every 10 increments as well as the stress components and stress invariants for element 25 as history data to the output database file The following option blocks define these output requests ELSET ELSET ELEMENT25 25 RESTART WRITE FREQUENCY 10 OUTPUT FIELD FREQUENCY 10 VARIABLE PRESELECT OUTPUT HISTORY ELEMENT OUTPUT ELSET ELEMENT25 S SINV End the step with the END STEP option Step 2 Extract modes and frequencies The second step extracts the natural frequencies of the extended pipe The required options are discussed below Step and analysis procedure definition In the second step you need to calculate the eigenmodes and eigenfrequencies of the pipe in its loaded state The eigenfrequency extraction procedure FREQUENCY option used in this step is a linear perturbation procedure Although only the first lowest eigenmode is of interest extract the first eight eigenmodes for the model Specify this number on the data line of the FREQUENCY option block The option blocks to define the analysis procedure should look similar to the following STEP PERTURBATION Extract modes and frequencies FREQUENCY 8 Loads
193. It will experience axial loads up to 5 5 kN distributed uniformly across the plates The cross section geometry and dimensions are given in Figure 10 39 You can use axisymmetric elements for this simulation since both the geometry of the structure and the loading are axisymmetric Therefore you only need to model a plane through the component each element represents a complete 360 ring You will examine the static response of the mount therefore you will use Abaqus Standard for your analysis 10 7 1 Symmetry You do not need to model the whole section of this axisymmetric component because the problem is symmetric about a horizontal line through the center of the mount By modeling only half of the section you can use half as many elements and hence approximately half the number of degrees of freedom 10 56 EXAMPLE AXISYMMETRIC MOUNT center line All dimensions in mm Plane to be modeled origin Figure 10 39 Axisymmetric mount This significantly reduces the run time and storage requirements for the analysis or alternatively allows you to use a more refined mesh Many problems contain some degree of symmetry For example mirror symmetry cyclic symmetry axisymmetry or repetitive symmetry shown in Figure 10 40 are common More than one type of symmetry may be present in the structure or component that you want to model When modeling just a portion of a symmetric component you have to add boundary conditio
194. KINETIC INCREMENT TIME TIME TIME INCREMENT ELEMENT ENERGY MONITOR O 0 000E 00 0 000E 00 00 00 00 8 186E 06 1024 0 000E 00 0 000E 00 ODB Field Frame Number 0 of 25 requested intervals at increment zero ODB Field Frame Number 0 of 5 requested intervals at increment zero 244 2 005E 03 2 005E 03 00 00 00 8 182E 06 2035 4 499E 03 4 224E 03 ODB Field Frame Number 1 of 25 requested intervals at 2 005236E 03 488 4 001E 03 4 001E 03 00 00 01 8 181E 06 2018 1 105E 04 2 506E 02 ODB Field Frame Number 2 of 25 requested intervals at 4 001393E 03 733 6 005E 03 6 005E 03 00 00 01 8 138E 06 2030 5 879E 03 4 555E 02 ODB Field Frame Number 3 of 25 requested intervals at 6 004539E 03 978 8 003E 03 8 003E 03 00 00 02 8 133E 06 2030 1 727E 02 4 976E 02 ODB Field Frame Number 4 of 25 requested intervals at 8 002752E 03 1224 1 000E 02 1 000E 02 00 00 02 8 139E 06 2030 2 299E 03 4 461E 02 ODB Field Frame Number 5 of 25 requested intervals at 1 000000E 02 Output for the node referenced on the MONITOR option is also included in this file 10 39 5 EXAMPLE BLAST LOADING ON A STIFFENED PLATE 10 5 7 Postprocessing Run Abaqus Viewer by entering the following command at the operating system prompt abaqus viewer odb blast base Changing the view The default view is isometric which does not provide a particularly clear view of the plate To improve the viewpoint rotate the view using the options in the View menu or the tools in the View Manipulation toolba
195. L NAME STEEL ELASTIC 200 E9 0 3 The value for the NAME parameter on the MATERIAL option must match the value of the MATERIAL parameter on the SOLID SECTION option 4 3 5 Reviewing the input file the history data The history data portion of the input file starts at the first STEP option Many preprocessors create a linear static step in the input file by default This example will use a general static step The following options define the step STEP lt possibly a title describing this step gt STATIC If these options are not in your input file add them at the end of the existing data It is easier for someone else to understand your model if you use the data lines following the STEP option to add a suitable title describing the event being simulated in the step Boundary conditions In the model of the connecting lug all the nodes need to be constrained in all three directions at the left hand end where it is attached to its parent structure see Figure 4 19 In this example each constrained degree of freedom is specified individually in the BOUNDARY option block as shown below BOUNDARY 3241 1 1 3241 2 2 3241 3 3 If a large number of nodes are constrained these data can occupy a great deal of space in the computer s memory Where a number of nodes all have the same boundary conditions it is more 4 18 EXAMPLE CONNECTING LUG Figure 4 19 Boundary conditions on the connecting lug effic
196. L TIME INCREMENT OF 0 100 AND A TOTAL TIME PERIOD OF 1 00 THE MINIMUM TIME INCREMENT ALLOWED IS 1 000E 05 THE MAXIMUM TIME INCREMENT ALLOWED IS 1 00 LINEAR EQUATION SOLVER TYPE DIRECT SPARSE CONVERGENCE TOLERANCE PARAMETERS FOR FORCE CRITERION FOR RESIDUAL FORCE FOR A NONLINEAR PROBLEM 5 000E 03 CRITERION FOR DISP CORRECTION IN A NONLINEAR PROBLEM 1 000E 02 INITIAL VALUE OF TIME AVERAGE FORCE 1 000E 02 AVERAGE FORCE IS TIME AVERAGE FORCE ALTERNATE CRIT FOR RESIDUAL FORCE FOR A NONLINEAR PROBLEM 2 000E 02 CRITERION FOR ZERO FORCE RELATIVE TO TIME AVRG FORCE 1 000E 05 CRITERION FOR RESIDUAL FORCE WHEN THERE IS ZERO FLUX 1 000E 05 CRITERION FOR DISP CORRECTION WHEN THERE IS ZERO FLUX 1 000E 03 CRITERION FOR RESIDUAL FORCE FOR A LINEAR INCREMENT 1 000E 08 FIELD CONVERSION RATIO 1 00 CRITERION FOR ZERO FORCE REL TO TIME AVRG MAX FORCE 1 000E 05 CRITERION FOR ZERO DISP RELATIVE TO CHARACTERISTIC LENGTH 1 000E 08 CONVERGENCE TOLERANCE PARAMETERS FOR MOMENT CRITERION FOR RESIDUAL MOMENT FOR A NONLINEAR PROBLEM 5 000E 03 CRITERION FOR ROTATION CORRECTION IN A NONLINEAR PROBLEM 1 000E 02 INITIAL VALUE OF TIME AVERAGE MOMENT 1 000E 02 AVERAGE MOMENT IS TIME AVERAGE MOMENT ALTERNATE CRIT FOR RESIDUAL MOMENT FOR A NONLINEAR PROBLEM 2 000E 02 CRITERION FOR ZERO MOMENT RELATIVE TO TIME AVRG MOMENT 1 000E 05 8 17 5 EXAMPLE NONLINEAR SKEW PLATE CRITERION FOR RESIDUAL MOMENT WHEN THERE IS ZERO FLUX 1 000E 05 CRITERION FOR ROTATION CORRECTION
197. LAE ETOTAL END STEP Save your input in a file called blast base inp since these results will serve as a base state from which to compare subsequent analyses Run the analysis using the following command abaqus job blast base 10 5 6 Output We now examine the output information contained in the status sta file Status file Information concerning model information such as total mass and center of mass and the initial stable time increment can be found at the top of the status file The 10 most critical elements 1 e those resulting in the smallest time increments in rank order are also shown here If your model contains a few elements that are much smaller than the rest of the elements in the model the small elements will be the most critical elements and will control the stable time increment The stable time increment information in the status file can indicate elements that are adversely affecting the stable time increment allowing you to change the mesh to improve the situation if necessary It is ideal to have a mesh of roughly uniformly sized elements In this example the mesh is uniform thus the 10 most critical elements share the same minimum time increment The beginning of the status file is shown below Total mass in model 838 50 Center of mass of model 1 000000E 00 3 488372E 03 1 000000E 00 Moments of Inertia About Center of Mass About Origin I XX 2 849002E 02 1 123410E 03 I YY 5 519482E 02 2 22
198. LANCE damping matrix equal to Gr times the stiffness matrix Stiffness proportional damping must be used with caution because it may significantly reduce the stability limit To avoid a dramatic drop in the stable time increment the stiffness proportional damping factor Gr should be less than or of the same order of magnitude as the initial stable time increment without damping 9 5 4 Discrete dashpots Yet another option is to define individual dashpot elements Each dashpot element provides a damping force proportional to the relative velocity of its two nodes The advantage of this approach 1s that it enables you to apply damping only at points where you decide it is necessary Dashpots always should be used in parallel with other elements such as springs or trusses so that they do not cause a significant reduction in the stability limit 9 6 Energy balance Energy output is often an important part of an Abaqus Explicit analysis Comparisons between various energy components can be used to help evaluate whether an analysis is yielding an appropriate response 9 6 1 Statement of energy balance An energy balance for the entire model can be written as Er Ey Erp Exe Erge Ew Epw Eow Emw Lar iota constant where 7 is the internal energy Hy is the viscous energy dissipated frp is the frictional energy dissipated Ex is the kinetic energy Erag is the internal heat energy Hw is the work done by the externally
199. LLVD ALLWK ETOTAL The step terminates with the following END STEP 7 5 3 Running the analysis The input file is called dynamics inp an example is listed in Cargo crane dynamic loading Section A 5 Use the following command to run the analysis in the background abaqus job dynamics 7 5 4 Results Examine the status sta file and printed output data dat file to evaluate the analysis results Status file Looking at the contents of the status file dynamics sta we can see that the time increment associated with the single increment in Step 1 is very small A FREQUENCY step uses no time because time is not relevant in a frequency extraction step The contents of the status file are shown below SUMMARY OF JOB INFORMATION STEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC OF DOF IF DISCON ITERS ITERS TIME TIME LPF TIME LPF MONITOR RIKS ITERS FREQ 1 i 0 0 0 0 000 1 00e 036 1 000e 036 2 1 1 0 0 0 0 000 0 00500 0 005000 2 2 1 0 0 0 0 000 0 0100 0 005000 2 3 21 0 0 0 0 000 0 0150 0 005000 7 14 NNN Oo U eA NNNNDNND o N HeH PRPPPPPP oo o oo0oo0oo0oo0oo0oo EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING 0 0 0 000 0 0200 0 005000 0 0 0 000 0 0250 0 005000 0 0 0 000 0 0300 0 005000 0 0 0 000 0 470 0 005000 0 0 0 000 0 475 0 005000 0 0 0 000 0 480 0 005000 0 0 0 000 0 485 0 005000 0 0 0 000 0 490 0 005000 0 0 0 000 0 495 0 005000 0 0 0 000 0 500 0 005000 The output in the status file fo
200. LSET RIVET MATERIAL NAME TITANIUM ELASTIC 112000 0 34 PLASTIC 907 00 O 934 86 0 001 944 28 0 002 961 77 0 005 973 73 0 008 983 28 0 011 12 40 993 1014 1023 1051 1099 1129 1164 1190 1212 89 o N WOOF W N Oo O0Oo0O O0OGOOODOO 015 025 030 050 100 140 200 250 300 Abaqus Standard 3 D EXAMPLE SHEARING OF A LAP JOINT 12 7 4 Contact definitions The contact definitions for the model are discussed here Defining contact Contact will be used to enforce the interactions between the plates and the rivet The friction coefficient between all parts is assumed to be 0 05 This problem could use either contact pairs or the general contact algorithm We will use general contact in this problem to demonstrate the simplicity of the contact definition The contact property is defined using the SURFACE INTERACTION option a friction coefficient of 0 05 is specified SURFACE INTERACTION NAME FRIC FRICTION 0 05 1 Use the CONTACT option to define a general contact interaction Use the ALL EXTERIOR parameter on the CONTACT INCLUSIONS option to specify self contact for the unnamed all inclusive surface defined automatically by Abaqus Standard The CONTACT PROPERTY ASSIGNMENT option is used to assign the contact property named FRIC to the general contact interaction CONTACT CONTACT INCLUSIONS ALL EXTERIOR CONTACT PROPE
201. ME MATERIAL STEEL 1 963E 5 MATERIAL NAME STEEL ELASTIC 200 E9 0 3 k k History data k STEP PERTURBATION 1OKN central load STATIC BOUNDARY 101 ENCASTRE 103 2 History data CLOAD 102 2 10 E3 NODE PRINT U RF EL PRINT S END STEP Figure 2 2 Input for overhead hoist model 2 6 FORMAT OF THE INPUT FILE Keywords and parameters are case independent and must use enough characters to make them unique Parameters are separated by commas If a parameter has a value an equal sign 1s used to associate the value with the parameter Occasionally so many parameters are required that they will not fit on a single 256 character line In this case a comma is placed at the end of the line to indicate that the next line is a continuation line For example the following keyword and parameters are a valid keyword line ELEMENT TYPE T2D2 ELSET FRAME Details of the keywords are documented in the Abaqus Keywords Reference Manual 2 2 2 Data lines Keyword lines are usually followed by data lines which provide data that are more easily specified as lists than as parameters on the keyword line Examples of such data include nodal coordinates element connectivities or tables of material properties such as stress strain curves The data required for particular option blocks are specified in the Abaqus Keywords Reference Manual For example the option block defining the nodes for the ove
202. MPARISON OF IMPLICIT AND EXPLICIT PROCEDURES Quantity Abaqus Standard Abaqus Explicit Solution technique Uses a stiffness based solution technique Uses an explicit integration solution that is unconditionally stable technique that is conditionally stable Disk space and Due to the large numbers of iterations Disk space and memory usage is memory possible in an increment disk space and typically much smaller than that for memory usage can be large Abaqus Standard 2 4 1 Choosing between implicit and explicit analysis For many analyses it is clear whether Abaqus Standard or Abaqus Explicit should be used For example as demonstrated in Chapter 8 Nonlinearity Abaqus Standard is more efficient for solving smooth nonlinear problems on the other hand Abaqus Explicit is the clear choice for a wave propagation analysis There are however certain static or quasi static problems that can be simulated well with either program Typically these are problems that usually would be solved with Abaqus Standard but may have difficulty converging because of contact or material complexities resulting in a large number of iterations Such analyses are expensive in Abaqus Standard because each iteration requires a large set of linear equations to be solved Whereas Abaqus Standard must iterate to determine the solution to a nonlinear problem Abaqus Explicit determines the solution without iterating by explicitly advancing the kinematic state
203. NODE 809 DOF 5 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED ITERATION SUMMARY FOR THE INCREMENT 4 TOTAL ITERATIONS OF WHICH 0 ARE SEVERE DISCONTINUITY ITERATIONS AND 4 ARE EQUILIBRIUM ITERATIONS TIME INCREMENT COMPLETED 0 100 FRACTION OF STEP COMPLETED 0 100 STEP TIME COMPLETED 0 100 TOTAL TIME COMPLETED 0 100 After four iterations g 0 997 N and r 1 581 x 10 N at node 1002 in degree of freedom 1 These values satisfy r lt 0 005 x q so the force residual check is satisfied Comparing c ax to the largest increment of displacement shows that the displacement correction is below the required tolerance The solution for the forces and displacements has therefore converged The checks for both the moment residual and the rotation correction continue to be satisfied as they have been since the second iteration With a solution that satisfies equilibrium for all variables displacement and rotation in this case the first load increment is complete The increment summary shows the number of iterations that were required for this increment the size of the increment and the fraction of the step that has been completed The second increment requires two iterations to converge as shown below INCREMENT 2 STARTS ATTEMPT NUMBER 1 TIME INCREMENT 0 100 CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 1 AVERAGE FORCE 10 2 TIME AVG FORCE 6 33 LARGEST RESIDUAL FORCE 4 11 AT NODE 459 DOF 2 LARGEST INCREMENT OF DISP 5
204. NSET PULL NSET NSET SYMM The first of these sets will be used to prevent rigid body motion in the 3 direction the next two will be used to fix the end of one plate and pull the end of the other respectively the last one will be used to impose symmetry conditions Section and material properties The plates are made from aluminum elastic modulus of 71 7 x 10 MPa v 0 33 Its stress strain behavior is shown in Figure 12 29 12 38 5 Abaqus Standard 3 D EXAMPLE SHEARING OF A LAP JOINT Aluminum Stress 0 00 0 10 0 20 0 30 0 40 0 50 0 60 Strain Figure 12 29 Aluminum stress strain curve The rivet is made from titanium elastic modulus of 112 x 10 MPa v 0 34 Its stress strain behavior is shown in Figure 12 30 The following input options are needed to define the material properties SOLID SECTION MATERIAL ALUMINUM ELSET PLATES MATERIAL NAME ALUMINUM ELASTIC 71700 0 33 PLASTIC 350 00 0 368 71 0 001 376 50 0 002 391 98 0 005 403 15 0 008 412 36 0 011 422 87 0 015 444 17 0 025 461 50 0 035 507 90 0 070 12 39 Abaqus Standard 3 D EXAMPLE SHEARING OF A LAP JOINT x1 E3 1 2 0 8 Stress 0 4 0 0 0 00 0 05 0 10 0 15 0 20 0 25 0 30 Strain Figure 12 30 Titanium stress strain curve 581 50 0 150 649 17 0 250 704 22 0 350 728 78 0 400 751 85 0 450 773 68 0 500 794 44 0 550 814 28 0 600 SOLID SECTION MATERIAL TITANIUM E
205. NUMBER 1 TIME INCREMENT 0 200 CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 1 AVERAGE FORCE 128 TIME AVG FORCE 128 LARGEST RESIDUAL FORCE 6 684E 10 AT NODE 10605 DOF 2 LARGEST INCREMENT OF DISP 1 685E 04 AT NODE 815 DOF 2 LARGEST CORRECTION TO DISP 1 685E 06 AT NODE 815 DOF 2 THE FORCE EQUILIBRIUM RESPONSE WAS LINEAR IN THIS INCREMENT ITERATION SUMMARY FOR THE INCREMENT 1 TOTAL ITERATION OF WHICH 0 ARE SEVERE DISCONTINUITY ITERATIONS AND 1 ARE EQUILIBRIUM ITERATIONS Abaqus requires several iterations to obtain a converged solution in the third increment which indicates that nonlinear behavior occurred in the model during this increment The only nonlinearity in the model is the plastic material behavior so the steel must have started to yield somewhere in the lug at this applied load magnitude The summaries of the iterations for the third increment are shown below INCREMENT 3 STARTS ATTEMPT NUMBER 1 TIME INCREMENT 0 300 CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 1 AVERAGE FORCE 794 TIME AVG FORCE 459 LARGEST RESIDUAL FORCE 831 AT NODE 13057 DOF 1 LARGEST INCREMENT OF DISP 2 573E 04 AT NODE 20815 DOF 2 LARGEST CORRECTION TO DISP 4 658E 06 AT NODE 10817 DOF 2 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 2 AVERAGE FORCE 797 TIME AVG FORCE 460 LARGEST RESIDUAL FORCE 23 5 AT NODE 12843 DOF 1 LARGEST INCREMENT OF DISP 2 690E 04 AT NODE 20815 DOF 2 LARGEST CORRECTION TO
206. Operate on XY data in the Create XY Data dialog box Click Continue 12 89 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST 2 In the Operate on XY Data dialog box filter the maximum principal logarithmic strain LEP Max using a second order Butterworth filter with a cutoff frequency of 500 Hz The expression at the top of the dialog box should appear as butterworthFilter xyData LEP Max cutoffFrequency 500 3 Click Save As to save the calculated maximum principal logarithmic strain as LEP Max FilterAfterCalc bw500 4 Similarly filter the logarithmic strain components LE11 LE12 and LE22 using the same second order Butterworth filter with a cutoff frequency of 500 Hz Save the resulting curves as LE11 bw500 LE12 bw500 and LE22 bw500 respectively 5 Now calculate the maximum principal logarithmic strain using the filtered logarithmic strain components The expression at the top of the Operate on XY Data dialog box should appear as LE11 bw500 LE22 bw500 2 sqrt power LE11 bw500 LE22 bw500 2 2 power LE12 bw500 2 2 6 Click Save As to save the calculated maximum principal logarithmic strain as LEP Max CalcAfterFilter bw500 7 In the XYData container of the Results Tree click mouse button 3 on LEP Max CalcAfterFilter bw500 and select Edit from the menu that appears 8 In the Edit XY Data dialog box choose Strain as the Y value type 9 Plot LEP Max CalcAfterFilter bw500 and LE
207. Output sorted by column Node Label Field Output reported at nodes for part Node Label U U1 Loc 1 PART 1 1 U U2 Loc 1 Minimum At Node Maximum At Node Reaction force output Field Output Report ODB Step Frame frame odb Step 1 Increment Loc 1 0 735 312E 06 1 47062E 03 1 47062E 03 433 681E 21 0 101 1 47062E 03 104 1 Step Time Nodal values from source 1 5 E 33 4 66977E 03 5 E 33 2 54716E 03 2 54716E 03 4 66977E 03 102 5 E 33 103 2 2200E 16 Output sorted by column Node Label Field Output reported at nodes for part Node Label RF RF1 Loc 1 PART 1 1 RF RF2 Loc 1 909 495E 15 0 0 0 2 36 Minimum At Node Maximum At Node Total EXAMPLE 0 909 495E 15 101 0 105 909 495E 15 CREATING A MODEL OF AN OVERHEAD HOIST 0 0 105 5 E 03 103 10 E 03 The information obtained in these tables is the same as that examined earlier when reviewing the printed results in the data dat file The advantage of using Abaqus Viewer to generate the tabular data is that you may create it as a postprocessing operation whereas writing it to the data dat file requires you to include the appropriate option in the input file a preprocessing operation Thus Abaqus Viewer offers greater flexibility to generate tabular output 2 3 10 Rerunning the analysis using Abaqus Explicit We will rerun the same anal
208. P Max FilterAfterCalc bw500 as shown in Figure 12 67 In Figure 12 67 you can see that there is a significant difference between filtering the strain data before and after the principal strain calculation The curve that was filtered after the principal strain calculation is distorted because some of the frequency content introduced by applying the nonlinear principal stress operator is higher than the 500 Hz filter cutoff frequency In general you should avoid directly filtering quantities that have been derived from nonlinear operators whenever possible filter the underlying components and then apply the nonlinear operator to the filtered components to calculate the desired derived quantity Strategy for recording and filtering Abaqus Explicit history output Recording output for every increment in Abaqus Explicit generally produces much more data than you need The real time filtering capability allows you to request history output less frequently without distorting the results due to aliasing However you should ensure that your output rate and filtering choices have not removed physically meaningful frequency content nor distorted the results for example by introducing a large time delay or by removing frequency content introduced by nonlinear operators Keep in mind that no amount of postprocessing filtering can recover frequency content filtered out during the analysis nor can postprocessing filtering recover an original signal
209. PLATE Figure 5 11 Suggested mesh design for the skewed plate simulation Node set rT Node set ENDB SSSA eeen oz 2 Jo wn Q Figure 5 12 Node sets needed for the skew plate simulation Before you start to build the model decide on a system of units The dimensions are given in cm but the loading and material properties are given in MPa and GPa Since these are not consistent units you must choose a consistent system to use in your model and convert the necessary input data 5 14 EXAMPLE SKEW PLATE 5 5 4 Reviewing the input file the model data At this point we assume that you have created the basic mesh using your preprocessor In this section you will review and make corrections to your input file as well as include additional information such as material data Model description The following would be a suitable description in the HEADING option for this simulation HEADING Linear Elastic Skew Plate 20 kPa Load S I Units meters newtons sec kilograms It clearly explains what you are modeling and what units you are using Element connectivity Check to make sure that you are using the correct element type S8R5 It is possible that you specified the wrong element type in the preprocessor or that the translator made a mistake when generating the input file The ELEMENT option block in your model should begin with the
210. PLE SHEARING OF A LAP JOINT 12 6 General contact in Abaqus Standard In the channel forming example in Abaqus Standard 2 D example forming a channel Section 12 5 contact interaction is defined using the contact pairs algorithm which requires you to explicitly define the surfaces that may potentially come into contact As an alternative you can specify contact in an Abaqus Standard analysis by using the general contact algorithm The contact interaction domain contact properties and surface attributes are specified independently for general contact offering a more flexible way to add detail incrementally to a model The simple interface for specifying general contact allows for a highly automated contact definition however it is also possible to define contact with the general contact interface to mimic traditional contact pairs Conversely specifying self contact of a surface spanning multiple bodies with the contact pair user interface if the surface to surface formulation is used mimics the highly automated approach often used for general contact In Abaqus Standard traditional pairwise specifications of contact interactions will often result in more efficient analyses as compared to an all inclusive self contact approach to defining contact Therefore there is often a trade off between ease of defining contact and analysis performance Abaqus CAE provides a contact detection tool that greatly simplifies the process of creating t
211. QUIRED MINIMIZE I O PER ITERATION MBYTES MBYTES 2 65E 002 13 20 THE ESTIMATE PRINTED IS THE MAXIMUM ESTIMATE FROM THE CURRENT STEP TO THE LAST STEP OF THE ANALYSIS WITH THE UNSYMMETRIC MATRIX AND SOLVER TAKEN INTO ACCOUNT IF APPLICABLE SINCE THE ESTIMATE IS BASED ON THE ACTIVE DEGREES OF FREEDOM IN THE FIRST ITERATION OF THE CURRENT STEP FOR PROBLEMS WITH SUBSTANTIAL CHANGES IN ACTIVE DEGREES OF FREEDOM BETWEEN STEPS OR EVEN WITHIN THE SAME STEP THE MEMORY ESTIMATE MIGHT BE NOTICEABLY DIFFERENT THAN THE ACTUAL USAGE A FEW EXAMPLES ARE PROBLEMS WITH SIGNIFICANT CONTACT CHANGES PROBLEMS WITH MODEL CHANGE PROBLEMS WITH BOTH STATIC STEP AND STEADY STATE DYNAMIC PROCEDURES WHERE THE ACOUSTIC ELEMENTS WILL ONLY BE ACTIVATED IN THE STEADY STATE DYNAMIC STEPS THE ESTIMATE FOR THE FLOATING POINT OPERATIONS ON EACH PROCESS IS BASED ON THE INITIAL LOAD SCHEDULING AND THIS MIGHT NOT REFLECT THE ACTUAL FLOATING POINT OPERATIONS COMPLETED ON EACH PROCESS DUE TO THE DYNAMIC LOAD BALANCING SCHEME THE ACTUAL LOAD BALANCE IS EXPECTED TO BE BETTER THAN THE ESTIMATE PRINTED HERE DEPENDING ON THE SETTING OF THE memory PARAMETER THE DISK USAGE BY SCRATCH DATA CAN VARY FROM CLOSE TO ZERO TO THE ESTIMATED MEMORY TO MINIMIZE I O USING RESTART WRITE CAN GENERATE A LARGE AMOUNT OF DATA INCREMENT 1 SUMMARY TIME INCREMENT COMPLETED 2 220E 16 FRACTION OF STEP COMPLETED 1 00 STEP TIME COMPLETED 2 220E 16 TOTAL TIME COMPLETED 0 00 ELEMENT OUTPUT
212. RIAL option block There are two damping factors associated with Rayleigh damping ag for mass proportional damping and Opr for stiffness proportional damping Mass proportional damping The ap factor defines a damping contribution proportional to the mass matrix for an element The damping forces that are introduced are caused by the absolute velocities of nodes in the model The resulting effect can be likened to the model moving through a viscous fluid so that any motion of any point in the model triggers damping forces Reasonable mass proportional damping does not reduce the stability limit significantly Stiffness proportional damping The Gr factor defines damping proportional to the elastic material stiffness A damping stress Od proportional to the total strain rate is introduced using the following formula Ga BRD where is the strain rate For hyperelastic and hyperfoam materials D is defined as the initial elastic stiffness For all other materials D is the material s current elastic stiffness This damping stress is added to the stress caused by the constitutive response at the integration point when the dynamic equilibrium equations are formed but it is not included in the stress output Damping can be introduced for any nonlinear analysis and provides standard Rayleigh damping for linear analyses For a linear analysis stiffness proportional damping is exactly the same as defining a 9 26 ENERGY BA
213. RTY ASSIGNMENT 1 1 FRIC 12 41 5 Abaqus Standard 3 D EXAMPLE SHEARING OF A LAP JOINT 12 7 5 Reviewing the input file the history data Step definition and boundary conditions Create a single static general step and include the effects of geometric nonlinearity Set the initial time increment to 0 05 and the total time to 1 0 Accept the default output requests One end of the assembly 1s fixed while the other 1s pulled along the length of the plates 1 direction In addition a single node is fixed in the vertical 3 direction to prevent rigid body motion and the nodes on the symmetry plane are fixed in the direction normal to the plane 2 direction The boundary conditions are summarized in Table 12 1 Table 12 1 Summary of boundary conditions Geometry Set BCs The complete step definition required for the model appears below STEP NLGEOM YES STATIC 0 05 1 BOUNDARY FIX 1 1 PULL 1 1 2 5 SYMM 2 2 CORNER 3 3 OUTPUT FIELD VARIABLE PRESELECT OUTPUT HISTORY VARIABLE PRESELECT END STEP 1 12 7 6 Running the analysis Save the input in the file lap joint inp see Shearing of a lap joint Section A 14 Run the simulation using the following command abaqus job lap joint 12 42 Abaqus Standard 3 D EXAMPLE SHEARING OF A LAP JOINT Check the status and message files while the job is running to see how it is progressing Status file This analysis should take appr
214. Standard 2 D EXAMPLE FORMING A CHANNEL 12 5 9 Postprocessing In Abaqus Viewer examine the deformation of the blank Deformed model shape and contour plots The basic result of this simulation is the deformation of the blank and the plastic strain caused by the forming process We can plot the deformed model shape and the plastic strain as described below To plot the deformed model shape 1 Plot the deformed model shape You can remove the die and the punch from the display and visualize just the blank 2 In the Results Tree expand the Element sets container underneath the output database file named channel odb 3 From the list of available element sets select PART 1 1 BLANK Click mouse button 3 and select Replace from the menu that appears to replace the current display group with the selected elements Click E3 if necessary to fit the model in the viewport The resulting plot is shown in Figure 12 21 2 H FH HHH Figure 12 21 Deformed shape of blank at the end of Step 2 To plot the contours of equivalent plastic strain 1 From the main menu bar select Plot Contours On Deformed Shape or click the IN tool from the toolbox to display contours of Mises stress 12 29 5 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL 2 Open the Contour Plot Options dialog box 3 Drag the Contour Intervals slider to change the number of contour intervals to 7 4 Click OK to apply these settings 5 Select Primary fro
215. T ATTEMPT THE PLASTICITY CALCULATION AT 16 POINTS NOTE MATERIAL CALCULATIONS FAILED TO CONVERGE OR WERE NOT ATTEMPTED AT ONE OR MORE POINTS CONVERGENCE IS JUDGED UNLIKELY INCREMENT 24 STARTS ATTEMPT NUMBER 2 TIME INCREMENT 1 000E 05 WARNING THE STRAIN INCREMENT HAS EXCEEDED FIFTY TIMES THE STRAIN TO CAUSE FIRST YIELD AT 120 POINTS WARNING THE STRAIN INCREMENT HAS EXCEEDED FIFTY TIMES THE STRAIN TO CAUSE FIRST YIELD AT 132 POINTS CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 1 AVERAGE FORCE 1 751E 03 TIME AVG FORCE 1 352E 03 LARGEST RESIDUAL FORCE 44 9 AT NODE 11841 DOF 2 LARGEST INCREMENT OF DISP 0 153 AT NODE 15817 DOF 2 LARGEST CORRECTION TO DISP 4 662E 02 AT NODE 10817 DOF 2 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE WARNING THE STRAIN INCREMENT HAS EXCEEDED FIFTY TIMES THE STRAIN TO CAUSE FIRST YIELD AT 136 POINTS WARNING THE STRAIN INCREMENT IS SO LARGE THAT THE PROGRAM WILL NOT ATTEMPT THE PLASTICITY CALCULATION AT 4 POINTS NOTE MATERIAL CALCULATIONS FAILED TO CONVERGE OR WERE NOT ATTEMPTED AT ONE OR MORE POINTS CONVERGENCE IS JUDGED UNLIKELY ERROR TIME INCREMENT REQUIRED IS LESS THAN THE MINIMUM SPECIFIED If you look at the summary at the end of the message file you will find that Abaqus issued many warning messages during the analysis Reviewing the message file will show that most of these warnings were the result of numerical problems with the plasticity calculations You know
216. This is the first point at which error and warning messages appear All error messages are prefixed with ERROR while warnings begin with WARNING Since these messages always begin the same way searching the data file for warning and error messages is straightforward When the error is a syntax problem i e when Abaqus cannot understand the input the error message is followed by the line from the input file that is causing the error OPTIONS BEING PROCESSED k k k k k k k k k k k k k k k k k k k k k k k k k k k HEADING Two dimensional overhead hoist frame NODE NSET NALL ELEMENT TYPE T2D2 ELSET FRAME MATERIAL NAME STEEL ELASTIC SOLID SECTION ELSET FRAME MATERIAL STEEL BOUNDARY SOLID SECTION ELSET FRAME MATERIAL STEEL STEP PERTURBATION STEP PERTURBATION STEP PERTURBATION 2 21 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST 10kN central load STATIC BOUNDARY EL PRINT EL FILE END STEP STEP PERTURBATION STATIC BOUNDARY CLOAD NODE PRINT NODE FILE END STEP Model data The rest of the data file is a series of tables containing all of the model data and the history data that should be checked for any obvious errors or omissions These tables are generated by including the option PREPRINT MODEL YES HISTORY YES in the input file However these tables may take up a large amount of disk space for large models By default the parameters MODEL and HISTORY are set to NO
217. To do this we will integrate the acceleration data to calculate the chip velocity and displacement and compare the results to the velocity and displacement data recorded directly by Abaqus Explicit To integrate the bottom chip acceleration history 1 In the Results Tree filter the History Output container according to Node 403 select the acceleration A3 of node 403 and save the data as A3 12 75 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST 2 In the Results Tree double click XYData then select Operate on XY data in the Create XY Data dialog box Click Continue 3 In the Operate on XY Data dialog box integrate acceleration A3 to calculate velocity and subtract the initial velocity magnitude of 4 43 m s The expression at the top of the dialog box should appear as integrate A3 4 43 4 Click Plot Expression to plot the calculated velocity curve 5 In the Results Tree click mouse button 3 on the velocity V3 history output for node 403 and select Add to Plot from the menu that appears The X Y plot appears in the viewport As before customize the plot appearance to obtain a plot similar to Figure 12 59 The velocity curve you produced by integrating the acceleration data may be different from the one pictured here The reason for this will be discussed later V3 calculated from A3 at node 403 V3 N 403 NSET CHIPS Vertical Velocity m s 0 5 10 15 20 x1 E 3 Time s Figure 12 59
218. True Stress True Strain Plastic Stress B Eo N Eo a 200E6 0 00095 00095 200 266 2E6 0 00095 00095 240E6 0 025 246E6 0 0247 a While there are few differences between the nominal and true values at small strains there are very significant differences at larger strain values therefore it is extremely important to provide the proper stress strain data to Abaqus 1f the strains in the simulation will be large 10 7 5 PLASTICITY IN DUCTILE METALS Data regularization in Abaqus Explicit When performing an analysis Abaqus Explicit may not use the material data exactly as defined by the user for efficiency all material data that are defined in tabular form are automatically regularized Material data can be functions of temperature external fields and internal state variables such as plastic strain For each material point calculation the state of the material must be determined by interpolation and for efficiency Abaqus Explicit fits the user defined curves with curves composed of equally spaced points These regularized material curves are the material data used during the analysis It 1s important to understand the differences that might exist between the regularized material curves used in the analysis and the curves that you specified To illustrate the implications of using regularized material data consider the following two cases Figure 10 5 shows a case in which the user has defined data that are not regula
219. UPDATE NO BLANK IMPORT NSET CENTER MIDLEFT Setting the STATE parameter equal to YES causes the state of the model stresses strains etc to be imported Setting the UPDATE parameter equal to NO causes the strains and displacements to be imported as well instead of being reset to zero The data line following the IMPORT option supplies the name of the element set containing the elements that are to be imported The MPORT NSET option identifies node set names to be imported Next create a general static step Set the initial time increment to 0 1 and include the effects of geometric nonlinearity note that the Abaqus Explicit analysis considered them this is the default setting in Abaqus Explicit Springback analyses can suffer from instabilities that adversely affect convergence Thus include automatic stabilization to prevent this problem Use the default value for the dissipated energy fraction You must redefine the boundary conditions which are not imported Impose the same XSYMM type displacement boundary conditions that were imposed in the Abaqus Explicit model on the set Center To remove rigid body motion it is necessary to fix a single point in the blank such as set MidLe ft in the 2 direction in this way you impose no unnecessary constraints Rather than apply a displacement boundary condition to this point apply a zero velocity boundary condition to fix this point at its final position at the end of the forming stag
220. Y EDGE 1 6 Amplitude definition for blast load Since the plate will be subjected to a load that varies with time you must define an appropriate amplitude curve to describe the variation The amplitude curve shown in Figure 10 24 can be defined as follows AMPLITUDE NAME BLAST 0 0 0 0 1 0E 3 7 0E5 10E 3 7 0E5 20E 3 0 0 50E 3 0 0 The pressure increases rapidly from zero at the start of the analysis to its maximum of 7 0 x 10 Pa in 1 ms at which point it remains constant for 9 ms before dropping back to zero in another 10 ms It then remains at zero for the remainder of the analysis 10 5 5 Reviewing the input file the history data The history data begin with the STEP option which is followed immediately by a title for the step After the title this step is defined as a DYNAMIC EXPLICIT procedure with a time period of 50 ms STEP Apply blast loading 10 35 5 EXAMPLE BLAST LOADING ON A STIFFENED PLATE x10 0 8 0 6 0 4 Pressure Pa 0 2 0 0 0 1 2 3 4 5 x10 Time s Figure 10 24 Pressure load as a function of time Explicit analysis with a time duration of 50 ms DYNAMIC EXPLICIT 50E 03 Applying the blast load The DLOAD option is used to apply the blast load to the plate It is important to ensure that the pressure load is being applied in the correct direction Positive pressure is defined as acting in the direction of the positive shell normal For shell elements the
221. You require the natural frequencies of the extended pipe section This does not involve the application of any perturbation loads and the fixed boundary conditions are carried over from the previous general step Therefore you do not need to specify any loads or boundary conditions in this step 11 13 5 EXAMPLE VIBRATION OF A PIPING SYSTEM Output requests Any output requests required in a linear perturbation step must be redefined since the requests from the previous general step do not carry over You want data to be written to the restart and output database files The following option blocks define these requests RESTART WRITE OUTPUT FIELD VARIABLE PRESELECT Again mark the termination of the step definition with the END STEP option 11 3 6 Running the analysis Store the input option blocks in a file called pipe inp Run the analysis in the background using the command abaqus job pipe 11 3 7 Status file Check the status file as the job 1s running When the analysis completes the contents of the status file will look similar to SUMMARY OF JOB INFORMATION STEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC OF DOF IF DISCON ITERS ITERS TIME TIME LPF TIME LPF MONITOR RIKS ITERS FREQ 1 1 1 0 1 1 0 100 0 100 0 1000 1 2 1 0 1 1 0 200 0 200 0 1000 1 3 1 0 1 1 0 350 0 350 0 1500 1 4 1 0 1 1 0 575 0 575 0 2250 1 5 1 0 1 1 0 913 0 913 0 3375 1 6 1 0 1 1 1 00 1 00 0 08750 2 1 1 0 4 Oo 1 00 1 00e 36 1 000e 36 Bo
222. _2kHz order2 x1 E3 1 5 1 0 0 5 0 0 bp y he A 1i 0 5 1 0 Vertical Acceleration m s 0 0 2 0 4 0 6 0 0 x1 E 3 Time s Figure 12 65 Comparison of acceleration filtered with Butterworth and Chebyshev Type I filters Note The Abaqus Viewer postprocessing filters are second order by default To define a higher order filter you can use the filterOrder parameter with the butterworthFilter and the chebyshevi1Filter operators For example use the following expression in the Operate on XY Data dialog box to filter A3 a11 with a sixth order Chebyshev Type I filter using a cutoff frequency of 2 kHz and a ripple factor of 0 017 chebyshevlFilter xyData A3 all cutoffFrequency 2000 rippleFactor 0 017 filterOrder 6 The second order Chebyshev Type I filter with a ripple factor of 0 071 is a relatively weak filter so some of the frequency content above the 2 kHz cutoff frequency 1s not filtered out When the filter order is increased the filter response is improved so that the results are more like the equivalent Butterworth filter For more information on the X Y data filters available in Abaqus Viewer see Operating on saved X Y data objects Section 47 4 of the Abaqus CAE User s Manual Filtering strain history in Abaqus Viewer Strain in the circuit board near the location of the chips is another result that may assist us in determining the effectiveness of the foam packaging Ifthe strain under the
223. a lines the format is lt node gt lt dof1 gt lt A1 gt lt nodez gt lt dof2 gt lt A gt lt NOdEen gt lt do fn lt n gt Exactly four terms must be given on each data line except the final one which can have fewer terms In the crane model the tips of the two trusses are connected together such that degrees of freedom 1 and 2 the translations in the 1 and 2 directions of each tip node are equal while the other degrees of freedom 3 6 at the nodes are independent We need two linear constraints one equating degree of freedom 1 at node 104 to degree of freedom 1 at node 204 Jui t 1 u7 0 and the other equating degree of freedom 2 at node 104 to degree of freedom 2 at node 204 1u 1 u3 0 You may have to change the node numbers if you created this model using a preprocessor The following option block defines the appropriate constraints at point E in the crane model see Figure 6 11 EQUATION 2 104 1 1 0 204 1 1 0 2 104 2 1 0 204 2 1 0 6 22 EXAMPLE CARGO CRANE The degrees of freedom at the first node defined in an MPC or EQUATION are eliminated from the stiffness matrix Therefore these nodes should not appear in other MPCs or constraint equations Nor should boundary conditions be applied to the eliminated degrees of freedom Boundary conditions The crane is attached firmly to the parent structure The following BOUNDARY option block constrains all of the nodes
224. a right handed set see Figure 5 6 1 Global Cartesian coordinate system Figure 5 6 Default local shell material directions The default set of local material directions can sometimes cause problems a case in point is the cylinder shown in Figure 5 7 5 8 SHELL MATERIAL DIRECTIONS Figure 5 7 Default local material 1 direction in a cylinder For most of the elements in the figure the local 1 direction is circumferential However there is a line of elements that are normal to the global 1 axis For these elements the local 1 direction is the projection of the global 3 axis onto the shell making the local 1 direction axial instead of circumferential A contour plot of the direct stress in the local 1 direction 7 looks very strange since for most elements aj 1s the circumferential stress whereas for some elements it is the axial stress In such cases it is necessary to define more appropriate local directions for the model as discussed in the next section 5 3 2 Creating alternative material directions The ORIENTATION option allows you to control the local material directions directly With it you can replace the global Cartesian coordinate system with a local rectangular cylindrical or spherical coordinate system You define the orientation of the local x y z coordinate system by specifying the location of two points a and b as shown in Figure 5 8 For example a local rectangular system is defined wi
225. abaqus fromansys translates an ANSYS input file to an Abaqus input file abaqus fromdyna translates an LS DYNA keyword file to an Abaqus input file abaqus fromnastran translates a Nastran bulk data file to an Abaqus input file abaqus frompamcrash translates a PAM CRASH input file into an Abaqus input file abaqus fromradioss translates a RADIOSS input file into an Abaqus input file abaqus tonastran translates an Abaqus input file to Nastran bulk data file format abaqus toOutput2 translates an Abaqus output database file to the Nastran Output2 file format abaqus tozaero enables the exchange of aeroelastic data between Abaqus and ZAERO The translator utilities are not discussed in this guide 1 2 Getting started with Abaqus This guide is an introductory text designed to give new users guidance in analyzing solid shell beam and truss models with Abaqus Standard and Abaqus Explicit and viewing the results in Abaqus Viewer GETTING STARTED WITH Abaqus or another postprocessor You do not need any previous knowledge of Abaqus to benefit from this guide although some previous exposure to the finite element method is recommended If you are already familiar with the Abaqus solver products Abaqus Standard or Abaqus Explicit but would like an introduction to the Abaqus CAE interface refer to the Getting Started with Abaqus Interactive Edition manual This document covers primarily stress displacement simulations concentrating on both
226. ach of the scaled analyses with the unscaled analysis results Figure 13 18 shows PEEQ for a speedup of v5 mass scaling of 5 Figure 13 19 shows PEEQ for a speedup of v10 mass scaling of 10 and Figure 13 20 shows PEEQ for a speedup of 5 mass scaling of 25 Figure 13 21 compares the internal and kinetic energy histories for each case of mass 13 23 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit scaling The mass scaling case using a factor of 5 yields results that are not significantly affected by the increased loading rate The case with a mass scaling factor of 10 shows a high kinetic to internal energy ratio yet the results seem reasonable when compared to those obtained with slower loading rates Thus this is likely close to the limit on how much this analysis can be sped up The final case with a mass scaling factor of 25 shows evidence of strong dynamic effects the kinetic to internal energy ratio is quite high and a comparison of the final deformed shapes among the three cases demonstrates that the deformed shape is significantly affected in the last case Figure 13 18 Equivalent plastic strain PEEQ for speedup of v5 mass scaling of 5 Discussion of speedup methods As the mass scaling increases the solution time decreases The quality of the results also decreases because dynamic effects become more prominent but there is usually some level of scaling that improves th
227. after any of the requested output If error messages are generated during the datacheck analysis it will not be possible to perform the analysis until the causes of the error messages are corrected The causes of warning messages should always be investigated Sometimes warning messages are indications of mistakes in the input data other times they are harmless and can be ignored safely The final section of the data file not shown in this guide includes a summary of the size of the numerical model and an estimate of the file sizes required for the simulation When analyzing large models use this output to ensure that you have enough disk space available to perform the analysis 2 3 7 Running the analysis Make any necessary corrections to your input file When the datacheck analysis completes with no error messages run the analysis itself by using the command abaqus job frame continue interactive Messages like those below will appear on the screen Abaqus JOB frame Abaqus 6 12 1 Begin Abaqus Standard Analysis 9 23 2010 9 30 19 AM 2 25 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST Run standard exe Abaqus License Manager checked out the following licenses Abaqus Foundation checked out 3 tokens 9 23 2010 9 30 20 AM End Abaqus Standard Analysis Abaqus JOB frame COMPLETED You should always perform a datacheck analysis before running a simulation to ensure that the input data are correct and to check that there is enou
228. al attention to accurate calculation of the initial surface curvature Abaqus automatically calculates the surface normals at the nodes of every shell element to estimate the initial curvature of the shell The surface normal at each node is determined using a fairly elaborate algorithm which is discussed in detail in Defining the initial geometry of conventional shell elements Section 29 6 3 of the Abaqus Analysis User s Manual With a coarse mesh as shown in Figure 5 3 Abaqus may determine several independent surface normals at the same node for adjoining elements Physically multiple normals at a single node mean that there is a fold line between the elements sharing the node While it is possible that you intend to model such a structure it is more likely that you intend to model a smoothly curved shell Abaqus will try to smooth the shell by creating an averaged normal at a node Physical structure Structure modeled by Abaqus Coarse mesh Refined mesh The angle between successive element There is a single normal at each normals is greater than 20 so separate node for adjacent elements and the normals are retained at each node for behavior is that of a curved shell adjacent elements and the behavior is that of a folded sheet Figure 5 3 Effect of mesh refinement on the nodal surface normals The basic smoothing algorithm used is as follows if the normals at a node for each shell element attached to the node
229. al coordinate system for boundary condition application The skew plate example in Chapter 5 Using Shell Elements demonstrates how to use this option in such cases Loading Loading is anything that causes the displacement or deformation of the structure including e concentrated loads e pressure loads e distributed traction loads e distributed edge loads and moment on shells e nonzero boundary conditions e body loads and e temperature with thermal expansion of the material defined In reality there is no such thing as a concentrated or point load the load will always be applied over some finite area However if the area being loaded is similar to or smaller than the elements in that area it is an appropriate idealization to treat the load as a concentrated load applied to a node Concentrated loads are specified using the CLOAD option The data lines for this option have the form lt node number gt lt dof gt lt load magnitude gt In this simulation a load of 10 KN is applied in the 2 direction to node 102 The option block is CLOAD 102 2 10 E3 Output requests Finite element analyses can create very large amounts of output Abaqus allows you to control and manage this output so that only data required to interpret the results of your simulation are produced Four types of output are available e Results stored in a neutral binary file used by Abaqus Viewer for postprocessing This file is ca
230. al name gt lt thickness gt lt number of section points gt Or SHELL GENERAL SECTION ELSET lt element set name gt MATERIAL lt material name gt lt thickness gt If you specify the SHELL SECTION option Abaqus uses numerical integration to calculate the behavior at selected points through the thickness of the shell These points are called section points as shown in Figure 3 6 The MATERIAL parameter refers to a material property definition which may be linear or nonlinear You can specify any odd number of section points through the shell thickness Figure 3 6 Section points through the thickness of a shell element The SHELL GENERAL SECTION option allows you to define the cross section behavior in a number of general ways to model linear or nonlinear behavior Since Abaqus models the shell s cross section behavior directly in terms of section engineering quantities area moments of inertia etc with this option there is no need for Abaqus to integrate any quantities over the element cross section Therefore SHELL GENERAL SECTION is less expensive computationally than SHELL SECTION The response is calculated in terms of force and moment resultants the stresses and strains are calculated only when they are requested for output Reference surface offsets The reference surface of the shell 1s defined by the shell element s nodes and normal definitions When modeling with shell elements the reference surface
231. al overclosure of two contact surfaces All of the nodes on the contact surfaces lie exactly on the same arc of a circle but since the mesh of the inner surface is finer than that of the outer surface and since the element edges are linear some nodes on the finer inner surface initially penetrate the outer surface Assuming that the pure master slave approach is used Figure 12 48 shows the initial strain free displacements applied to the slave surface nodes by Abaqus Explicit In the absence of external loads this geometry is stress free If the default balanced master slave approach is used a different initial set of displacements is obtained and the resulting mesh is not entirely stress free 12 10 Abaqus Explicit example circuit board drop test In this example you will investigate the behavior of a circuit board in protective crushable foam packaging dropped at an angle onto a rigid surface Your goal is to assess whether the foam packaging is adequate to prevent circuit board damage when the board is dropped from a height of 1 meter You will use the general contact capability in Abaqus Explicit to model the interactions between the different components 12 58 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST Figure 12 47 Original overclosure of two contact surfaces Figure 12 48 Corrected contact surfaces Figure 12 49 shows the dimensions of the circuit board and foam packaging in millimeters and the material properties
232. al stress is around 88 2 kPa The easiest way to check the range of the principal strains in the model is to display the maximum and minimum values in the contour legend To check the principal nominal strain magnitude 1 From the main menu bar select Viewport Viewport Annotation Options The Viewport Annotation Options dialog box appears Click the Legend tab and toggle on Show min max values Click OK The maximum and minimum values appear at the bottom of the contour legend in the viewport In the Field Output toolbar select Primary as the variable type if it is not already selected Abaqus Viewer automatically changes the current plot state to display a contour plot of the maximum in plane principal stresses on the deformed model shape From the list of output variables select NE From the list of invariants in the Field Output toolbar select Max Principal if it is not already selected The contour plot changes to display values for maximum principal nominal strain Note the value of the maximum principal nominal strain from the contour legend From the list of invariants select Min Principal The contour plot changes to display values for minimum principal nominal strain Note the value of the minimum principal nominal strain from the contour legend The maximum and minimum principal nominal strain values indicate that the maximum tensile nominal strain in the model 1s about 100 and the max
233. alog box The resulting plot is shown in Figure 10 28 The plot shows that the displacement reaches a maximum of 50 2 mm at 7 7 ms and then oscillates after the blast load is removed The other quantities saved as history output in the output database are the total energies of the model The energy histories can help identify possible shortcomings in the model as well as highlight significant physical effects Display the histories of five different energy output variables ALLAE ALLIE ALLKE ALLPD and ALLSE To generate history plots of the model energies 1 Save the history results for the ALLAE ALLIE ALLKE ALLPD and ALLSE output variables as X Y data A default name is given to each curve rename each according to its output variable name ALLAE ALLKE etc In the Results Tree expand the XYData container The ALLAE ALLIE ALLKE ALLPD and ALLSE X Y data objects are listed underneath Select ALLAE ALLIE ALLKE ALLPD and ALLSE using Ctrl Click click mouse button 3 and select Plot from the menu that appears to plot the energy curves To more clearly distinguish between the different curves in the plot open the Curve Options dialog box and change their line styles e For the curve ALLSE select a dashed line style e For the curve ALLPD select a dotted line style e For the curve ALLAE select a chain dashed line style e For the curve ALLIE select the second thinnest line type To change the posit
234. alues Volumetric compression data only need to be given if the material s compressibility 1s important Normally in Abaqus Standard it is not important and the default fully incompressible behavior is used As noted earlier Abaqus Explicit assumes a small amount of compressibility 1f no volumetric test data are given Obtaining the best material model from your data The quality of the results from a simulation using hyperelastic materials strongly depends on the material test data that you provide Abaqus Typical tests are shown in Figure 10 38 There are several things that you can do to help Abaqus calculate the best possible material parameters Wherever possible try to obtain experimental test data from more than one deformation state this allows Abaqus to form a more accurate and stable material model However some of the tests shown in Figure 10 38 produce equivalent deformation modes for incompressible materials The following are equivalent tests for incompressible materials e Uniaxial tension lt gt Equibiaxial compression e Uniaxial compression lt gt Equibiaxial tension e Planar tension gt Planar compression You do not need to include data from a particular test if you already have data from another test that models a particular deformation mode In addition the following may improve your hyperelastic material model e Obtain test data for the deformation modes that are likely to occur in your simulation For exam
235. alyses Figure 13 15 shows contour plots of the equivalent plastic strain in the blank and Figure 13 16 shows an overlay plot of the final deformed shape predicted by the two analyses The equivalent plastic strain results for the Abaqus Standard and Abaqus Explicit analyses are within 5 of each other In addition the final deformed shape comparison shows that the explicit quasi static analysis results are in excellent agreement with the results from the Abaqus Standard static analysis You should also compare the steady punch force predicted by the Abaqus Standard and Abaqus Explicit analyses 13 18 PEEQ Avg 75 2 507e 01 2 298e 01 2 089e 01 1 880e 01 1 671e 01 1 462e 01 1 254e 01 1 045e 01 8 357e 02 6 268e 02 4 178e 02 2 089e 02 0 000e 00 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit PEEQ Avg 75 2 310e 01 2 118e 01 1 925e 01 1 733e 01 1 540e 01 1 348e 01 1 155e 01 9 627e 02 7 701e 02 5 776e 02 3 851e 02 1 925e 02 0 000e 00 Figure 13 15 Contour plot of PEEQ in Abaqus Standard left and Abaqus Explicit right channel forming analyses Abaqus Explicit Abaqus Standard Figure 13 16 Final deformed shape in Abaqus Standard and Abaqus Explicit forming analyses 13 19 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit To compare the punch force displacement histories 1 Save the punch displacement U2 and reaction force RF2 history
236. ample shows how Abaqus automatically controls the increment size and therefore the proportion of load applied in each increment In this analysis Abaqus applied 10 of the total load in the first increment you specified AT nitial to be 0 1 and the step time to be 1 0 Abaqus needed four iterations to converge to a solution in the first increment Abaqus only needed two iterations in the second increment so it automatically increased the size of the next increment by 50 to AT 0 15 Abaqus also increased AT in both the fourth and fifth increments It adjusted the final increment size to be just enough to complete the analysis in this case the final increment size was 0 0875 Message file The message file contains more detailed information about the progress of the analysis than the status file Abaqus lists all of the tolerances and parameters to control the analysis at the start of each step in the message file as shown below This is done for each step because these controls can be modified from step to step The default values of these controls are appropriate for most analyses so normally it is not necessary for you to modify them The modification of control tolerances and parameters is beyond the scope of this guide it is discussed in Commonly used control parameters Section 7 2 2 of the Abaqus Analysis User s Manual STEP 1 STATIC ANALYSIS Uniform pressure 20 0 kPa load AUTOMATIC TIME CONTROL WITH A SUGGESTED INITIA
237. an interactive datacheck analysis of the input data in the frame xp1 input file abaqus job frame xpl datacheck interactive Make any necessary corrections to your input file When the datacheck analysis completes with no error messages run the analysis itself by using the command abaqus job frame xpl continue interactive 2 38 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST 2 3 11 Postprocessing the dynamic analysis results For the static linear perturbation analysis done in Abaqus Standard you examined the deformed shape as well as stress displacement and reaction force output For the Abaqus Explicit analysis you can similarly examine the deformed shape and generate field data reports Because this is a dynamic analysis you should also examine the transient response resulting from the loading You will do this by animating the time history of the deformed model shape and plotting the displacement history of the bottom center node in the truss Start by opening the frame xp1 output database using the instructions in Postprocessing Section 2 3 9 then plot the deformed shape of the model For large displacement analyses the default formulation in Abaqus Explicit the displaced shape scale factor has a default value of 1 Change the Deformation Scale Factor to 20 so that you can more easily see the deformation of the truss To create a time history animation of the deformed model shape 1 From the main menu bar select Animat
238. and springback analyses efficiently 5 GETTING STARTED WITH Abaqus 1 2 2 Conventions used in this guide This manual adheres to the following conventions Typographical conventions Different text styles are used in the tutorial examples to indicate specific actions or identify items e Input in COURIER FONT should be typed into Abaqus Viewer or your computer exactly as shown For example abaqus viewer would be typed on your computer to run Abaqus Viewer e Menu selections tabs within dialog boxes and labels of items on the screen in Abaqus Viewer are indicated in bold View Graphics Options Contour Plot Options View orientation triad By default Abaqus Viewer uses the alphabetical option z y z for labeling the view orientation triad In general this manual adopts the numerical option 1 2 3 to permit direct correspondence with degree of freedom and output labeling 1 2 3 Basic mouse actions Figure 1 2 shows the mouse button orientation for a left handed and a right handed 3 button mouse BIE iY left handed right handed mouse mouse Figure 1 2 Mouse buttons The following terms describe actions you perform using the mouse 1 3 Abaqus DOCUMENTATION Click Press and quickly release the mouse button Unless otherwise specified the instruction click means that you should click mouse button 1 Drag Press and hold down mouse button 1 while moving the mouse Point Move the
239. anual 4 52 SUGGESTED READING 4 6 Suggested reading The volume of literature that has been written on the finite element method and the applications of finite element analysis is enormous In most of the remaining chapters of this guide a list of suggested books and articles is provided so that you can explore the topics in more depth if you wish While the advanced references will not be of interest to most users they provide detailed theoretical information for the interested user General texts on the finite element method e NAFEMS Ltd A Finite Element Primer 1986 e Becker E B G F Carey and J T Oden Finite Elements An Introduction Prentice Hall 1981 e Carey G F and J T Oden Finite Elements A Second Course Prentice Hall 1983 e Cook R D D S Malkus and M E Plesha Concepts and Applications of Finite Element Analysis John Wiley amp Sons 1989 e Hughes T J R The Finite Element Method Prentice Hall Inc 1987 e Zienkiewicz O C and R L Taylor The Finite Element Method Volumes 1 II and TII Butterworth Heinemann 2000 Performance of linear solid elements e Prathap G The Poor Bending Response of the Four Node Plane Stress Quadrilaterals International Journal for Numerical Methods in Engineering vol 21 825 835 1985 Hourglass control in solid elements e Belytschko T W K Liu and J M Kennedy Hourglass Control in Linear and Nonlinear Problems
240. applications Similar concepts apply for fluid dynamics Discretized geometry Finite elements and nodes define the basic geometry of the physical structure being modeled in Abaqus Each element in the model represents a discrete portion of the physical structure which is in turn represented by many interconnected elements Elements are connected to one another by shared nodes The coordinates of the nodes and the connectivity of the elements that 1s which nodes belong to which elements comprise the model geometry The collection of all the elements and nodes in a model is called the mesh Generally the mesh will be only an approximation of the actual geometry of the structure The element type shape and location as well as the overall number of elements used in the mesh affect the results obtained from a simulation The greater the mesh density 1 e the greater the number of elements in the mesh the more accurate the results As the mesh density increases the analysis results converge to a unique solution and the computer time required for the analysis increases The solution obtained from the numerical model is generally an approximation to the solution of the physical problem being simulated The extent of the approximations made in the model s geometry material behavior boundary conditions and loading determines how well the numerical simulation matches the physical problem Element section properties Abaqus has a wi
241. approximately one fifth the wave speed of steel The stable time increment for the lead bar would be five times the stable time increment of our steel bar 9 5 Damping of dynamic oscillations There are two reasons for adding damping to a model to limit numerical oscillations or to add physical damping to the system Abaqus Explicit provides several methods of introducing damping into the analysis 9 5 1 Bulk viscosity Bulk viscosity introduces damping associated with volumetric straining Its purpose is to improve the modeling of high speed dynamic events Abaqus Explicit contains linear and quadratic forms of bulk viscosity You can set bulk viscosity to nondefault values from step to step by using the BULK VISCOSITY option although it is rarely necessary to do so The bulk viscosity pressure is not included in the material point stresses because it is intended as a numerical effect only As such it is not considered part of the material s constitutive response Linear bulk viscosity By default linear bulk viscosity is always included to damp ringing in the highest element frequency It generates a bulk viscosity pressure that is linear in the volumetric strain rate according to the following equation pi bipcaL evo where b is a damping coefficient whose default value is 0 06 p is the current material density Ca 1s the current dilatational wave speed L is the element characteristic length and og 1s the volume
242. aqus Explicit is 0 475 Some analyses may require increasing Poisson s ratio to model incompressibility more accurately e Polynomial Ogden Arruda Boyce Marlow van der Waals Mooney Rivlin neo Hookean reduced polynomial and Yeoh strain energy functions are available for rubber elasticity hyperelasticity 10 81 SUMMARY All models allow the material coefficients to be determined directly from experimental test data The test data must be specified as nominal stress and nominal strain values e Stability warnings may indicate that a hyperelastic material model is unsuitable for the strain ranges you wish to analyze e The presence of symmetry can be used to reduce the size of a simulation since only part of the component needs to be modeled The effect of the rest of the component is represented by applying appropriate boundary conditions e Mesh design for large distortion problems is more difficult than for small displacement problems The elements in the mesh must not become too distorted at any stage of the analysis e Volumetric locking can be alleviated by permitting a small amount of compressibility Care must be taken to ensure that the amount of compressibility introduced into the problem does not grossly affect the overall results e The X Y plotting capabilities in Abaqus Viewer allow data in curves to be manipulated to create new curves Two curves or a curve and a constant can be added subtracted multiplied or divi
243. aqus Standard 2 D EXAMPLE FORMING A CHANNEL The parameter TYPE SEGMENTS specifies that a two dimensional rigid surface is being defined The NAME parameter specifies the name of the surface PUNCH The data lines define the geometry of the surface The first data line always has the word START followed by the 1 and 2 coordinates of the starting point for the surface The subsequent lines define line circular and parabolic segments For this surface the second data line defines a straight line from the start position 0 05 0 060 to 0 050 0 006 The third data line defines a circular arc from the end of the straight line 0 05 0 006 to 0 045 0 001 with the center of the circle located at 0 045 0 006 The last data line defines a straight line from the end of the arc to 0 010 0 001 This definition should produce a smooth rigid surface but to be safe the FILLET RADIUS parameter specifies that a 1 mm fillet radius should be used to smooth any discontinuities in the surface definition Itis always good practice to add the FILLET RADIUS parameter to the definition of any analytical rigid surface The RIGID BODY option is used to bind the analytical surface to a rigid body with its rigid body reference node specified by the REF NODE parameter and the surface referred to by its name using the ANALYTICAL SURFACE parameter The rigid surfaces for the blank holder and the die are defined in a similar way The following option blocks d
244. are its yield stress 380 MPa and its strain at failure 0 15 You decide to assume that the steel 1s perfectly plastic the material does not harden and the stress can never exceed 380 MPa see Figure 10 8 True stress 380 E6 E 200 E9 l el True strain Figure 10 8 Stress strain behavior for the steel In reality some hardening will probably occur but this assumption is conservative if the material hardens the plastic strains will be less than those predicted by the simulation The steps that follow assume that you have access to the full input file for this example This input file Lug_plas inp is provided in Connecting lug with plasticity Section A 8 in the online HTML 10 11 5 EXAMPLE CONNECTING LUG WITH PLASTICITY version of this manual Instructions on how to fetch and run the script are given in Appendix A Example Files If you wish to create the entire model using Abaqus CAE please refer to Example connecting lug with plasticity Section 10 4 of Getting Started with Abaqus Interactive Edition 10 4 1 Modifications to the input file the model data In this example the material definition specifies the post yield behavior of the material using the PLASTIC option The Young s modulus for the material 1s 200 GPa and the initial yield stress at zero plastic strain is 380 MPa Since you are modeling the steel as perfectly plastic no other yield stresses are given on the PLASTIC
245. are not necessary for the frequency analysis 3 Delete all steps except for the first one Change the procedure type to FREQUENCY and change its step description to Frequency modes Request five eigenvalues using the default Lanczos eigensolver 4 Delete all boundary conditions except the boundary condition applied to the set CENTER This leaves the blank constrained with a symmetry boundary condition applied to the left end The revised history data appears below STEP PERTURBATION Frequency modes FREQUENCY 5 BOUNDARY CENTER XSYMM END STEP 13 9 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit Note Since the frequency extraction step is a linear perturbation procedure nonlinear material properties will be ignored In this analysis the left end of the blank is constrained in the x direction and cannot rotate about the normal however it is not constrained in the y direction Therefore the first mode extracted will be a rigid body mode The frequency of the second mode will determine the appropriate time period for the quasi static analysis in Abaqus Explicit 5 Save the channel freq inp input file submit the job for analysis and monitor the solution progress 6 When the analysis is complete enter Abaqus Viewer and open the output database file created by this analysis From the main menu bar select Plot Deformed Shape or use the i tool in the toolbox The deformed model shape for the first vibratio
246. are within 20 of each other the normals will be averaged The averaged normal will be used at that node for all elements attached to the node If Abaqus cannot smooth the shell a warning message is issued in the data dat file You may override the default algorithm To introduce fold lines into a curved shell or to model a curved shell with a coarse mesh use the NODE and NORMAL options to define the normals manually With the NODE option you specify the surface normal at a node as the 4th 5th and 6th values on the data line following the nodal coordinates A normal you define with NODE is the normal used for ELEMENT GEOMETRY all elements sharing that node unless NORMAL is also used Use the NORMAL option to specify a normal at a node for selected elements only Normals defined with NORMAL override normals defined with NODE See Defining the initial geometry of conventional shell elements Section 29 6 3 of the Abaqus Analysis User s Manual for further details 5 1 4 Reference surface offsets The reference surface of the shell 1s defined by the shell element s nodes and normal definitions When modeling with shell elements the reference surface 1s typically coincident with the shell s midsurface However many situations arise in which it is more convenient to define the reference surface as offset from the shell s midsurface For example surfaces created in CAD packages usually represent either the top or bott
247. ariables S11 S22 S33 S12 S23 and S13 You will see that there are significant variations in these stresses across the elements at the built in end This causes the extrapolated nodal stresses to be higher than the values at the integration points The Mises stress calculated from these values will therefore also be higher Note Element type C3D10I does not suffer from this extrapolation problem The integration points of this element type are located at the nodes resulting in improved surface stress visualization The Mises stress at an integration point can never exceed the current yield stress of the element s material however the extrapolated nodal values reported in a contour plot may do so In addition the individual stress components may have magnitudes that exceed the value of the current yield stress only the Mises stress is required to have a magnitude less than or equal to the value of the current yield stress You can use the query tools in the Visualization module to check the Mises stress at the integration points To query the Mises stress 1 From the main menu bar select Tools Query or use the Q tool in the Query toolbar The Query dialog box appears 2 In the Visualization Module Queries field select Probe values The Probe Values dialog box appears 3 Make sure that Elements and the output position Integration Pt are selected 4 Use the cursor to select elements near the constrained end of the lug
248. as used to define one of the elements in lug inp 4 40 EXAMPLE CONNECTING LUG ELEMENT TYPE C3D20R 1 1 401 405 5 10001 10401 10405 10005 201 403 205 3 10201 10403 10205 10003 5001 5401 5405 5005 In lug xpl1 inp this option block has two changes the element type has been changed to C3D8R and the nodal connectivity consists of the first eight nodes in the original list which define the corner nodes of the element ELEMENT TYPE C3D8R 1 L 401 405 5 10001 10401 10405 10005 Because the C3D8R element employs reduced integration use the enhanced strain algorithm to control hourglassing You can specify enhanced hourglassing with the SECTION CONTROLS option SOLID SECTION ELSET LUG MATERIAL STEEL CONTROLS EC 1 SECTION CONTROLS NAME EC 1 HOURGLASS ENHANCED Edit the material definition Since Abaqus Explicit performs a dynamic analysis a complete material definition requires that you specify the material density For this problem assume the density is equal to 7800 kg m You can modify the material definition by adding the DENSITY option to the material option block The complete material definition for the connecting lug is MATERIAL NAME STEEL ELASTIC 200 E9 0 3 DENSITY 7800 Replace the static step with a dynamic explicit step Revise the step definition to examine the dynamic response of the lug over a period of 0 005 s This change requires that you change the STEP
249. as for the static analysis with the modifications described below These modifications are most easily made using an editor although you may change the model in a preprocessor if you prefer 5 EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING Material In dynamic simulations the density of every material must be specified so that the mass matrix can be formed The steel in the crane has a density of 7800 kg m The beam element properties were defined using the BEAM GENERAL SECTION option so there are no material property definitions in this input file The density must be specified using the DENSITY parameter on the BEAM GENERAL SECTION option For example BEAM GENERAL SECTION SECTION BOX ELSET OUTA DENSITY 7800 0 10 0 05 0 005 0 005 0 005 0 005 0 1118 0 0 0 9936 200 E9 80 E9 The DENSITY parameter has been added to all the element property options If material data are defined using the MATERIAL option the density 1s included by using the DENSITY option and giving the mass density on the data line For example MATERIAL NAME STEEL ELASTIC lt Young s modulus gt lt Poisson s ratio gt DENSITY lt density gt Initial conditions In this example the structure has no initial velocities or accelerations which 1s the default However if you wanted to define initial velocities you could do so using the following option INITIAL CONDITIONS TYPE VELOCITY The nodes or node sets the direction and the magni
250. at the attachment points which should have been grouped into node set ATTACH BOUNDARY ATTACH ENCASTRE 6 4 5 Reviewing the input file the history data The following options specify a static linear perturbation simulation STEP PERTURBATION Static tip load on crane STATIC Loading A concentrated load of 10 KN is applied in the negative y direction to node 104 Since there is a constraint equation connecting the y displacement of nodes 104 and 204 the load is carried equally by both nodes The following CLOAD option block provides an equal load on both nodes CLOAD 104 2 1 0E4 Output requests Write the displacements U and reaction forces and moments RF at the nodes and the section forces and moments SF in the elements to the output database for postprocessing with Abaqus Viewer as shown in the following option blocks OUTPUT FIELD NODE OUTPUT U RF ELEMENT OUTPUT SF END STEP 6 23 5 EXAMPLE CARGO CRANE 6 4 6 Running the analysis Store the input in a file called crane inp Run the analysis using the command abaqus job crane 6 4 7 Postprocessing Start Abaqus Viewer by typing the following command at the operating system prompt abaqus viewer odb crane Abaqus Viewer plots the undeformed shape of the crane model Plotting the deformed model shape To begin this exercise plot the deformed model shape with the undeformed model shape superimposed on it Specify a nondefault view
251. ata to convert this model from a linear simulation to a nonlinear simulation If you wish you can follow the guidelines at the end of this example to extend the simulation to perform a dynamic analysis using Abaqus Explicit The steps that follow assumes that you have access to the full input file for this example This input file skew nl inp is available in Nonlinear skew plate Section A 6 in the online HTML version of this manual Instructions on how to fetch and run the script are given in Appendix A Example Files If you wish to create the entire model using Abaqus CAE please refer to Example nonlinear skew plate Section 8 4 of Getting Started with Abaqus Interactive Edition 8 13 5 EXAMPLE NONLINEAR SKEW PLATE End built in zero 2 rotation 1 Figure 8 11 Skew plate 8 4 1 Modifications to the input file the history data This example does not change any model data in the original skew plate example only history data changes are included Applying NLGEOM to the step Set the NUGEOM parameter equal to YES on the STEP option and remove the PERTURBATION parameter This indicates that the analysis now includes nonlinear geometric effects The default maximum number of increments is 100 Abaqus may use fewer increments than this upper limit but it will stop the analysis if it needs more The modified STEP option looks like STEP NLGEOM YES You may also wish to modify the description of the ste
252. aterial behavior is called hyperelasticity The deformation of hyperelastic materials such as rubber remains elastic up to large strain values often well over 100 Abaqus makes the following assumptions when modeling a hyperelastic material e The material behavior is elastic e The material behavior is isotropic e The simulation will include nonlinear geometric effects NLGEOM YES will be used In addition Abaqus Standard assumes the hyperelastic material is incompressible by default Abaqus Explicit assumes the material is nearly incompressible Poisson s ratio is 0 475 by default Elastomeric foams are another class of highly nonlinear elastic materials They differ from rubber materials in that they have very compressible behavior when subjected to compressive loads They are modeled with a separate material model in Abaqus and are not discussed in detail in this guide 10 6 2 Compressibility Most solid rubber materials have very little compressibility compared to their shear flexibility This behavior is not a problem with plane stress shell or membrane elements However it can be a problem when using other elements such as plane strain axisymmetric and three dimensional solid elements For example in applications where the material is not highly confined it would be quite satisfactory to assume that the material is fully incompressible the volume of the material cannot change except for 10 51 HYPERELASTICITY thermal ex
253. ational and rotational degrees of freedom and must be defined for every rigid body The position of the rigid body reference node is not important unless rotations are applied to the body or reaction moments about a certain axis through the body are desired 3 16 RIGID BODIES In either of these situations the node should be placed such that it lies on the desired axis through the body RIGID BODY REF NODE lt node gt ELSET lt element set name gt PIN NSET lt node setname gt TIE NSET lt node set name gt In addition to the rigid body reference node discrete rigid bodies consist of a collection of nodes that are generated by assigning elements and nodes to the rigid body These nodes known as the rigid body slave nodes see Figure 3 7 provide a connection to other elements Nodes that are part of a rigid body are one of two types e Pin nodes which have only translational degrees of freedom e Tie nodes which have both translational and rotational degrees of freedom The rigid body node type is determined by the type of elements on the rigid body to which the node is attached The node type also can be specified or modified when assigning nodes directly to a rigid body For pin nodes only the translational degrees of freedom are part of the rigid body and the motion of these degrees of freedom is constrained by the motion of the rigid body reference node For tie nodes both the translational and rotational degrees of f
254. available from the Support page at www simulia com When contacting your local support office please specify whether you would like technical support you have encountered problems performing an Abaqus analysis or systems support Abaqus will not install correctly licensing does not work correctly or other hardware related issues have arisen We welcome any suggestions for improvements to Abaqus software the support program or documentation We will ensure that any enhancement requests you make are considered for future releases If you wish to make a suggestion about the service or products provided by SIMULIA refer to www simulia com Complaints should be addressed by contacting your local office or through www simulia com by visiting the Quality Assurance section of the Support page 1 5 1 Technical support SIMULIA technical support engineers can assist in clarifying Abaqus features and checking errors by giving both general information on using Abaqus and information on its application to specific analyses If you have concerns about an analysis we suggest that you contact us at an early stage since it 1s usually easier to solve problems at the beginning of a project rather than trying to correct an analysis at the end Please have the following information ready before calling the technical support hotline and include it in any written contacts e The release of Abaqus that are you using The release numbers for Abaqus Standard
255. ay Groups in the Results Tree or use the 35 tool in the Display Group toolbar The Create Display Group dialog box appears In the Create Display Group dialog box click Save As and enter MainA as the name for your display group Click Dismiss to close the Create Display Group dialog box This display group now appears underneath the Display Groups container in the Results Tree Beam cross section orientation You will now plot the section axes and beam tangents on the undeformed model shape To plot the beam section axes 1 From the main menu bar select Plot Undeformed Shape or use the tool in the toolbox to display only the undeformed model shape From the main menu bar select Options Common then click the Normals tab in the dialog box that appears 3 Toggle on Show normals and accept the default setting of On elements 4 In the Style area at the bottom of the Normals page specify the Length to be Long 5 Click OK The section axes and beam tangents are displayed on the undeformed shape The resulting plot is shown in Figure 6 19 The text annotations in Figure 6 19 that identify the section axes and beam tangent will not appear in your image The vector showing the local beam l axis n4 is blue the vector showing the beam 2 axis ng is red and the vector showing the beam tangent t 1s white 6 25 5 EXAMPLE CARGO CRANE pe a Beam 1 axis 7 gt aq gt 2 D N Y
256. baqus Standard It is useful for modeling very stiff links whose stiffness is much greater than that of the overall structure Element output variables Axial stress and strain are available as output for truss elements 3 2 Rigid bodies In Abaqus a rigid body is a collection of nodes and elements whose motion is governed by the motion of a single node known as the rigid body reference node as shown in Figure 3 7 Rigid body slave nodes Rigid body reference node Figure 3 7 Elements forming a rigid body The shape of the rigid body is defined either as an analytical surface obtained by revolving or extruding a two dimensional geometric profile or as a discrete rigid body obtained by meshing the body with nodes and elements The shape of the rigid body does not change during a simulation but can undergo large rigid body motions The mass and inertia of a discrete rigid body can be calculated based on the contributions from its elements or they can be assigned directly The motion of a rigid body can be prescribed by applying boundary conditions at the rigid body reference node Loads on a rigid body are generated from concentrated loads applied to nodes and 3 15 RIGID BODIES distributed loads applied to elements that are part of the rigid body or from loads applied to the rigid body reference node Rigid bodies interact with the rest of the model through nodal connections to deformable elements and through contact with deforma
257. ber bushings e Axisymmetric elements with asymmetric deformation model an initially axisymmetric geometry that can deform asymmetrically typically as a result of bending They are useful for simulating problems such as an axisymmetric rubber mount that is subjected to shear loads The latter three classes of two dimensional continuum elements are not discussed in this guide Two dimensional solid elements must be defined in the 1 2 plane so that the node order is counterclockwise around the element perimeter as shown in Figure 3 4 4 3 T 2 1 2 1 2 gt 1 Quadrilateral element Triangular element Figure 3 4 Correct nodal connectivity for two dimensional elements When using a preprocessor to generate the mesh ensure that the element normals all point in the same direction as the positive global 3 axis Failure to provide the correct element connectivity will cause Abaqus to issue an error message stating that elements have negative area Degrees of freedom All of the stress displacement continuum elements have translational degrees of freedom at each node Correspondingly degrees of freedom 1 2 and 3 are active in three dimensional elements while only degrees of freedom 1 and 2 are active in plane strain elements plane stress elements and axisymmetric elements without twist To find the active degrees of freedom in the other classes FINITE ELEMENTS of two dimensional solid elements see Two dimensional solid eleme
258. ble elements The use of rigid bodies is illustrated in Chapter 12 Contact 3 2 1 Determining when to use a rigid body Rigid bodies can be used to model very stiff components that are either fixed or undergoing large rigid body motions They can also be used to model constraints between deformable components and they provide a convenient method of specifying certain contact interactions When Abaqus is used for quasi static forming analyses rigid bodies are ideally suited for modeling tooling such as a punch die drawbead blank holder roller etc and may also be effective as a method of constraint It may be useful to make parts of a model rigid for verification purposes For example in complex models elements far away from the particular region of interest could be included as part of a rigid body resulting in faster run times at the model development stage When you are satisfied with the model you can remove the rigid body definitions and incorporate an accurate deformable finite element representation throughout The principal advantage to representing portions of a model with rigid bodies rather than deformable finite elements is computational efficiency Element level calculations are not performed for elements that are part of a rigid body Although some computational effort is required to update the motion of the nodes of the rigid body and to assemble concentrated and distributed loads the motion of the rigid body is determi
259. blems in Abaqus Standard that involve rigid surfaces These issues are discussed in detail in Common difficulties associated with contact modeling in Abaqus Standard Section 38 1 2 of the Abaqus Analysis User s Manual but some of the more important issues are described here e The rigid surface is always the master surface in a contact interaction e The rigid surface should be large enough to ensure that slave nodes do not slide off and fall behind the surface If this happens the solution usually will fail to converge Extending the rigid surface or including corners along the perimeter see Figure 12 11 will prevent slave nodes from falling behind the master surface 12 14 MODELING ISSUES FOR RIGID SURFACES IN Abaqus Standard A node falling behind a rigid surface Extending the rigid surface prevents a can cause convergence problems node from falling behind the surface Figure 12 11 Extending rigid surfaces to prevent convergence problems e The deformable mesh must be refined enough to interact with any feature on the rigid surface There is no point in having a 10 mm wide feature on the rigid surface if the deformable elements that will contact it are 20 mm across the rigid feature will just penetrate into the deformable surface as shown in Figure 12 12 TET Ensure that the mesh density on the slave surface is appropriate to model the interaction with the smallest features on the rigid surface Fig
260. boundary conditions should not be defined at a given node multi point constraints and contact conditions enforced with the kinematic method generally should not be defined at the same node because they may generate conflicting kinematic constraints Unless the constraints are entirely orthogonal to one another the model will be overconstrained the resulting solution will be quite noisy as Abaqus Explicit tries to satisfy the conflicting constraints Penalty contact constraints and multi point constraints acting on the same nodes will not generate conflicts because the penalty constraints are not enforced as strictly as the multi point constraints 12 9 3 Mesh refinement For contact as well as all other types of analyses the solution improves as the mesh 1s refined For contact analyses using a pure master slave approach it 1s especially important that the slave surface is refined adequately so that the master surface facets do not overly penetrate the slave surface The balanced master slave approach does not require high mesh refinement on the slave surface to have adequate contact compliance Mesh refinement is generally most important with pure master slave contact between deformable and rigid bodies in this case the deformable body is always the pure slave surface and thus must be refined enough to interact with any feature on the rigid body Figure 12 46 shows an example of the penetration that can occur if the discretization of the slave su
261. c material data e single elem2 inp A 12 Vibration of a piping system e pipe inp e pipe 2 inp A 13 Forming a channel with Abaqus Standard e channel inp A 14 Shearing of a lap joint e lap joint inp A 15 Circuit board drop test circuit inp Appendix A EXAMPLE FILES A 16 Forming a channel with Abaqus Explicit e channel freq inp e channel xpl inp e channel xpl 5 inp e channel xpl 10 inp e channel xpl 25 inp e channel springback inp About SIMULIA SIMULIA is the Dassault Systemes brand that delivers a scalable portfolio of Realistic Simulation solutions including the Abaqus product suite for Unified Finite Element Analysis multiphysics solutions for insight into challenging engineering problems and lifecycle management solutions for managing simulation data processes and intellectual property By building on established technology respected quality and superior customer service SIMULIA makes realistic simulation an integral business practice that improves product performance reduces physical prototypes and drives innovation Headquartered in Providence RI USA with R amp D centers in Providence and in V lizy France SIMULIA provides sales services and support through a global network of regional offices and distributors For more information visit www simulia com About Dassault Systemes As a world leader in 3D and Product Lifecycle Management PLM solutions Dassault Systemes brings value to more tha
262. can also define almost any thin walled cross section using the arbitrary cross section definition For a detailed discussion of the beam cross sections available in Abaqus see Beam cross section library Section 29 3 9 of the Abaqus Analysis User s Manual The basic format of the BEAM SECTION option is BEAM SECTION ELSET lt element set name gt SECTION lt section type gt MATERIAL lt material name gt lt cross section dimensions gt lt ni gt lt ni gt lt n gt 5 BEAM CROSS SECTION GEOMETRY C Q C Arbitrary Box Circular Hexagonal l beam L section Pipe Rectangular Trapezoid Figure 6 1 Beam cross sections Set the SECTION parameter to one of the cross sections shown in Figure 6 1 Provide the required cross section dimensions which are different for each type of cross section as specified in Beam cross section library Section 29 3 9 of the Abaqus Analysis User s Manual The vector on the second data line defines the approximate normal n which is explained later in this section The basic format of the BEAM GENERAL SECTION option is BEAM GENERAL SECTION ELSET lt element set name gt SECTION lt section type gt lt cross section dimensions gt or lt section engineering properties gt lt ni gt lt ni gt lt n gt lt Young s modulus E gt lt torsional shear modulus G gt To define the section s properties geometrically set the SECTION parameter to one of the cross section
263. cept its frame A help window appears in your browser window The help window displays information about the item you selected 3 Scroll to the bottom of the help window At the bottom of the window a list of blue underlined items appears These items are links to the Abaqus CAE User s Manual which includes all Abaqus Viewer help topics 4 Click any one of the items A book window appears in your default web browser The window is arranged into four frames as follows e The Abaqus CAE User s Manual appears in a text frame on the right side of the window The manual is turned to the item that you selected e An expandable table of contents is available on the lower left side of the window for easy navigation throughout the book e The table of contents control tools in the upper left frame allow you to vary the level of detail displayed in the table of contents frame or to change the size of the frame Click fs to expand several levels in the table of contents of an online book Click E to collapse all expanded sections in the table of contents Click and respectively to widen or narrow the table of contents frame e The navigation frame at the top of the book window allows you to select another book from the entire Abaqus documentation collection The navigation frame also allows you to search the entire manual 5 Click any item in the table of contents The text frame changes to reflect the 1tem you selected 6 Click the
264. cept resulting from the numerical model Since the finite element program has all of the relevant details it can determine an efficient and conservative stability limit However Abaqus Explicit does allow the user to override the automatic time incrementation if desired The time increment used in an explicit analysis must be smaller than the stability limit of the central difference operator Failure to use a small enough time increment will result in an unstable solution When the solution becomes unstable the time history response of solution variables such 9 7 5 AUTOMATIC TIME INCREMENTATION AND STABILITY as displacements will usually oscillate with increasing amplitudes The total energy balance will also change significantly If the model contains only one material type the initial time increment is directly proportional to the size of the smallest element in the mesh If the mesh contains uniform size elements but contains multiple material descriptions the element with the highest wave speed will determine the initial time increment In nonlinear problems those with large deformations and or nonlinear material response the highest frequency of the model will continually change which consequently changes the stability limit Abaqus Explicit has two strategies for time incrementation control fully automatic time incrementation where the code accounts for changes in the stability limit and fixed time incrementation Two types of
265. ces and moments and displacements at the midspan of the plate the following output requests are included in the input file OUTPUT FIELD OP NEW NODE OUTPUT U RF ELEMENT OUTPUT S E OUTPUT HISTORY OP NEW NODE OUTPUT NSET MIDSPAN U EL PRINT S E 5 18 EXAMPLE SKEW PLATE NODE PRINT SUMMARY NO TOTALS YES GLOBAL YES RF NODE PRINT NSET MIDSPAN U Specifying the OUTPUT option overrides the default output selections noted in the previous chapters The option is used with the FIELD and HISTORY parameters to request field and history output to the output database file In general field output is used to generate contour plots symbol plots and deformed shape plots history output is used for X Y plotting In conjunction with the QUTPUT option the NODE OUTPUT option is used to request output of nodal variables and the ELEMENT OUTPUT option is used for output of element variables 5 5 6 Running the analysis After storing your input in a file called skew inp run the analysis interactively If you do not remember how to run the analysis see Running the analysis Section 4 3 6 If your analysis does not complete check the data file skew dat for error messages Modify your input file to remove the errors if you still have trouble running your model compare your input file to the one given in Skew plate Section A 3 5 5 7 Results After running the simulation successfully look at t
266. ch the load is applied over 5 units of time and the initial time increment is 1 unit of time the minimum and maximum time increments are set to 0 0001 and 1 5 respectively STATIC 1 0 5 0 0 0001 tt ow Abaqus will apply 20 1 0 5 0 of the total load in the first increment and it will terminate the analysis if it has problems converging and requires an increment smaller than 0 0001 If the time increment grows because the solution is converging easily the maximum time increment Abaqus can use is 1 5 AT initial Local directions In a geometrically nonlinear analysis the local material directions may rotate with the deformation in each element For shell beam and truss elements the local material directions always rotate with the deformation For solid elements the local material directions rotate with the deformation only if the elements refer to an ORIENTATION option otherwise the default local material directions remain constant throughout the analysis Local directions defined at nodes by using the TRANSFORM option remain fixed throughout the analysis they do not rotate with the deformation See Transformed coordinate systems Section 2 1 5 of the Abaqus Analysis User s Manual for further details 8 12 EXAMPLE NONLINEAR SKEW PLATE Effect on subsequent steps Once you include geometric nonlinearity in a step it is considered in all subsequent steps If nonlinear geometric effects are not requested in a
267. chips exceeds a limiting value the solder securing the chips to the board will fail We wish to identify the peak strain in 12 87 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST any direction Therefore the maximum and minimum principal logarithmic strains are of interest Principal strains are one of a number of Abaqus results that are derived from nonlinear operators in this case a nonlinear function is used to calculate principal strains from the individual strain components Some other common results that are derived from nonlinear operators are principal stresses Mises stress and equivalent plastic strains Care must be taken when filtering results that are derived from nonlinear operators because nonlinear operators unlike linear ones can modify the frequency of the original result Filtering such a result may have undesirable consequences for example if you remove a portion of the frequency content that was introduced by the application of the nonlinear operator the filtered result will be a distorted representation of the derived quantity In general you should either avoid filtering quantities derived from nonlinear operators or filter the underlying quantities before calculating the derived quantity using the nonlinear operator The strain history output for this analysis was recorded every 0 07 ms using the built in anti aliasing filter To verify that the anti aliasing filter did not distort the principal strain results we
268. ckage pac file and the selected results se1 file are also used for restarting an analysis and must be saved upon completion of the first job In addition both products require the output database odb file Restart files can become very large for large models when restart data are requested they are written for every increment or interval by default Thus it is important to control the frequency at which restart data are written Sometimes it is useful to allow data to be overwritten on the restart file during a step This means that at the end of the analysis there 1s only one set of restart data for each step corresponding to the state of the model at the end of each step However if the analysis is interrupted for some reason such as a computer malfunction the analysis can be continued from the point where restart data were last written 11 4 2 Writing a restart file The RESTART option controls the writing of the restart file While the option can appear anywhere in the input file it normally appears as part of a step definition As with other output request options the values defined in a RESTART option apply during the current step and any subsequent general steps until the option is modified in a later step The option RESTART WRITE FREQUENCY lt n gt writes data to the restart file every nth increment Restart data are also written at the end of each step regardless of whether the last increment is divisible by n If t
269. click Plot to view the path plot Click Save As to save the plot The path plot appears as shown in Figure 12 34 12 45 5 DEFINING CONTACT IN Abaqus Explicit 600 500 400 Stress 200 100 0 0 2 0 4 0 6 0 8 0 True distance along path Figure 12 34 CPRESS distribution around the bolt hole in top plate 12 8 Defining contact in Abaqus Explicit Abaqus Explicit provides two algorithms for modeling contact interactions The general automatic contact algorithm allows very simple definitions of contact with very few restrictions on the types of surfaces involved see Defining general contact interactions in Abaqus Explicit Section 35 4 1 of the Abaqus Analysis User s Manual The contact pair algorithm has more restrictions on the types of surfaces involved and often requires more careful definition of contact however it allows for some interaction behaviors that currently are not available with the general contact algorithm see Defining contact pairs in Abaqus Explicit Section 35 5 1 of the Abaqus Analysis User s Manual General contact interactions typically are defined by specifying self contact for a default element based surface defined automatically by Abaqus Explicit that includes all bodies in the model To refine the contact domain you can include or exclude specific surface pairs Contact pair interactions are defined by specifying each of the individual surface pairs that can interact with
270. coincide for curved shells If these local axes do not create the desired material directions you can specify a rotation about the selected axis The other two local axes are rotated by this amount before they are projected onto the shell s surface to give the final material directions The following option block would create the local system shown in Figure 5 9 5 10 SELECTING SHELL ELEMENTS ORIENTATION SYSTEM RECTANGULAR NAME LOCALR lt x gt lt gt lt x gt lt rl gt lt 23 gt lt gt 1 a Again it is the rotated y and z axes that Abaqus projects onto the surface of the shell elements For the projections to be interpreted easily the selected axis should be as close as possible to the shell normal a Rotated y axis Oo y Oo 7 Rotation is specified about the x axis Rotated z axis Figure 5 9 Rotation of the local coordinate system for shell elements If the centerline of the cylinder shown in Figure 5 7 coincides with the global 3 axis the following option block could be used to define consistent material directions ORIENTATION SYSTEM CYLINDRICAL NAME CYLIND1 Ong Osz Ong Vey Osy dx 1 0 Points a and b lie along the centerline of the cylinder Since the orientation of the cylinder matches the orientation of our newly defined cylindrical coordinate system the x axis is radial the y axis is circumferential and the z axis is axial The x axis corresponds approximately
271. compared in Figure 10 47 Figure 10 48 and Figure 10 49 The Abaqus and experimental results for the biaxial tension test match very well The computational and experimental results for the uniaxial tension and planar tests match well at strains less than 100 The hyperelastic material model created from these material test data is probably not suitable for use in general simulations where the strains may be larger than 100 However the model will be adequate for this simulation if the principal strains remain within the strain magnitudes where the data and the hyperelastic model fit well If you find that the results are beyond these magnitudes or if you are asked to perform a different simulation you will have to insist on getting better material data Otherwise you will not be able to have much confidence in your results Material properties elastic properties for the steel The steel is modeled with linear elastic properties only 200 GPa v 0 3 because the loads should not be large enough to cause inelastic deformations Thus the material option blocks for the steel are 10 63 5 EXAMPLE AXISYMMETRIC MOUNT Xx x BIAX COMP Nominal Stress Pa 0 0 0 0 OS 1 0 1 5 2 0 25 3 0 ee 4 0 Nominal Strain Figure 10 47 Comparison of experimental data BIAXIAL and Abaqus results BIAX COMP biaxial tension x x UNI_COMP 6 UNIAXIAL x10
272. continuity iterations this occurs when small contact changes are detected in each iteration and equilibrium is ultimately satisfied 12 13 5 MODELING ISSUES FOR RIGID SURFACES IN Abaqus Standard Begin increment Identify initially Form and identify changes active contact solve system 3 in contact constraints of equations constraint stat Newton S Determine iF Z Check if End E tending toward H solution has convergence converged vas Reduce increment At least one Cvvithin size and try again convergence criterion convergence is not satisfied tolerances Figure 12 10 Contact algorithm in Abaqus Standard Abaqus Standard applies sophisticated criteria involving changes in penetration changes in the residual force and the number of severe discontinuities from one iteration to the next to determine whether iteration should be continued or terminated Hence it is in principle not necessary to limit the number of severe discontinuity iterations This makes it possible to run contact problems that require large numbers of contact changes without having to change the control parameters The default limit for the maximum number of severe discontinuity iterations is 50 which in practice should always be more than the actual number of iterations in an increment 12 4 Modeling issues for rigid surfaces in Abaqus Standard There are a number of issues that you should consider when modeling contact pro
273. ct Surfaces as the Item and Pick from viewport as the Method 6 In the prompt area set the selection method to by angle and accept the default angle 7 Select the surface highlighted in Figure 4 33 to define the free body cut cross section a From the Selection toolbar toggle off the Select the Entity Closest to the Screen tool and ensure that the Select From All Entities tool is selected b As you move the cursor in the viewport Abaqus CAE highlights all of the potential selections and adds ellipsis marks next to the cursor arrow to indicate an ambiguous selection Position the cursor so that one of the faces of the desired surface is highlighted and click to display the first surface selection i a Ss FT 7 xX A 4 CSA a ae _ PON KK ra ZN A A jf EX pee es EN Y ff _ JK Figure 4 33 Selected faces for the free body cross section c Use the Next and Previous buttons to cycle through the possible selections until the appropriate vertical surface is highlighted and click OK Click Done in the prompt area to indicate your selection is complete Click OK in the Free Body Cross Section dialog box In the Edit Free Body Cut dialog box accept the default settings for the Summation Point and the Component Resolution Click OK to close the dialog box Click Options
274. d model shape 1 From the main menu bar select Options Common The Common Plot Options dialog box appears 2 Set the render style to filled all visible element edges will be displayed for convenience a Toggle on Filled under Render Style b Toggle on All edges under Visible Edges 3 Click the Labels tab and toggle on Show element labels and Show face labels 4 Click Apply to apply the plot options jim 5 From the main menu bar select Plot Undeformed Shape or use the tool in the toolbox Abaqus Viewer displays the element and face identification labels in the current display group 6 Click Defaults in the Common Plot Options dialog box to restore the default plot settings and then click OK to close the dialog box Displaying a free body cut You can define a free body cut to view the resultant forces and moments transmitted across a selected surface of a model Force vectors are displayed with a single arrowhead and moment vectors with a double arrowhead To create a free body cut 1 To display the entire model in the viewport select Tools Display Group Plot All from the main menu bar 2 From the main menu bar select Tools Free Body Cut Manager 3 Click Create in the Free Body Cut Manager 4 33 5 EXAMPLE CONNECTING LUG 10 From the dialog box that appears select 3D element faces as the Selection method and click Continue In the Free Body Cross Section dialog box sele
275. d Options dialog box 2 In this dialog box switch to the Area tabbed page 3 In the Position region of this page toggle on Inset 4 To display the minimum and maximum values in the legend switch to the Contents tabbed page of the dialog box In the Numbers region of this page toggle on Show min max 5 Click Dismiss 6 Drag the legend in the viewport to reposition it The resulting plot which has been customized is shown in Figure 7 9 The curves for the two nodes at the top of each truss points B and C are almost a reflection of those for the nodes on the bottom of each truss points A and D Note To modify the curve styl lick Vv yles clic Options dialog box in the Visualization toolbox to open the Curve At the attachment points at the top of each truss structure the peak tensile force is around 80 kN which is below the 100 KN capacity of the connection Keep in mind that a negative reaction force in the 1 direction means that the member is being pulled away from the wall The lower attachments are in compression positive reaction force while the load is applied but oscillate between tension and compression after the load has been removed The peak tensile force is about 40 KN well below the allowable value To find this value probe the X Y plot 7 20 XMIN XMAX 5 000E 01 YMIN EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING RF1 Point A RF1 Point B RF1 Point C RF1 Point D 0 000E 00 8 076E 04
276. d also in the Abaqus Analysis User s Manual which describes every element available in Abaqus The index of element types Section EI 1 Abaqus Standard Element Index of the Abaqus Analysis User s Manual makes locating a particular element easy Whenever you are using an element for the first time you should read the description which includes the element connectivity and any element section properties needed to define the element s geometry The connectivity for the truss elements used in the overhead hoist model is shown in Figure 2 5 Figure 2 5 Connectivity for the 2 node truss element T2D2 Node and element numbers are merely identification labels They are usually generated automatically by Abaqus CAE or another preprocessor The only requirement for node and element numbers is that they must be positive integers Gaps in the numbering are allowed and the order in which nodes and elements are defined does not matter Any nodes that are defined but not associated with an element are removed automatically and are not included in the simulation In this case we use the node and element numbers shown in Figure 2 6 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST 104 7 105 101 102 103 Figure 2 6 Node and element numbers for the hoist model 2 3 4 Model data The first part of the input file must contain all of the model data These data define the structure being analyzed In the overhead hoist example the model
277. d and legend positions have been changed The nonlinear nature of this simulation is clearly seen in these curves as the analysis progresses the plate stiffens In this simulation the increase in the plate stiffness with the deformation is due to membrane effects Therefore the resulting peak displacement is less than that predicted by the linear analysis which did not include this effect You can create X Y curves from either history or field data stored in the output database odb X Y curves can also be read from an external file or they can be typed into the Visualization module interactively Once curves have been created their data can be further manipulated and plotted to the screen in graphical form The X Y plotting capability of Abaqus Viewer is discussed further in Chapter 10 Materials 8 25 5 EXAMPLE NONLINEAR SKEW PLATE U3 N 1 NSET MIDSPAN ai U3 N 2 NSET MIDSPAN x10 0 00 5 00 10 00 15 00 20 00 25 00 30 00 35 00 40 00 45 00 50 00 0 00 0 20 0 40 0 60 0 80 1 00 Time U3 Figure 8 14 Midspan displacement history at the edges of the skew plate Tabular data Create a tabular data report of the midspan displacements Use the node set PART 1 1 MIDSPAN to create the appropriate display group and the frame selector to choose the final frame The contents of the report are shown below Source 1 ODB skew_nl odb Step Step 1 Frame Increment 6 Step Time
278. d earlier in Selecting elements for elastic plastic problems Section 10 3 in the context of plastic incompressibility Volumetric locking arises in this problem from overconstraint The steel is very stiff compared to the rubber Thus along the bond line the rubber elements cannot deform laterally Since these elements must also satisfy incompressibility requirements they are highly constrained and locking occurs Analysis techniques that address volumetric locking are discussed in Techniques for reducing volumetric locking Section 10 9 Contouring the maximum principal stress Plot the maximum in plane principal stress in the model Follow the procedure given below to create a filled contour plot on the actual deformed shape of the mount with the plot title suppressed To contour the maximum principal stress 1 By default Abaqus Viewer displays S Mises as the primary field output variable In the Field Output toolbar select Max Principal as the invariant Abaqus Viewer automatically changes the current plot state to display a contour plot of the maximum in plane principal stresses on the deformed model shape 2 Open the Contour Plot Options dialog box 3 Drag the uniform contour intervals slider to 8 4 Click OK to view the contour plot and to close the dialog box 10 75 5 EXAMPLE AXISYMMETRIC MOUNT Create a display group showing only the elements in the rubber mount 5 Inthe Results Tree expand the Ma
279. d is called mass scaling 13 22 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit Unless the model has rate dependent materials or damping these two methods effectively do the same thing Determining acceptable mass scaling Loading rates Section 13 2 and Metal forming problems Section 13 2 3 discuss how to determine acceptable scaling of the loading rate or mass to reduce the run time of a quasi static analysis The goal is to model the process in the shortest time period in which inertial forces remain insignificant There are bounds on how much scaling can be used while still obtaining a meaningful quasi static solution As discussed in Loading rates Section 13 2 we can use the same methods to determine an appropriate mass scaling factor as we would use to determine an appropriate load rate scaling factor The difference between the two methods is that a load rate scaling factor of f has the same effect as a mass scaling factor of f Originally we assumed that a step time on the order of the period of the fundamental frequency of the blank would be adequate to produce quasi static results By studying the model energies and other results we were satisfied that these results were acceptable This technique produced a punch velocity of approximately 4 3 m s Now we will accelerate the solution time using mass scaling and compare the results against our unscaled solution to determine whether the scaled results are acceptabl
280. d of every Abaqus simulation It tells you if the analysis job ran to completion 1 e whether it terminated without a FORTRAN error and it gives the number of error and warning messages Abaqus issued during the simulation Always investigate any errors or warnings All warnings and errors generated during the analysis are found in the message msg file Warnings issued during user input processing are found in the data dat file Data file The tables of displacements and reaction forces that you requested are in the data dat file The midspan deflections at the end of the step can be found near the end of the file THE FOLLOWING TABLE IS PRINTED FOR NODES BELONGING TO NODE SET MIDSPAN NODE FOOT Ul U2 U3 UR1 UR2 UR3 NOTE 601 1 2795E 04 4 4921E 05 1 0831E 02 602 1 2457E 04 4 5147E 05 1 0749E 02 603 1 2218E 04 4 5645E 05 1 0679E 02 604 1 2070E 04 4 5966E 05 1 0625E 02 605 1 1891E 04 4 6602E 05 1 0581E 02 606 1 1749E 04 4 6822E 05 1 0553E 02 607 1 1489E 04 4 7487E 05 1 0537E 02 608 1 1213E 04 4 7541E 05 1 0541E 02 609 1 0685E 04 4 8026E 05 1 0561E 02 MAXIMUM 1 0685E 04 4 4921E 05 1 0537E 02 0 000 0 000 0 000 AT NODE 609 601 607 MINIMUM 1 2795E 04 4 8026E 05 1 0831E 02 0 000 0 000 0 000 AT NODE 601 609 601 0 0 0 Compare these with the displacements from the linear analysis in Chapter 5 Using Shell Elements The maximum displacement at the midspan in this simulation is about 9 less than
281. d rotate about the impacted corner until the opposite side of the foam packaging impacts the floor at about 8 ms further reducing the kinetic energy The deformation of the foam packaging during impact causes a transfer of kinetic energy to internal energy in the foam packaging and the circuit board From Figure 12 57 we can see that the internal energy increases as the kinetic energy decreases In fact the internal energy is composed of elastic energy and plastically dissipated energy both of which are also plotted in Figure 12 57 Elastic energy rises to a peak and then falls as the elastic deformation recovers but the plastically dissipated energy continues to rise as the foam is deformed permanently Another important energy output variable is the artificial energy which is a substantial fraction approximately 15 of the internal energy in this analysis By now you should know that the quality of the solution would improve if the artificial energy could be decreased to a smaller fraction of the total internal energy What causes high artificial strain energy in this problem Contact at a single node such as the corner impact in this example can cause hourglassing especially in a coarse mesh Two common strategies for reducing the artificial strain energy are to refine the mesh or to round the impacting corner For the current exercise however we shall continue with the original mesh realizing that improving the mesh would lead to an
282. d updates the load path through which the contact forces are transmitted If geometric nonlinearity is not included in the model any rotation or deformation of the master surface 1s ignored and the load path remains fixed 12 11 a DEFINING CONTACT IN Abaqus Standard The finite sliding contact formulation requires that Abaqus Standard continually track which part of the master surface is in contact with each slave node This is a very complex calculation especially if both the contacting bodies are deformable The structures in such simulations can be either two or three dimensional Abaqus Standard can also model the finite sliding self contact of a deformable body Such a situation occurs when a structure folds over onto itself The finite sliding formulation for contact between a deformable body and a rigid surface is not as complex as the finite sliding formulation for two deformable bodies Finite sliding simulations where the master surface is rigid can be performed for both two and three dimensional models The contact pair algorithm can consider either small or finite sliding effects general contact only considers finite sliding effects 12 3 6 Element selection Selection of elements for contact depends heavily on the contact enforcement used For example for traditional contact formulations 1 e the node to surface discretization it is generally better to use first order elements for those parts of a model that will form a slav
283. data items to define the initial yield behavior CRUSHABLE FOAM HARDENING VOLUMETRIC 1 1 0 1 The first data item is the the ratio of initial yield stress in uniaxial compression to initial yield stress in hydrostatic compression o p we have chosen it to be 1 1 The second data item is the ratio of yield stress in hydrostatic tension to initial yield stress in hydrostatic compression p p This data item is given as a positive value in this problem we have chosen it to be 0 1 Include hardening effects with the CRUSHABLE FOAM HARDENING option The first data item on each line is the yield stress in uniaxial compression given as a positive value the second data item on each line is the absolute value of the corresponding plastic strain The crushable foam hardening model follows the curve shown in Figure 12 55 12 66 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST Uniaxial compression original surface softened nas s surface hardened Va surface Figure 12 54 Crushable foam model yield surface in the p q plane x10 0 6 0 4 initial volumetric plastic strain e 0 2 Size of the Yield Surface Pa 0 2 4 6 8 10 initial size of the Volumetric Plastic Strain yield surface P p Figure 12 55 Foam hardening material data 12 67 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST CRUSHABLE FOAM HARDENING 0 22000E6 0 0 0 24651E6 0 1 0 27294E6 0 2
284. data using a Butterworth filter with a cutoff frequency of 1100 Hz The expression at the top of the dialog box should appear as butterworthFilter xyData RF2 xpl cutof fFrequency 1100 Note Choosing an appropriate filter cutoff frequency takes engineering judgment and a good understanding of the physical system being modeled Often an iterative approach beginning with a relatively high cutoff frequency and then gradually reducing it can be used to find a cutoff frequency that removes solution noise with minimal distortion of the underlying physical solution Knowledge of the system s natural frequencies can also assist in the determination of appropriate filter cutoff frequencies For this example we performed a frequency extraction analysis to determine the fundamental frequency of the undeformed blank 140 Hz however the blank at the end of the forming step will have a fundamental frequency that 1s considerably higher If you perform a natural frequency extraction analysis on the final model configuration you will find that the fundamental frequency at the end of the forming step is approximately 1000 Hz Hence a cutoff frequency that is slightly larger than this value 1s a good choice for this model Click Save As to save the calculated displacement curve as RF2 xp1 bw1100 Similarly filter the displacement history data using a Butterworth filter with a cutoff frequency of 1100 Hz The expression at the top of the Operate on XY Da
285. de range of elements many of which have geometry not defined completely by the coordinates of their nodes For example the layers of a composite shell or the dimensions of an I beam section are not defined by the nodes of the element Such additional geometric data are defined as physical properties of the element and are necessary to define the model geometry completely see Chapter 3 Finite Elements and Rigid Bodies COMPONENTS OF AN Abaqus ANALYSIS MODEL Material data Material properties for all elements must be specified While high quality material data are often difficult to obtain particularly for the more complex material models the validity of the Abaqus results is limited by the accuracy and extent of the material data Loads and boundary conditions Loads distort the physical structure and thus create stress in it The most common forms of loading include e point loads e pressure loads on surfaces e distributed tractions on surfaces e distributed edge loads and moments on shell edges e body forces such as the force of gravity and e thermal loads Boundary conditions are used to constrain portions of the model to remain fixed zero displacements or to move by a prescribed amount nonzero displacements In a static analysis enough boundary conditions must be used to prevent the model from moving as a rigid body in any direction otherwise unrestrained rigid body motion causes the stiffness matrix to be singular
286. ded Curves can also be differentiated integrated and combined 10 82 11 GENERAL ANALYSIS PROCEDURES Multiple Step Analysis The general goal of an Abaqus simulation is to predict the response of a structure to applied loads Recall that in a general sense the term load in Abaqus refers to anything that induces a change in the response of a structure from its initial state for example nonzero boundary conditions or applied displacements point forces pressures fields etc In some cases loads are relatively simple such as a single set of point loads on a structure In other problems the loads applied to a structure can be very complex For example different loads may be applied to different portions of the model in a particular sequence over some period of time or the magnitude of the loads may vary as a function of time The term load history is used to refer to such complex loading of a model In Abaqus the user divides the complete load history of the simulation into a number of steps Each step 1s a period of time specified by the user for which Abaqus calculates the response of the model to a particular set of loads and boundary conditions The user must specify the type of response known as the analysis procedure during each step and may change analysis procedures from step to step For example static dead loads perhaps gravitational loads could be applied to a structure in one step and the dynamic response of the loa
287. ded structure to earthquake accelerations could be calculated in the next step Both implicit and explicit analyses can contain multiple steps however implicit and explicit steps cannot be combined in the same analysis job To combine a series of implicit and explicit steps the results transfer or import capability can be used This feature is discussed in Transferring results between Abaqus Explicit and Abaqus Standard Section 9 2 2 of the Abaqus Analysis User s Manual and is not discussed further here Abaqus divides all of its analysis procedures into two main groups linear perturbation and general General analysis steps can be included in an Abaqus Standard or an Abaqus Explicit analysis linear perturbation steps are available only in Abaqus Standard Loading conditions and time are defined differently for the two cases Furthermore the results from each type of procedure should be interpreted differently The response of the model during a general analysis procedure known as a general step may be either nonlinear or linear In a step that uses a perturbation procedure which 1s called a perturbation step the response can only be linear Abaqus Standard treats such steps as a linear perturbation about the preloaded predeformed state known as the base state created by any previous general steps therefore its capability for doing linear simulations is rather more general than that of a purely linear analysis program 11
288. der of fastest to slowest since the solution time is inversely proportional to the punch velocity Examine the results of the analyses and get a feel for how the deformed shapes stresses and strains vary with punch speed Some indications of excessive punch speeds are unrealistic localized stretching and thinning as well as the suppression of wrinkling If you begin with a punch speed of for example 50 m s and decrease it from there at some point the solutions will become similar from one punch speed to the next an indication that the solutions are converging on a quasi static solution As inertial effects become less significant differences in simulation results also become less significant As the loading rate is increased artificially it becomes more and more important to apply the loads in a gradual and smooth manner For example the simplest way to load the punch is to impose a constant velocity throughout the forming step Such a loading causes a sudden impact load onto the sheet metal blank at the start of the analysis which propagates stress waves through the blank and may produce undesired results The effect of any impact load on the results becomes more pronounced as the loading rate 1s increased Ramping up the punch velocity from zero using a smooth step amplitude curve minimizes these adverse effects Springback Springback is often an important part of a forming analysis because the springback analysis determines the shape of th
289. determine which slave nodes are tied to the master surface By default all slave nodes that lie within a given distance of the master surface are tied The default distance is based on the typical element size of the master surface This default can be overridden in one of two ways by specifying the distance within which slave nodes must lie from the master surface to be constrained or by specifying the name of a set containing the nodes that will be constrained 12 5 a DEFINING CONTACT IN Abaqus Standard Slave nodes can also be adjusted so that they lie exactly on the master surface If slave nodes have to be adjusted by distances that are a large fraction of the length of the side of the element to which the slave node is attached the element can become severely distorted avoid large adjustments 1f possible Tie constraints are particularly useful for rapid mesh refinement between dissimilar meshes 12 3 Defining contact in Abaqus Standard The first step in defining contact pairs in Abaqus Standard is to create the surfaces using the SURFACE option The next step is to specify the surfaces that interact with one another using the CONTACT PAIR option Each contact interaction refers to a surface interaction definition which is created with the x SURFACE INTERACTION option A contact pressure clearance relationship and friction properties can be assigned to a surface interaction definition The definition of surfaces is optional for gen
290. distance can be used but the resulting estimate is not always conservative The shorter the element length the smaller the stability limit The wave speed is a property of the material For a linear elastic material with a Poisson s ratio of zero E Cd a pP where is Young s modulus and p is the mass density The stiffer the material the higher the wave speed resulting in a smaller stability limit The higher the density the lower the wave speed resulting in a larger stability limit Our simplified stability limit definition provides some intuitive understanding The stability limit 1s the transit time of a dilatational wave across the distance defined by the characteristic element length If we know the size of the smallest element dimension and the wave speed of the material we can estimate the stability limit For example if the smallest element dimension is 5 mm and the dilatational wave speed is 5000 m s the stable time increment is on the order of 1 x 10 s 9 3 3 Fully automatic time incrementation versus fixed time incrementation in Abaqus Explicit Abaqus Explicit uses equations such as those discussed in the previous section to adjust the time increment size throughout the analysis so that the stability limit based on the current state of the model is never exceeded Time incrementation is automatic and requires no user intervention not even a suggested initial time increment The stability limit is a mathematical con
291. divided into a series of steps each defining a different portion of the structure s loading Each step contains the following information e the type of simulation static dynamic etc e the loads and constraints and e the output required In this example we are interested in the static response of the overhead hoist to a 10 KN load applied at the midspan with the left hand end fully constrained and a roller constraint on the right hand end see Figure 2 1 This is a single event so only a single step is needed for the simulation The STEP option is used to mark the start of a step Like the HEADING option this option may be followed by data lines containing a title for the step In your hoist model use the following STEP option block STEP PERTURBATION 10kN central load The PERTURBATION parameter indicates that this is a linear analysis If this parameter 1s omitted the analysis may be linear or nonlinear The use of the PERTURBATION parameter is discussed further in Chapter 11 Multiple Step Analysis Analysis procedure The analysis procedure the type of simulation must be defined immediately following the STEP option block In this case we want the long term static response of the structure The option for a static simulation is STATIC For linear analysis this option has no parameters or data lines so add the following line to your input file STATIC The remaining input data in the step define t
292. dom for any one mode as shown below The total mass of the model is given earlier in the data file and is 414 34 kg EFFECTIVE MASS MODE NO X COMPONENT Y COMPONENT Z COMPONENT X ROTATION Y ROTATION Z ROTATION 1 5 68446E 05 5 73740E 03 309 98 309 61 5515 3 0 17021 2 1 0304 1 9917 2 09036E 05 1 33181E 04 1 10585E 03 95 175 3 2 7495 217 62 2 15407E 03 2 83449E 03 9 51822E 02 7923 1 4 1 89478E 06 2 31603E 02 1 7003 16 582 381 34 0 22180 5 3 99800E 03 3 57904E 04 0 25553 101 79 853 85 0 11155 6 0 68105 62 760 1 80631E 02 9 34950E 02 2 22352E 02 476 44 7 6 82949E 03 2 77557E 03 4 2485 7 4203 98 873 3 64709E 04 25 1 4134 10 244 0 26075 5 43401E 02 9 87406E 02 4 4000 26 5 02489E 02 15 656 0 27034 4 16008E 04 2 06766E 02 4 0887 27 0 36609 0 78385 0 63677 1 41330E 03 2 3112 0 46216 28 0 74103 0 25787 4 6522 1 77231E 02 19 329 0 18700 29 2 63530E 02 3 62651E 03 5 90071E 03 1 94668E 04 6 68780E 02 1 63456E 02 30 0 15200 2 23444E 02 1 1708 0 13119 8 3622 0 11979 TOTAL 22 198 378 26 373 68 558 02 8348 4 8695 0 To ensure that enough modes have been used the total effective mass in each direction should be a large proportion of the mass of the model say 90 However some of the mass of the model is associated with nodes that are constrained This constrained mass is approximately one quarter of the mass of all the elements attached to the constrained nodes which in this case is approximately 28 kg Therefore the mass of the model that 1s able to move is
293. e Time History or use the 2 tool in the toolbox The time history animation begins in a continuous loop at its fastest speed Abaqus Viewer displays the movie player controls in the right side of the context bar immediately above the viewport 2 From the main menu bar select Options Animation or use the animation options H tool in the toolbox located directly underneath the 2 tool The Animation Options dialog box appears 3 Change the Mode to Play Once and slow the animation down by moving the Frame Rate slider 4 You can use the animation controls to start pause and step through the animation From left to right of Figure 2 14 these controls perform the following functions play pause first previous next and last Launch First Next Frame image image Selector boo he d i gt PH Play Previous Last Pause image image Figure 2 14 Postprocessing animation controls 2 39 5 COMPARISON OF IMPLICIT AND EXPLICIT PROCEDURES The truss responds dynamically to the load You can confirm this by plotting the vertical displacement history of the node set CENTER You can create X Y curves from either history or field data stored in the output database odb file X Y curves can also be read from an external file or they can be typed into Abaqus Viewer interactively Once curves have been created their data can be further manipulated and plotted to the screen in graphical form In this exam
294. e PRINT CONTACT YES option to write contact diagnostics to the message file The complete step definition in your model appears below STEP NLGEOM YES Apply holder force STATIC 0 05 1 0 BOUNDARY CENTER XSYMM REFDIE 1 6 REFPUNCH 1 6 REFHOLD 1 1 REFHOLD 6 6 CLOAD REFHOLD 2 4 4E5 OUTPUT FIELD FREQ 20 VAR PRESELECT OUTPUT HISTORY FREQ 1 VAR PRESELECT NODE OUTPUT NSET REFPUNCH RF2 U2 PRINT CONTACT YES END STEP Step 2 Move the punch down to complete the forming operation Between the frictional sliding the changing contact conditions and the inelastic material behavior there is significant nonlinearity in this step therefore set the maximum number of increments to a large value for example set INC 1000 on the STEP option Set the initial time increment to be 0 05 and the total step time to be 1 0 To alleviate convergence difficulties that may arise due to the changing contact states in particular for contact between the punch and the blank define contact controls to invoke automatic 12 26 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL contact stabilization for the contact pair involving the punch and the blank Reduce the default damping factor by a factor of 1 000 to minimize the effects of stabilization on the solution IS 12 5 7 Your output requests from the previous step will be propagated to this step The input for Step 2 STEP NLGEOM YES INC 1000 Appl
295. e This will allow the model to retain continuity in the blank location through any additional forming stages that may follow The complete history definition 1s as follows STEP NLGEOM YES STATIC STABILIZE ALLSDTOL 0 0 1 1 BOUNDARY CENTER XSYMM BOUNDARY TYPE VELOCITY MIDLEFT 2 2 END STEP Save your input in a file named channel springback inp and run the analysis using the following command abaqus job channel springback oldjob channel xpl 5 Results of the springback analysis Figure 13 22 overlays View Overlay Plot the deformed shape of the blank after the forming and springback stages the forming stage corresponds to the last frame of the Abaqus Explicit output database file while the springback stage corresponds to the final frame of the Abaqus Standard 13 27 SUMMARY 13 6 output database file The springback result 1s necessarily dependent on the accuracy of the forming stage preceding it In fact springback results are highly sensitive to errors in the forming stage more sensitive than the results of the forming stage itself springback fr formed shape ra i A Figure 13 22 Deformed model shapes following forming and springback You should also plot the blank s internal energy ALLIE and compare it with the static stabilization energy ALLSD that is dissipated The stabilization energy should be a small fraction of the internal
296. e We assume that scaling can only diminish not improve the quality of the results The objective is to use scaling to decrease the computer time and still produce acceptable results Our goal is to determine what scaling values still produce acceptable results and at what point the scaled results become unacceptable To see the effects of both acceptable and unacceptable scaling factors we investigate a range of scaling factors on the stable time increment size from 5 to 5 specifically we choose v5 v10 and 5 These speedup factors translate into mass scaling factors of 5 10 and 25 respectively To apply mass scaling of 5 add the following option to the history definition FIXED MASS SCALING ELSET BLANK FACTOR 5 and save the modified input in a file named channel xpl_5 inp and submit it for analysis also create input files named channel xpl_10 inpandchannel xpl_ 25 inp with mass scaling factors of 10 and 25 respectively and submit them for analysis First we will look at the effect of mass scaling on the equivalent plastic strains and the displaced shape We will then see whether the energy histories provide a general indication of the analysis quality Evaluating the results with mass scaling One of the results of interest in this analysis is the equivalent plastic strain PEEQ Since we have already seen the contour plot of PEEQ at the completion of the unscaled analysis in Figure 13 15 we can compare the results from e
297. e analysis to keep the size of the output database file reasonable In this analysis saving information every 2 ms should provide sufficient detail to study the response of the structure visually This model requests field output for the stresses plastic strains and nodal displacements OUTPUT FIELD NUMBER INTERVAL 25 ELEMENT OUTPUT S PE NODE OUTPUT U A more detailed set of output can be saved for selected parts of the model by using the OQUTPUT HISTORY option Set the TIME INTERVAL parameter to 1 0E 4 seconds to write the required data at 500 points during the analysis Write von Mises stress MISES equivalent plastic strain PEEQ and volumetric strain rate ERV for the elements in element set STIFFMAX Since the nodes that will undergo the maximum displacements are at the center of the plate use node set NOUT to output displacement and velocity history data for the center of the plate In addition save the following energy variables kinetic energy ALLKE recoverable strain energy ALLSE work done ALLWK energy lost in plastic dissipation ALLPD total internal energy ALLIE 10 37 5 EXAMPLE BLAST LOADING ON A STIFFENED PLATE energy lost in viscous dissipation ALLVD artificial energy ALLAE and the energy balance ETOTAL OUTPUT HISTORY TIME INTERVAL 1 0E 4 ELEMENT OUTPUT ELSET STIFFMAX PEEQ MISES NODE OUTPUT NSET NOUT U V ENERGY OUTPUT ALLKE ALLSE ALLWK ALLPD ALLIE ALLVD AL
298. e in which a sudden event initiates the dynamic response such as an impact or when the structural response involves large amounts of energy being dissipated by plasticity or viscous damping In such studies the high frequency response which is important initially is damped out rapidly by the dissipative mechanisms in the model An alternative for nonlinear dynamic analyses is the explicit dynamics procedure available in Abaqus Explicit As discussed in Chapter 2 Abaqus Basics the explicit algorithm propagates the solution as a stress wave through the model one element at a time Thus it is most suitable for applications in which stress wave effects are important and in which the event time being simulated is short typically less than one second Another advantage associated with the explicit algorithm is that it can model discontinuous nonlinearities such as contact and failure more easily than Abaqus Standard Large highly discontinuous problems are often more easily modeled with Abaqus Explicit even if the response is quasi static Explicit dynamic analyses are discussed further in Chapter 9 Nonlinear Explicit Dynamics 7 10 Related Abaqus examples e Linear analysis of the Indian Point reactor feedwater line Section 2 2 2 of the Abaqus Example Problems Manual e Explosively loaded cylindrical panel Section 1 3 3 of the Abaqus Benchmarks Manual e Eigenvalue analysis of a cantilever plate Section 1 4 6
299. e 1f the relative 12 9 a DEFINING CONTACT IN Abaqus Standard motion of the two surfaces is less than a small proportion of the characteristic length of an element face The small sliding formulation is selected by including the SMALL SLIDING parameter on the CONTACT PAIR option Using the small sliding formulation will result in a more efficient analysis Each contact pair must refer to a surface interaction definition in much the same way that each element must refer to an element property definition Use the INTERACTION parameter on the CONTACT PAIR option to refer to a SURFACE INTERACTION option where the different surface interaction models such as FRICTION can be defined The following example CONTACT PAIR INTERACTION FRIC SMALL SLIDING FLANGE1 FLANGE2 SURFACE INTERACTION NAME FRIC FRICTION 0 1 specifies that surfaces FLANGE1 and FLANGE2 might interact with each other and that the amount of relative sliding that occurs will be considered to be small The interaction between the surfaces includes friction with a friction coefficient of 0 1 With the general contact approach you do not need to explicitly define and pair individual surfaces By using the CONTACT option and its related sub options Abaqus Standard automatically defines an all inclusive element based surface and enforces contact between the members of that surface The contact definition as a result is considerably simplified The following exam
300. e Ni 1 a L Beam tangent Y Beam 2 axis Figure 6 19 Plot of beam section axes and tangents for elements in display group MainA Rendering beam profiles You will now display an idealized representation of the beam profile and contour the stress results To render beam profiles 1 From the main menu bar select View ODB Display Options The ODB Display Options dialog box appears 2 In the General tabbed page toggle on Render beam profiles and accept the default scale factor of 1 3 Click OK Abaqus Viewer displays beam profiles with the appropriate dimensions and in the correct orientations Figure 6 20 shows the beam profiles on the whole model Your changes are saved for the duration of the session 4 Click IN to contour the Mises stress on the rendered profile Creating a hard copy You can save the current image to a file for hardcopy output To create a PostScript file of the current image 1 From the main menu bar select File Print The Print dialog box appears 6 26 EXAMPLE CARGO CRANE Figure 6 20 Cargo crane with beam profiles displayed 2 From the Settings area in the Print dialog box select Black amp White as the Rendition type and toggle on File as the Destination 3 Select PS as the Format and enter beam ps as the File name Baa 4 Click O The PostScript Options dialog box appears 5 From the PostScript Options dialog box select 600 dpi as the Reso
301. e a simulation with complex changing contact conditions e Use quadratic fully integrated elements CAX8 CPE8 CPS8 C3D20 etc locally where stress concentrations may exist They provide the best resolution of the stress gradients at the lowest cost e For contact problems use a fine mesh of linear reduced integration elements or incompatible mode elements CAX4I CPE4I CPS4I C3D8I etc See Chapter 12 Contact 4 3 Example connecting lug In this example you will use three dimensional continuum elements to model the connecting lug shown in Figure 4 14 The lug is welded firmly to a massive structure at one end The other end contains a hole When it is in service a bolt will be placed through the hole of the lug You have been asked to determine the static deflection of the lug when a 30 KN load is applied to the bolt in the negative 2 direction Because 4 11 5 EXAMPLE CONNECTING LUG 50 MPa pressure load Figure 4 14 Sketch of the connecting lug the goal of this analysis is to examine the static response of the lug you should use Abaqus Standard as your analysis product You decide to simplify this problem by making the following assumptions e Rather than include the complex bolt lug interaction in the model you will use a distributed pressure over the bottom half of the hole to load the connecting lug see Figure 4 14 e You will neglect the variation of pressure magnitude around the circumference o
302. e algorithm that Abaqus Viewer uses to create contour plots for element variables such as stress The contouring algorithm requires data at the nodes however Abaqus Standard calculates element variables at the integration points Abaqus Viewer calculates nodal values of element variables by extrapolating the data from 10 20 EXAMPLE CONNECTING LUG WITH PLASTICITY Step Step 1 Increment 4 Step Time 1 000 Deformed Var U Deformation Scale Factor 2 000e 00 Figure 10 12 Deformed model shape for the simulation with plastic hardening Maximum stress gt 580 MPa 267e 07 Figure 10 13 Contour of Mises stress the integration points to the nodes The extrapolation order depends on the element type for 10 21 5 EXAMPLE CONNECTING LUG WITH PLASTICITY second order reduced integration elements Abaqus Viewer uses linear extrapolation to calculate the nodal values of element variables To display a contour plot of Mises stress Abaqus Viewer extrapolates the stress components from the integration points to the nodal locations within each element and calculates the Mises stress If the differences in Mises stress values fall within the specified averaging threshold nodal averaged Mises stresses are calculated from each surrounding element s invariant stress value Invariant values exceeding the elastic limit can be produced by the extrapolation process Try plotting contours of each component of the stress tensor v
303. e central stiffener Figure 10 20 Node and element sets 10 5 4 Reviewing the input file the model data We now review the model data for this problem including the model description node and element definitions element properties and shell offsets material properties boundary conditions and amplitude definition for the blast load Model description The HEADING option is used to include a title and model description in the input file The heading is useful for future reference purposes and may contain information on model revisions and the evolution of complex models It can be several lines long but only the first line will be printed as a title on the output pages Below is the HEADING definition used for this analysis HEADING Blast load on a flat plate with stiffeners S4R elements 20x20 mesh Normal stiffeners 20x2 SI units kg m s N Nodal coordinates and element connectivity The mesh is shown in Figure 10 19 and the sets are shown in Figure 10 20 10 31 EXAMPLE BLAST LOADING ON A STIFFENED PLATE Element properties and shell offset Each element set in the model has the section properties shown below To insure that each set of elements refers to a material definition the appropriate MATERIAL parameter has been included on each SHELL SECTION option SHELL SECTION MATERIAL STEEL ELSET PLATE OFFSET SPOS 0 025 SHELL SECTION MATERIAL STEEL ELSET STIFF 0 0125 The material named STEEL will
304. e creates a separate table of data that can have a maximum of nine columns For this analysis we are interested in the displacements of the nodes output variable U the reaction forces at the constrained nodes output variable RF and the stress in the members output variable S Use the following in your input file NODE PRINT U RF EL PRINT S to request that Abaqus generate three tables of output data in the data file Since you have now finished the definition of all the data required for the step use the END STEP option to mark the end of the step END STEP The input file is now complete Compare the input file you have generated to the complete input file given in Figure 2 2 Save the data as frame inp and exit the editor 2 3 6 Checking the model Having generated the input file for this simulation you are ready to run the analysis Unfortunately it is possible to have errors in the input file because of typing errors or incorrect or missing data You should perform a datacheck analysis first before running the simulation To run a datacheck analysis make sure that you are in the directory where the input file frame inp is located and type the following command abaqus job frame datacheck interactive If this command results in an error message the Abaqus installation on your computer has been customized You should contact your systems administrator to find out the appropriate command to run Abaqus The job
305. e dimensional models You can use the other render style tools to select the hidden line and filled render styles shown in Figure 4 28 and Figure 4 29 respectively These render styles are more useful when viewing complex three dimensional models Figure 4 28 Hidden line plot 4 27 5 EXAMPLE CONNECTING LUG 2 ncremen 1 Step Time 2 2200E 16 Deformed Var U Deformation Scale Factor 2 968e 01 Figure 4 29 Filled element plot Contour plots Contour plots display the variation of a variable across the surface of a model You can create filled or shaded contour plots of field output results from the output database To generate a contour plot of the Mises stress 1 From the main menu bar select Plot Contours On Deformed Shape The filled contour plot shown in Figure 4 30 appears The Mises stress S Mises indicated in the legend title is the default variable chosen by Abaqus for this analysis You can select a different variable to plot 2 From the main menu bar select Result Field Output The Field Output dialog box appears by default the Primary Variable tab is selected 3 From the list of available output variables select a new variable to plot 4 Click OK The contour plot in the current viewport changes to reflect your selection Tip You can also use the Field Output toolbar located above the viewport to change the displayed field output variable For more information see
306. e displayed at section point 1 by default To plot stresses at nondefault section points select Result Section Points from the main menu bar to open the Section Points dialog box 9 Select the desired nondefault section point for plotting 10 In a complex model the element edges can obscure the symbol plots To suppress the display of the element edges choose Feature edges in the Basic tabbed page of the Common Plot Options dialog box Figure 5 16 shows a symbol plot of the principal stresses at the default section point with only feature edges visible 5 24 5 EXAMPLE SKEW PLATE Figure 5 16 Symbol plot of principal stresses using feature edges Material directions Abaqus Viewer also allows you visualize the element material directions This feature is particularly useful if you would like to verify that the material directions were assigned correctly in the simulation To plot the material directions 1 From the main menu bar select Plot Material Orientations On Undeformed Shape or use the tool in the toolbox The material orientation directions are plotted on the undeformed shape By default the triads that represent the material orientation directions are plotted without arrowheads 2 From the main menu bar select Options Material Orientation or use the Material E D Orientation Options tool in the toolbox to display the triads with arrowheads The Material Orientation Plot Options d
307. e final unloaded part While Abaqus Explicit is well suited for forming simulations springback poses some special difficulties The main problem with performing springback simulations within Abaqus Explicit is the amount of time required to obtain a steady state solution Typically the loads must be removed very carefully and damping must 13 5 MASS SCALING be introduced to make the solution time reasonable Fortunately the close relationship between Abaqus Explicit and Abaqus Standard allows a much more efficient approach Since springback involves no contact and usually includes only mild nonlinearities Abaqus Standard can solve springback problems much faster than Abaqus Explicit can Therefore the preferred approach to springback analyses is to import the completed forming model from Abaqus Explicit into Abaqus Standard You must create an Abaqus Standard input file that will import the forming results and perform the springback analysis Using the IMPORT option within the Abaqus Standard input file you specify the element sets that you wish to import Usually the entire deformable mesh is imported The nodes elements and section properties are imported automatically but you must redefine the materials and boundary conditions Once the springback analysis is complete you can import the model back into Abaqus Explicit to continue with another forming stage 13 3 Mass scaling Mass scaling enables an analysis to be performed econ
308. e flow problems including laminar and turbulent flow thermal convective flow and deforming mesh problems Abaqus CFD is discussed in this guide Abaqus CAE Abaqus CAE Complete Abaqus Environment is an interactive graphical environment for Abaqus It allows models to be created quickly and easily by producing or importing the geometry of the structure to be analyzed and decomposing the geometry into meshable regions Physical and material properties can be assigned to the geometry together with loads and boundary conditions Abaqus CAE contains very powerful options to mesh the geometry and to verify the resulting THE Abagqus PRODUCTS analysis model Once the model is complete Abaqus CAE can submit monitor and control the analysis jobs The Visualization module can then be used to interpret the results Abaqus Viewer which is a subset of Abaqus CAE that contains only the postprocessing capabilities of the Visualization module 1s discussed in this guide The other Abaqus CAE modules are not discussed in this guide Abaqus Aqua Abaqus Aqua is a set of optional capabilities that can be added to Abaqus Standard and Abaqus Explicit It is intended for the simulation of offshore structures such as oil platforms Some of the optional capabilities include the effects of wave and wind loading and buoyancy Abaqus Aqua is not discussed in this guide Abaqus Design Abaqus Design is a set of optional capabilities that can be added to Abaqus
309. e freely at the joints The frame is prevented from moving out of plane A simulation is performed to determine the structure s deflection and the peak stress in its members when a 10 KN load is applied as shown in Figure 2 1 Since this problem is very simple the Abaqus input file is compact and easily understood The complete Abaqus input file for this example which is shown in Figure 2 2 and also in Overhead hoist frame Section A 1 is split into two distinct parts The first section contains model data and includes all the information required to define the structure being analyzed The second section contains history data that define what happens to the model the sequence of loading or events for which the response of the structure is required This history is divided into a sequence of steps each defining a separate part of the simulation For example the first step may define a static loading while the second step may define a dynamic loading etc The input file is composed of a number of option blocks that contain data describing a part of the model Each option block begins with a keyword line which is usually followed by one or more data lines These lines cannot exceed 256 characters FORMAT OF THE INPUT FILE All members are 1m circular steel rods 5 mm in diameter 10 000 N Material properties General properties p 7800 kg m Elastic properties E 200x10 Pa v 0 3 Figure 2 1 Schematic of an
310. e in the directory containing the output database file skew _n1 odb type the following command at the operating system prompt abaqus viewer odb skew nl Showing the available frames To begin this exercise determine the available output frames the increment intervals at which results were written to the output database To show the available frames 1 From the main menu bar select Result Step Frame The Step Frame dialog box appears During the analysis Abaqus Standard wrote field output results to the output database file every second increment as was requested Abaqus Viewer displays the list of the available frames as shown in Figure 8 12 MS Step Frame x Step Name Step 1 Uniform pressure 20 0 kPa load Frame Increment Step Time 0 000 Increment Step Time 0 z000 Increment Step Time 0 5750 Increment 6 Step Time 1 000 Field Output Cancel Figure 8 12 Available frames The list tabulates the steps and increments for which field variables are stored This analysis consisted of a single step with six increments The results for increment 0 the initial state of the step are saved by default and you saved data for increments 2 4 and 6 By default 8 23 5 EXAMPLE NONLINEAR SKEW PLATE Abaqus Viewer always uses the data for the last available increment saved in the output database file 2 Click OK to dismiss the Step Frame dialog box Displaying the deformed and undeformed m
311. e material parameters The material model is stable at all strains with these material test data and this strain energy function However if you specified that a second order N 2 polynomial strain energy function be used you would see the following warnings in the data file HYPERELASTIC N 2 POLYNOMIAL TEST DATA INPUT WARNING UNSTABLE HYPERELASTIC MATERIAL FOR UNIAXIAL TENSION WITH A NOMINAL STRAIN LARGER THAN 6 9700 FOR UNIAXIAL COMPRESSION WITH A NOMINAL STRAIN LESS THAN 0 9795 FOR BIAXIAL TENSION WITH A NOMINAL STRAIN LARGER THAN 5 9800 FOR BIAXIAL COMPRESSION WITH A NOMINAL STRAIN LESS THAN 0 6458 FOR PLANE TENSION WITH A NOMINAL STRAIN LARGER THAN 7 0400 FOR PLANE COMPRESSION WITH A NOMINAL STRAIN LESS THAN 0 8756 POLYNOMIAL STRAIN ENERGY FUNCTION WITH N 2 D1 C10 col D2 C20 C11 C02 0 0000E 00 0 1934E 06 148 2 0 0000E 00 805 7 180 0 3 967 If you only had the uniaxial test data available for this problem you would find that the Mooney Rivlin material model Abaqus creates would have unstable material behavior above certain strain magnitudes 10 7 9 Postprocessing Use Abaqus Viewer to look at the analysis results by issuing the following command at the operating system prompt abaqus viewer odb mount Calculating the stiffness of the mount Determine the stiffness of the mount by creating an X Y plot of the displacement of the steel plate as a function of the applied load You will first create a plot of the ver
312. e solution time without sacrificing the quality of the results Clearly a speedup of 5 is too great to produce quasi static results for this analysis A smaller speedup such as v5 does not alter the results significantly These results would be adequate for most applications including springback analyses With a scaling factor of 10 the quality of the results begins to diminish while the general magnitudes and trends of the results remain intact Correspondingly the ratio of kinetic energy to internal energy increases noticeably The results for this case would be adequate for many applications but not for accurate springback analysis 13 24 PEEQ Ave 2 349e 01 2 000e 01 1 714e 01 1 429e 01 1 143e 01 C 45 3714e 02 Crit 75 857e 02 0 000e 00 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit Figure 13 19 Equivalent plastic strain PEEQ for speedup of v 10 mass scaling of 10 857e 02 000e 00 SS a E Figure 13 20 Equivalent plastic strain PEEQ for speedup of 5 mass scaling of 25 13 25 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit JE25 x10 Internal Energy 0 00 2 00 4 00 6 00 k10 Figure 13 21 Kinetic and internal energy histories for mass scaling factors of 5 10 and 25 corresponding to speedup factors of V5 V10 and 5 respectively 13 5 5 Springback analysis in Aba
313. e strain energy stored in the static steps This effect introduces a natural order dependency in the model nonlinear general analysis steps follow one another in the order in which the events they define occur with linear 11 6 LINEAR PERTURBATION ANALYSIS perturbation analysis steps inserted at the appropriate times in this sequence to investigate the linear behavior of the system at those times A more complex load history is illustrated in Figure 11 7 which shows a schematic representation of the steps in the manufacture and use of a stainless steel sink The sink is formed from sheet steel using a punch a die and a blank holder This forming simulation will consist of a number of general steps Typically the first step may involve the application of blank holder pressure and the punching operation will be simulated in the second step The third step will involve the removal of the tooling allowing the sink to spring back into its final shape Each of these steps is a general step since together they model a sequential load history where the starting condition for each step is the ending condition from the previous step These steps obviously include many nonlinear effects plasticity contact large deformations At the end of the third step the sink will contain residual stresses and inelastic strains caused by the forming process Its thickness will also vary as a direct result of the manufacturing process The sink is then insta
314. e surface Second order elements can sometimes cause problems in this case because of the way these elements calculate consistent nodal loads for a constant pressure The consistent nodal loads for a constant pressure P on a second order two dimensional element with area A are shown in Figure 12 9 Pressure P PA P eS 2PA aaa F Fe Fa Figure 12 9 Equivalent nodal loads for a constant pressure on a two dimensional second order element The node to surface contact formulation bases important decisions on the forces acting on the slave nodes It is difficult for the algorithm to tell if the force distribution shown in Figure 12 9 represents a constant contact pressure or an actual variation across the element The equivalent nodal forces for a three dimensional second order brick element are even more confusing because they do not even have the same sign for a constant pressure making it very difficult for the algorithm to work correctly especially for nonuniform contact Therefore to avoid such problems Abaqus Standard automatically adds a midface node to any face of a second order three dimensional brick or wedge element that defines 12 12 DEFINING CONTACT IN Abaqus Standard a slave surface when it is used with the node to surface formulation The equivalent nodal forces for a second order element face with a midface node have the same sign for a constant pressure although they still differ considerably in magnitude The equiva
315. e swapped data by the constant total force value differentiate SWAPPED 5500 appears in the text field 6 Save the differentiated data object by clicking Save As at the bottom of the dialog box The Save XY Data As dialog box appears 7 In the Name text field type STIFFNESS and click OK to close the dialog box 8 Click Cancel to close the Operate on XY Data dialog box 9 Customize the X and Y axis labels as they appear in Figure 10 51 if you have not already done SO 10 In the Results Tree click mouse button 3 on STIFFNESS underneath the XYData container and select Plot from the menu that appears to view the plot in Figure 10 51 that shows the variation of the mount s axial stiffness as the mount deforms Model shape plots You will begin by plotting the undeformed model shape of the mount To plot the undeformed model shape From the main menu bar select Plot Undeformed Shape or use the tool in the Visualization module toolbox to plot the undeformed model shape see Figure 10 52 If the figure obscures the plot title you can move the plot by clicking the Pp tool and holding down mouse button 1 to pan the deformed shape to the desired location Alternatively you can turn the plot title off Viewport Viewport Annotation Options 10 72 EXAMPLE AXISYMMETRIC MOUNT tt tj l r N pera Sen
316. e the X Y data 33 T1 and click OK S33 T1 appears in the XYData container of the Results Tree Repeat Steps 7 through 9 to create X Y data for frames 2 and 3 Name the data sets S33 _T2 and 33 T3 respectively To close the XY Data from Path dialog box click Cancel 9 18 EXAMPLE STRESS WAVE PROPAGATION IN A BAR To plot the stress curves 1 In the XYData container drag the cursor to select all three X Y data sets 2 Click mouse button 3 and select Plot from the menu that appears Abaqus Viewer plots the stress in the 3 direction along the center of the bar for frames 1 2 and 3 corresponding to approximate simulation times of 5 x 10 s 1 x 10 s and 1 5 x 10 s respectively 3 Click A in the prompt area to cancel the current procedure To customize the X Y plot 1 Double click the Y axis The Axis Options dialog box appears The Y Axis is selected 2 In the Tick Mode region of the Scale tabbed page select By increment and specify that the Y axis major tick marks occur at 20E3 Pa increments You can also customize the axis titles 3 Switch to the Title tabbed page 4 Enter Stress S33 Pa as the Y axis title 5 To edit the X axis select the axis label in the X Axis field of the dialog box In the Title tabbed page of the dialog box enter Distance along bar m as the X axis title 6 Click Dismiss to close the Axis Options dialog box To customize the appearance of the curves in the X Y plo
317. e using the correct element type C3D8R It is possible that the preprocessor specified the element type incorrectly The ELEMENT option block in this model begins with the following ELEMENT TYPE C3D8R ELSET BAR If you created this input file using a preprocessor the name given for the ELSET parameter in your model may not be BAR If necessary change the name to BAR Section properties The section properties are the same for all elements In the following option statement the element set BAR is used to assign the material properties to the elements SOLID SECTION ELSET BAR MATERIAL STEEL 5 EXAMPLE STRESS WAVE PROPAGATION IN A BAR Material properties The bar is made of steel which we assume to be linear elastic with a Young s modulus of 207 x 10 Pa a Poisson s ratio of 0 3 and a density of 7800 kg m The following material option block specifies these values MATERIAL NAME STEEL ELASTIC 207 0E9 0 3 DENSITY 7800 0 Fixed boundary conditions In this model we fix all the translations at the built in right hand end of the bar then constrain the front back top and bottom faces of the bar so that these faces are on rollers and the strain 1s uniaxial Using the node sets defined previously the following boundary conditions are used in this model BOUNDARY NFIX 1 3 NFRONT 1 1 NBACK 1 1 NTOP 2 2 NBOT 2 2 Amplitude definition The blast load is applied at its maximum value instanta
318. e value of total strain see Figure 10 3 10 5 5 PLASTICITY IN DUCTILE METALS True stress a P pa l HHMH True strain Figure 10 3 Decomposition of the total strain into elastic and plastic components This relationship is written where arl is true plastic strain g is true total strain g is true elastic strain o is true stress and E is Young s modulus Example of converting material test data to Abaqus input The nominal stress strain curve in Figure 10 4 will be used as an example of how to convert the test data defining a material s plastic behavior into the appropriate input format for Abaqus The six points shown on the nominal stress strain curve will be used as the data for the PLASTIC option 10 6 5 PLASTICITY IN DUCTILE METALS 400 200 Nominal Stress MPa E 210 GPa 0 1 0 2 Nominal Strain Figure 10 4 FElastic plastic material behavior The first step is to use the equations relating the true stress to the nominal stress and strain and the true strain to the nominal strain shown earlier to convert the nominal stress and nominal strain to true stress and true strain Once these values are known the equation relating the plastic strain to the total and elastic strains shown earlier can be used to determine the plastic strains associated with each yield stress value The converted data are shown in Table 10 1 Table 10 1 Stress and strain conversions Nominal Nominal
319. eature edges visible To display only feature edges 1 From the main menu bar select Options Common The Common Plot Options dialog box appears 2 Click the Basic tab if it is not already selected 3 From the Visible Edges options choose Feature edges 4 Click Apply The deformed plot in the current viewport changes to display only feature edges as shown in Figure 4 26 Render style A shaded plot is a filled plot in which a lightsource appears to be directed at the model This is the default render style and can be very useful when viewing complex three dimensional models Three other render styles provide additional display options wireframe hidden line and filled You can select a render style from the Common Plot Options dialog box or from the tools on the 4 26 EXAMPLE CONNECTING LUG Render Style toolbar wireframe H hidden line B filled T and shaded D To display the wireframe plot shown in Figure 4 27 select Exterior edges in the Common Plot Options dialog box click OK to close the dialog box and select wireframe plotting by clicking the pz tool All subsequent plots will be displayed in the wireframe render style until you select another render style IN f O vA XAN HA I LKS A J i Deformed Var U Deformation Scale Factor 2 968e 01 Figure 4 27 Wireframe plot A wireframe model showing internal edges can be visually confusing for complex thre
320. ecrease the analysis s susceptibility to aliasing For example an elastically dominated impact problem would be even more susceptible to aliasing than this circuit board drop test which includes energy absorbing packaging The safest way to ensure that aliasing is not a problem in your results is to request output at every increment When you do this the output rate is determined by the stable time increment which is based on the highest possible frequency response of the model However requesting output at every increment is often not practical because it would result in very large output files In addition output at every increment is usually much more data than you need there 1s no need to capture high frequency solution noise when what you are really interested in is the lower frequency structural response An alternative method for avoiding aliasing is to request output at a lower rate and use the Abaqus Explicit real time filtering capabilities to remove high frequency content from the result before writing data to the output database file This technique uses less disk space than requesting output every increment however it is up to you to ensure that your output rate and filter choices are appropriate to avoid aliasing or other distortions related to digital signal processing Abaqus Explicit offers filtering capabilities for both field and history data Filtering of history data only is discussed here 12 10 9 Rerunning the analysis w
321. ed inp four elements through the depth are used 10 44 EXAMPLE BLAST LOADING ON A STIFFENED PLATE to model the stiffener instead of two This increase in the number of elements increases the solution time by approximately 20 In addition the stable time increment decreases by approximately a factor of two as a result of the reduction of the smallest element dimension in the stiffeners Since the total increase in solution time is a combination of the two effects the solution time of the refined mesh increases by approximately a factor of 1 2 x 2 or 2 4 over that of the original mesh Figure 10 30 shows the histories of artificial energy for both the original mesh and the mesh with the refined stiffeners The artificial energy is slightly lower in the refined mesh As a result we would not expect the results to change significantly from the original to the refined mesh x10 4 1 00 0 80 gt gt 2 0 60 LU i 2 E 0 40 Original lt Refined 0 20 0 00 0 00 0 01 0 02 0 03 0 04 0 05 Time s Figure 10 30 Artificial energy in the original and refined meshes Figure 10 31 shows that the displacement of the plate s central node is almost identical in both cases indicating that the original mesh is capturing the overall response adequately One advantage of the refined mesh however is that it better captures the variation of stress and plastic strain through the stiffeners Contour plots In t
322. ed to determine the face identifier label of the free element faces For the model defined in Stress wave propagation in a bar Section A 7 the free face is face number 3 which corresponds to the pressure identifier P3 The face identifier depends on the order in which the nodes are defined on the ELEMENT option as shown in Figure 9 7 Use the amplitude named BLAST when applying the pressure load DLOAD AMPLITUDE BLAST ELOAD lt PI P2 P3 P4 P5 or P6 gt 1 0E5 If you define the pressure load in your preprocessor the correct face identifier should be determined automatically Figure 9 7 Face label identifier for a C3D8R element Bulk viscosity To keep the stress wave as sharp as possible the quadratic bulk viscosity discussed in Bulk viscosity Section 9 5 1 is set to zero BULK VISCOSITY 0 06 0 0 9 15 5 EXAMPLE STRESS WAVE PROPAGATION IN A BAR Output requests By default many preprocessors create an Abaqus input file that has a large number of output request options If you created your input file using a preprocessor and you find that these default output options were created delete them all because they will generally generate too much output You want to have an output database file created during the analysis so that you can use Abaqus Viewer to postprocess the results Four output database frames intervals at which data are written to the output database are adequate to show the stress
323. eed only a single node at each welded joint in the model The bolted joints which connect the cross bracing to the truss structures and the connection at the tip of the truss structures are different Since these joints do not provide complete continuity for all nodal degrees of freedom separate nodes are needed for each element at the connection Appropriate constraints between these separate nodes must then be given by using the MPC BOUNDARY or EQUATION options The MPC and EQUATION options are discussed in more detail later The node numbers for the various members of the cargo crane model are shown in Figure 6 14 6 13 EXAMPLE CARGO CRANE Figure 6 13 Mesh for cargo crane Truss B Cross bracing 402 Truss A Figure 6 14 Node numbers in crane model 6 14 EXAMPLE CARGO CRANE These are the node numbers from the input file given in Cargo crane Section A 4 Separate nodes have been defined on the cross bracing elements and the truss structures that they connect Separate nodes are also needed at the end of each truss structure point E in Figure 6 11 The node numbers in your model may be different from those shown here The element numbers for the various members of the cargo crane model are shown in Figure 6 15 Truss B Truss A Figure 6 15 Element numbers in crane model These are the element numbers from the input file given in Cargo crane Section A 4 The element numbers in
324. efine the surfaces on these tools SURFACE TYPE SEGMENTS NAME HOLDER FILLET RADIUS 0 001 START 0 110 0 001 LINE 0 056 0 001 CIRCL 0 051 0 006 0 056 0 006 LINE 0 051 0 060 RIGID BODY ANALYTICAL SURFACE HOLDER REF NODE 8000 k SURFACE TYPE SEGMENTS NAME DIE FILLET RADIUS 0 001 START 0 051 0 060 LINE 0 051 0 005 CIRCL 0 056 0 0 056 0 005 LINE 0 11 0 RIGID BODY ANALYTICAL SURFACE DIE REF NODE 9000 All of the rigid surfaces in this simulation extend beyond the deformable blank to ensure that there is no possibility that slave nodes will slide behind any of them The initial configuration of these surfaces and the locations of their reference nodes are shown in Figure 12 20 Deformable surfaces Using the two element sets defined on the blank create a contact surface on the top of the blank called BLANK T and one on the bottom called BLANK B If you use the automatic free surface generation capability the option blocks will look like 12 23 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL 7000 REFPUNCH 8000 REFHOLD Punch reference Holder reference node x x node x lt 9000 REFDIE Die reference node Figure 12 20 Rigid body reference nodes SURFACE NAME BLANK B BLANK B SURFACE NAME BLANK T BLANK T Contact pairs Contact must be defined between the top of the blank and the punch the top of the blank and the blank holder and the bottom of the blank and the die The rigid
325. el size in using the explicit and implicit methods Summary e The Abaqus input file contains a complete description of the analysis model It is the means of communication between the preprocessor Abaqus CAE for example and the analysis product Abaqus Standard or Abaqus Explicit e The input file contains two sections the model data defining the structure being analyzed and the history data defining what happens to the structure e Each section of the input file comprises a number of option blocks each consisting of a keyword line which may be followed by data lines 2 43 SUMMARY e You can perform a datacheck analysis once you have created the input file Error and warning messages are printed to the data file After a successful datacheck analysis estimates of the computer resources required for the simulation are printed to the data file e Use Abaqus Viewer to verify the model geometry and boundary conditions graphically using the output database file generated during the datacheck phase e It is often easiest to check for mistakes in material properties in the data dat file geometry loads and boundary conditions are more easily checked with a graphical postprocessor such as Abaqus Viewer e Always check that the results satisfy basic engineering principles such as equilibrium e Abaqus Viewer allows you to visualize analysis results graphically in a variety of ways and also allows you to write tabular data report
326. ell element s normal determines the positive and negative surfaces of the element To define contact and interpret element output correctly you must know which surface 1s which The shell normal also defines the direction of positive pressure loads applied to the element and can be plotted in Abaqus Viewer Shell elements use material directions local to each element In large displacement analyses the local material axes rotate with the element ORIENTATION can be used to define non default local coordinate systems The element variables such as stress and strain are output in the local directions TRANSFORM defines local coordinate systems for nodes Concentrated loads and boundary conditions are applied in the local coordinate system All printed nodal output such as displacements also refer to the local system by default Symbol plots can help you visualize the results from a simulation They are especially useful for visualizing the motion and load paths of a structure 5 29 6 1 BEAM CROSS SECTION GEOMETRY Using Beam Elements Use beam elements to model structures in which one dimension the length is significantly greater than the other two dimensions and in which the longitudinal stress is most important Beam theory is based on the assumption that the deformation of the structure can be determined entirely from variables that are functions of position along the structure s length For beam theory to produce acceptable r
327. els Open section beams are not covered in this guide Abaqus Standard also has hybrid beam elements that are used for modeling very slender members such as flexible risers on offshore oil installations or for modeling very stiff links Hybrid beams are not covered in this guide 3 13 FINITE ELEMENTS Element output variables The stress components in three dimensional shear deformable beam elements are the axial stress c11 and the shear stress due to torsion a12 The shear stress acts about the section wall in a thin walled section Corresponding strain measures are also available The shear deformable beams also provide estimates of transverse shear forces on the section The slender cubic beams in Abaqus Standard have only the axial variables as output Open section beams in space also have only the axial variables as output since the torsional shear stresses are negligible in this case All two dimensional beams use only axial stress and strain The axial force bending moments and curvatures about the local beam axes can also be requested for output For details of what components are available with which elements see Beam modeling overview Section 29 3 1 of the Abaqus Analysis User s Manual Details of how the local beam axes are defined are given in Chapter 6 Using Beam Elements 3 1 5 Truss elements Truss elements are rods that can carry only tensile or compressive loads They have no resistance t
328. ement formulation and integration Section 4 1 Element output variables By default element output variables such as stress and strain refer to the global Cartesian coordinate system Thus the 7 component of stress at the integration point shown in Figure 3 5 a acts in the global 1 direction Even if the element rotates during a large displacement simulation as shown in Figure 3 5 b the default is still to use the global Cartesian system as the basis for defining the element variables However Abaqus allows you to define a local coordinate system for element variables see Example skew plate Section 5 5 This local coordinate system rotates with the motion of the element in large displacement simulations A local coordinate system can be very useful if the object being modeled has some natural material orientation such as the fiber directions in a composite material 3 1 3 Shell elements Shell elements are used to model structures in which one dimension the thickness is significantly smaller than the other dimensions and the stresses in the thickness direction are negligible FINITE ELEMENTS b Figure 3 5 Default material directions for continuum elements Shell element names in Abaqus begin with the letter S Axisymmetric shells all begin with the letters SAX Abaqus Standard also provides axisymmetric shells with asymmetric deformations which begin with the letters SAXA The first number
329. ement set PACK contains all foam packaging elements Element set FLOOR contains the rigid element for the floor Node set PACK contains all foam packaging nodes YW H Node set REF contains the reference node for the rigid floor Figure 12 53 Necessary node and element sets Include the circuit board elements in an element set called BOARD and include the corresponding circuit board nodes in a node set called BOARD Similarly for the foam packaging include the elements in an 12 63 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST element set called PACK and include the nodes in a node set called PACK The element sets will be used to refer to material properties and the node sets will be used to apply initial conditions Create an element set called FLOOR containing the floor s rigid element and a node set called REF containing the reference node for the rigid surface modeling the floor Include the mass elements modeling the chips in an element set called CHIPS 12 10 4 Simulating free fall Two methods could be used to simulate the circuit board being dropped from a height of 1 meter You could model the circuit board and foam at a height of 1 meter above the rigid surface and allow Abaqus Explicit to calculate the motion under the influence of gravity however this method 1s clearly impractical because of the large number of increments required to complete the free fall part of the simulation The most efficient
330. en used to calculate dynamic equilibrium at nodes and 2 1 2 li 0 1 A P Tei Uy Uy ee 7 f dt E11 A f nat M l Len gold TA gt i unat gt 1 Eo AEQ 2 li gt Oe Een Figure 1 8 Configuration of the rod at the beginning of increment 2 The process continues so that at the start of the third increment there are stresses in both elements 1 and 2 and there are forces at nodes 1 2 and 3 as shown in Figure 1 9 The process continues until the analysis reaches the desired total time A QUICK REVIEW OF THE FINITE ELEMENT METHOD Figure 1 9 Configuration of the rod at the beginning of increment 3 Abaqus BASICS 2 Abaqus Basics A complete Abaqus analysis usually consists of three distinct stages preprocessing simulation and postprocessing These three stages are linked together by files as shown below Preprocessing Abaqus CAE or other software Input file job inp Simulation Abaqus Standard or Abaqus Explicit Output files job odb job dat job res job fil Postprocessing Abaqus CAE or other software Preprocessing Abaqus CAE In this stage you must define the model of the physical problem and create an Abaqus input file The model is usually created graphically using Abaqus CAE or another preprocessor although the Abaqus input file for a simple analysis can be created directly using a text editor Simulation Abaqus Standard o
331. end the output from the abaqus info support command 5 A QUICK REVIEW OF THE FINITE ELEMENT METHOD 1 5 3 Support for academic institutions Under the terms of the Academic License Agreement we do not provide support to users at academic institutions unless the institution has also purchased technical support Please contact us for more information 1 6 A quick review of the finite element method This section reviews the basics of the finite element method The first step of any finite element simulation is to discretize the actual geometry of the structure using a collection of finite elements Each finite element represents a discrete portion of the physical structure The finite elements are joined by shared nodes The collection of nodes and finite elements 1s called the mesh The number of elements per unit of length area or in a mesh is referred to as the mesh density In a stress analysis the displacements of the nodes are the fundamental variables that Abaqus calculates Once the nodal displacements are known the stresses and strains in each finite element can be determined easily 1 6 1 Obtaining nodal displacements using implicit methods A simple example of a truss constrained at one end and loaded at the other end as shown in Figure 1 3 is used to introduce some terms and conventions used in this document N Figure 1 3 Truss problem The objective of the analysis is to find the displacement of the free end of the truss t
332. ends an angle of approximately 30 with the original reference normal it has an independent normal at node 102 as shown in the data file This incorrect average normal means that elements 101 102 and 113 have a section geometry that twists about the beam axis from one end of the element to the other which is not the intended geometry You must use the NORMAL option to define the normals at node 102 for element 113 explicitly Explicitly specifying the normal directions prevents Abaqus from applying its averaging algorithm You must also use NORMAL for the corresponding elements on the opposite side of the crane element 213 node 202 of truss B There is also a problem with the normals at nodes 104 and 204 at the tip of each truss structure again because the angle between elements 103 and 104 is less than 20 Since we are modeling straight beam elements the normals are constant at both nodes in each element Thus the NORMAL option block that you should put in your input file has six data lines If you used the numbering scheme shown in Figure 6 14 and Figure 6 15 the following option block should be added to your input file NORMAL TYPE ELEMENT eee 102 0 3962 0 9171 0 0446 105 0 3962 0 9171 0 0446 Nace 213 ZOZ 0 3962 0 9171 0 0446 213 205 0 3962 0 9171 0 0446 103 104 0 1820 0 9829 0 0205 203 204 0 1820 9829 0 0205 Normal at node O 6 20 EXAMPLE CARGO CRANE Multi point c
333. ensions we can use shell elements of type S4R for the model 10 5 2 Mesh design The mesh in this model is based on the design shown in Figure 10 19 which is a relatively coarse mesh of 20 x 20 elements in the plate and 2 x 20 elements in each of the stiffeners This mesh corresponds to the input file shown in Blast loading on a stiffened plate Section A 9 It provides moderate accuracy while keeping the solution time to a minimum Define the mesh so that the element normals for the plate 10 28 EXAMPLE BLAST LOADING ON A STIFFENED PLATE 2 0 5 m stiffeners are evenly spaced 1 0 Plate thickness 25 mm loom Stiffener thickness 12 5 mm 2 0m oe Material properties General properties p 7800 kg m Elastic properes E 210x 10 Pa v 0 3 Plastic properties True Stress Pa True Plastic Strain 300 x 10 0 000 000 350 x 10 _ 375 x 10 0 100 394 x 10 0 200 400 x 10 0 350 Figure 10 18 Problem description for blast load on a stiffened plate all point in the positive 2 direction Doing so ensures that the stiffeners lie on the SPOS face of the plate which will be important when defining the element properties and shell offsets later 10 29 5 EXAMPLE BLAST LOADING ON A STIFFENED PLATE Figure 10 19 Mesh design for the stiffened plate 10 5 3 Node and element sets The steps that follow assume that you have access to the full input file for this example Thi
334. ent normals are all consistent otherwise an arbitrary positive orientation is chosen for the surface If it is not possible to make the facet normals consistent for example if the surface contains a T intersection of shells the surface can be used with the general contact algorithm but not with the contact pair algorithm 12 54 MODELING CONSIDERATIONS IN Abaqus Explicit orientation of the surface is in this direction ELEMENT TYPE SAX1 ELSET SHELL 1 101 102 2 102 103 3 104 103 4 105 104 5 105 106 6 106 107 SURFACE DEFINITION NAME WALL 1 SPOS 2 SPOS 3 SNEG 4 SNEG 5 SPOS 6 SPOS Figure 12 44 Inconsistent surface normals Highly warped surfaces No special treatment of warped surfaces is required for the general contact algorithm However when a surface used with the contact pair algorithm contains highly warped facets a more expensive tracking approach must be used than the approach required when the surface does not contain highly warped facets To keep the solution as efficient as possible Abaqus monitors the warpage of the surfaces and issues a warning if surfaces become too warped if the normal directions of adjacent facets differ by more than 20 Abaqus issues a warning message Once a surface is deemed to be highly warped Abaqus switches from the more efficient contact search approach to a more accurate search approach to account for the difficulties posed by the highly warped
335. ents subjected to bending loads These elements function perfectly well under direct or shear loads Shear locking is not a problem for quadratic elements since their edges are able to curve see Figure 4 6 The predicted tip displacements for the quadratic elements shown in Table 4 1 are close to the theoretical value However quadratic elements will also exhibit some locking if they are distorted or if the bending stress has a gradient both of which can occur in practical problems Figure 4 6 Deformation of a fully integrated quadratic element subjected to bending moment M Fully integrated linear elements should be used only when you are fairly certain that the loads will produce minimal bending in your model Use a different element type if you have doubts about the type of deformation the loading will create Fully integrated quadratic elements can also lock under complex states of stress thus you should check the results carefully if they are used exclusively in your model However they are very useful for modeling areas where there are local stress concentrations Volumetric locking is another form of overconstraint that occurs in fully integrated elements when the material behavior is almost incompressible It causes overly stiff behavior for deformations that should cause no volume changes It 1s discussed further in Chapter 10 Materials 4 1 2 Reduced integration Only quadrilateral and hexahedral elements can
336. enu bar select Plot Deformed Shape or use the li tool in the toolbox Figure 4 36 displays the deformed model shape at the end of the analysis As discussed earlier Abaqus Explicit assumes large deformation theory by default thus the deformation scale factor 1s automatically set to 1 If the displacements are too small to be seen scaling can be applied to aid the study of the response To see the vibrations in the lug more clearly change the deformation scale factor to 50 In addition animate the time history of the deformed shape of the lug and decrease the frame rate of the time history animation The time history animation of the deformed shape of the lug shows that the suddenly applied load induces vibrations in the lug Additional insights about the behavior of the lug under this type 4 42 EXAMPLE CONNECTING LUG Y Step Step 1 Dynamic lug loading I t 6762 S Time ae ncremen 5 0000E 03 z x Deformed Var U Deformation Scale Factor 1 000e 00 Figure 4 36 Deformed model shape for the explicit analysis shaded of loading can be gained by plotting the kinetic energy internal energy displacement and stress in the lug as a function of time Some of the questions to consider are 1 Is energy conserved 2 Was large displacement theory necessary for this analysis 3 Are the peak stresses reasonable Will the material yield X Y plotting X Y plots can display the variation of a variable as a function of time
337. ep 2 Add loads to deform the plate Step 3 Find the natural frequencies of the deformed plate e An increment is part of a step In nonlinear analyses the total load applied in a step is broken into smaller increments so that the nonlinear solution path can be followed In Abaqus Standard you suggest the size of the first increment and Abaqus Standard automatically chooses the size of the subsequent increments In Abaqus Explicit the default time incrementation is fully automatic and does not require user intervention Because the explicit method is conditionally stable there is a stability limit for the time increment The stable time increment is discussed in Chapter 9 Nonlinear Explicit Dynamics At the end of each increment the structure is in approximate equilibrium and results are available for writing to the output database restart data or results files The increments at which you select results to be written to the output database file are called frames The issues associated with time incrementation in Abaqus Standard and Abaqus Explicit analyses are quite different since time increments are generally much smaller in Abaqus Explicit e An iteration is an attempt at finding an equilibrium solution in an increment when solving with an implicit method If the model is not in equilibrium at the end of the iteration Abaqus Standard 5 THE SOLUTION OF NONLINEAR PROBLEMS tries another iteration With every iteration the sol
338. er force and the punch stroke Create a tabular amplitude curve for application of the holder force named Ramp1 using the data in Table 13 1 Define a second tabular amplitude curve for the punch stroke named Ramp2 using the data in Table 13 2 Table 13 1 Ramp amplitude data for Ramp1 Table 13 2 Ramp amplitude data for Ramp2 007 o 0 007 0 The ramp amplitude data are defined in AMPLITUDE statements as shown below 13 11 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit AMPLITUDE NAME RAMP1 O O 0 0001 1 AMPLITUDE NAME RAMP2 O Osy 0 007 1 As with the Abaqus Standard analysis you will need two steps for the Abaqus Explicit analysis In the first step the holder force is applied in the second step the punch stroke is applied This can be easily done by modifying the existing steps For each step replace the step procedure with the explicit dynamics procedure For the first step specify a time period of 0 0001 s This time period is appropriate for the application of the holder force because it is long enough to avoid dynamic effects but short enough to prevent a significant impact on the run time for the job Move the contact pair definitions from the model data to the first step definition but delete the TYPE SURFACE to SURFACE parameter for each contact pair as it is relevant only for Abaqus Standard In the step retain the boundary conditions and concentrated force definitions The amplitude curve ass
339. eral contact because an all inclusive element based surface is automatically created when the CONTACT option is used Specific surface pairings may be used however to include regions not included in the default surface CONTACT INCLUSIONS to preclude interaction between different regions of a model CONTACT EXCLUSIONS or to override global contact property assignments For example if you want to apply a certain friction coefficient to all but a few surfaces in your model you can assign a global friction coefficient and and override this property for a given pair of user defined surfaces using the CONTACT PROPERTY ASSIGNMENT option 12 3 1 Defining surfaces Surfaces are created with the SURFACE option by identifying all of the element faces that form the surface This is done in much the same way as defining distributed pressure loads Surfaces on continuum elements A two dimensional first order continuum element such as CPE4 has four faces consisting of the segments defined by nodes 1 2 2 3 3 4 and 4 1 respectively as shown in Figure 12 4 The face identifiers consist of the letter S followed by the face number For example use the following option block to include face 2 of the element shown in Figure 12 4 in a surface called FLANGEL1 SURFACE NAME FLANGE1 5 S2 12 6 DEFINING CONTACT IN Abaqus Standard Face 3 4 3 Face 4 Element 5 Pace j Face 1 2 Figure 12 4 Face numbers on a two dimensional
340. eratures and the other degrees of freedom mentioned in the previous section are calculated only at the nodes of the element At any other point in the element the displacements are obtained by interpolating from the nodal displacements Usually the interpolation order is determined by the number of nodes used in the element as illustrated in the examples in Figure 3 2 FINITE ELEMENTS lt gt lt gt a Linear element b Quadratic element c Modified second order element 8 node brick C3D8 20 node brick C3D20 10 node tetrahedron C3D10M Figure 3 2 Linear brick quadratic brick and modified tetrahedral elements e Elements that have nodes only at their corners such as the 8 node brick shown in Figure 3 2 a use linear interpolation in each direction and are often called linear elements or first order elements e Elements with midside nodes such as the 20 node brick shown in Figure 3 2 b use quadratic interpolation and are often called quadratic elements or second order elements e Modified triangular or tetrahedral elements with midside nodes such as the 10 node tetrahedron shown in Figure 3 2 c use a modified second order interpolation and are often called modified elements or modified second order elements Abaqus Standard offers a wide selection of both linear and quadratic elements Abaqus Explicit offers only linear elements with the exception of the quadratic beam and modified tetrahedron and triangle e
341. erclosures do not cause any initial strain or stress for contact defined in the first step of the analysis When conflicting constraints exist initial overclosures may not be completely resolved by repositioning nodes In this case severe mesh distortions can result near the beginning ofan analysis when the contact pair algorithm is used The general contact algorithm stores any unresolved initial penetrations as offsets to avoid large initial accelerations In subsequent steps any nodal adjustments to remove initial overclosures cause strains that often cause severe mesh distortions because the entire nodal adjustments occur in a single very brief increment This is especially true when the kinematic constraint method is used For example ifa node is overclosed by 1 0 x 10 m and the increment time is 1 0 x 10 s the acceleration applied to the node to correct the overclosure is 2 0 x 10 m s Such a large acceleration applied to a single node typically will cause warnings about deformation speed exceeding the wave speed of the material and warnings about severe mesh distortions a few increments later once the large acceleration has deformed the associated elements significantly Even a very slight initial overclosure can induce extremely large accelerations for kinematic contact In general it is important that in the second step and beyond any new contact surfaces that you define are not overclosed Figure 12 47 shows a common case of initi
342. erial properties Assume that both the plate and stiffeners are made of steel Young s modulus of 210 0 GPa and Poisson s ratio of 0 3 At this stage we do not know whether there will be any plastic deformation but we know the value of the yield stress and details of the post yield behavior for this steel We will add this information on the PLASTIC option in the material definition The initial yield stress is 300 MPa and the yield stress increases to 400 MPa at a plastic strain of 35 The plasticity data are shown below and the plasticity stress strain curve 1s shown in Figure 10 23 MATERIAL NAME STEEL ELASTIC 210 0E9 3 PLASTIC 300 0H6 0 000 350 0H6 0 025 375 0H6 0 100 394 0EH6 0 200 400 0H6 0 350 DENSITY 7800 0 10 33 5 EXAMPLE BLAST LOADING ON A STIFFENED PLATE 400 00 350 00 300 00 250 00 200 00 150 00 Yield Stress MPa 100 00 50 00 0 00 0 00 0 05 0 10 0 15 0 20 0 25 0 30 0 35 Plastic Strain Figure 10 23 Yield stress versus plastic strain During the analysis Abaqus calculates values of yield stress from the current values of plastic strain As discussed earlier the process of lookup and interpolation is most efficient when the data are regular when the stress strain data are at equally spaced values of plastic strain To avoid having the user input regular data Abaqus Explicit automatically regularizes the data In this case the data are regularized by Abaqus Explicit by e
343. es a list in the status sta file of the 10 elements in the mesh with the lowest stability limit If the model contains some elements whose stability limits are much lower than those of the rest of the mesh remeshing the model more uniformly may be worthwhile 9 3 7 Numerical instability Abaqus Explicit remains stable for most elements under most circumstances It 1s possible however to define spring and dashpot elements such that they become unstable during the course of an analysis Therefore it is useful to be able to recognize a numerical instability if it occurs in your analysis If it does occur the result typically will be unbounded nonphysical and often characterized by oscillatory solutions 9 4 Example stress wave propagation in a bar This example demonstrates some of the fundamental ideas in explicit dynamics described earlier in Chapter 2 Abaqus Basics It also illustrates stability limits and the effect of mesh refinement and material properties on the solution time The bar has the dimensions shown in Figure 9 1 9 9 5 EXAMPLE STRESS WAVE PROPAGATION IN A BAR front view side view a P O O O O0o0oo o p 1 0 x 10 Pa n O O O O O 0o Q ia te E 207 x10 Pa v 0 3 p 7800 kg m Figure 9 1 Schematic for wave propagation in a bar To make the problem a one dimensional strain problem all four lateral faces are on rollers thus the three dimensional model simulates a one dimen
344. ess distribution along the length of the bar changes with time To do so we will look at the stress distribution at three different times throughout the course of the analysis Create a curve of the variation of the stress in the 3 direction S33 along the axis of the bar for each of the first three frames of the output database file To create these plots you first need to define a straight path along the axis of the bar To create a point list path along the center of the bar 1 In the Results Tree double click Paths The Create Path dialog box appears 2 Name the path Center Select Point list as the path type and click Continue The Edit Point List Path dialog box appears 3 In the Point Coordinates table enter the coordinates of the centers of both ends of the bar The input specifies a path from the first point to the second point as defined in the global coordinate system of the model Note If you generated the geometry and mesh using the procedure described earlier the table entries are 0 O landO 0 0 If you used an alternate procedure to generate the bar 9 17 5 EXAMPLE STRESS WAVE PROPAGATION IN A BAR 4 geometry you can use the Q tool in the Query toolbar to determine the coordinates of the centers at each end of the bar When you have finished click OK to close the Edit Point List Path dialog box To save X Y plots of stress along the path at three different times 1 In the Results Tree
345. ested to a subset of the model otherwise the default subset which is the entire model will be used Finally request that reaction forces RF be printed for all the nodes in the model and that the displacements U be printed for the nodes at the midspan node set MIDSPAN You will need two NODE PRINT options because you are requesting results for two different subsets of the model Again use the FREQUENCY parameter to reduce the amount of output print the data every second increment The new list of output request option blocks looks like 8 15 5 EXAMPLE NONLINEAR SKEW PLATE OUTPUT FIELD FREQUENCY 2 VARIABLE PRESELECT OUTPUT HISTORY FREQUENCY 1 NODE OUTPUT NSET MIDSPAN U NODE PRINT NSET MIDSPAN FREQUENCY 2 U NODE PRINT SUMMARY NO TOTALS YES FREQUENCY 2 RF Finally the step definition is completed using the END STEP option END STEP 8 4 2 Running the analysis Store the modified input in a file called skew _n1l inp an example input file is listed in Nonlinear skew plate Section A 6 Run the analysis using the following command abaqus job skew nl interactive 8 4 3 Results During a nonlinear analysis two additional output files become very important They are the status file skew _nl sta and the message file skew _nl msg As the analysis progresses Abaqus will write data to both of these files You can view the data even as Abaqus continues your analysis You will need to lear
346. estimates are used to determine the stability limit element by element and global An analysis always starts by using the element by element estimation method and may switch to the global estimation method under certain circumstances The element by element estimate is conservative it will give a smaller stable time increment than the true stability limit that is based upon the maximum frequency of the entire model In general constraints such as boundary conditions and kinematic contact have the effect of compressing the eigenvalue spectrum and the element by element estimates do not take this into account The adaptive global estimation algorithm determines the maximum frequency of the entire model using the current dilatational wave speed This algorithm continuously updates the estimate for the maximum frequency The global estimator will usually allow time increments that exceed the element by element values A fixed time incrementation scheme is also available in Abaqus Explicit The fixed time increment size is determined either by the initial element by element stability estimate for the step or by a time increment specified directly by the user Fixed time incrementation may be useful when a more accurate representation of the higher mode response of a problem is required In this case a time increment size smaller than the element by element estimates may be used When fixed time incrementation is used Abaqus Explicit will not check that t
347. esults the cross section dimensions should be less than 1 10 of the structure s typical axial dimension The following are examples of typical axial dimensions e the distance between supports e the distance between gross changes in cross section and e the wavelength of the highest vibration mode of interest Abaqus beam elements assume that plane sections perpendicular to the axis of the beam remain plane during deformation Do not be confused into thinking that the cross section dimensions should be less than 1 10 of a typical element length A highly refined mesh may contain beam elements whose length is less than their cross section dimensions although this is not generally recommended continuum elements may be more suitable in such a case Beam cross section geometry You can use the BEAM SECTION option or the BEAM GENERAL SECTION option to define the beam section With either option you can define the beam cross section geometrically by specifying the shape and dimensions of the section The BEAM GENERAL SECTION option can also be used to define the beam section through section engineering properties such as area and moments of inertia Alternatively the beam section can be based on a mesh of special two dimensional elements for which geometric quantities are calculated numerically Abaqus offers a variety of common cross section shapes as shown in Figure 6 1 should you decide to define the beam profile geometrically You
348. ew iterations Some of the iteration summaries from the first attempt of the fourth increment are shown below INCREMENT 4 STARTS ATTEMPT NUMBER 1 TIME INCREMENT 0 300 CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 1 AVERAGE FORCE 1 196E 03 TIME AVG FORCE 645 LARGEST RESIDUAL FORCE 4 908E 03 AT NODE 12849 DOF 2 LARGEST INCREMENT OF DISP 5 806E 04 AT NODE 10817 DOF 2 LARGEST CORRECTION TO DISP 3 116E 04 AT NODE 10817 DOF 2 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 2 AVERAGE FORCE 1 286E 03 TIME AVG FORCE 668 LARGEST RESIDUAL FORCE 1 168E 04 AT NODE 13045 DOF 1 LARGEST INCREMENT OF DISP 1 484E 03 AT NODE 10817 DOF 2 LARGEST CORRECTION TO DISP 9 038E 04 AT NODE 10817 DOF 2 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 3 AVERAGE FORCE 1 486E 03 TIME AVG FORCE 717 LARGEST RESIDUAL FORCE 1 721E 04 AT NODE 13049 DOF 2 LARGEST INCREMENT OF DISP 6 796E 03 AT NODE 10817 DOF 2 LARGEST CORRECTION TO DISP 5 311E 03 AT NODE 817 DOF 2 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE WARNING THE STRAIN INCREMENT HAS EXCEEDED FIFTY TIMES THE STRAIN TO CAUSE FIRST YIELD AT 120 POINTS CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 4 AVERAGE FORCE 2 356E 03 TIME AVG FORCE 935 LARGEST RESIDUAL FORCE 4 587E 04 AT NODE 12447 DOF 1 LARGEST INCREMENT OF DISP 7 530E 02 AT NODE 10817 DOF 2 LARGEST CORRECTION TO DISP 6 850E 02 AT NODE 5817 DOF 2
349. excites high frequency modes Consider for example the plate shown in Figure 7 3 The mesh of first order shell elements is adequate for a static analysis of the plate under a uniform load and is also suitable for the prediction of the first mode shape However the mesh is clearly too coarse to be able to model the sixth mode accurately a Mode 1 31 1 Hz b Mode 6 140 Hz Figure 7 3 Vibration frequencies and corresponding mode shapes of the plate based on the coarse mesh Figure 7 4 shows the same plate modeled with a refined mesh of first order elements The displaced shape for the sixth mode now looks much better and the frequency predicted for this mode 1s more accurate If the dynamic loading on the plate is such that there 1s significant excitation of this mode the refined mesh must be used the results from the coarse mesh will not be accurate 5 EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING HEZ SS TALI VARNES AZ ANNIZA XN STEROLS FFT D a Mode 1 30 2 Hz b Mode 6 124 Hz Figure 7 4 Vibration frequencies and corresponding mode shapes of the plate based on the fine mesh 7 5 Example cargo crane under dynamic loading This example uses the same cargo crane that you analyzed in Example cargo crane Section 6 4 but you have now been asked to investigate what happens when a load of 10 KN is dropped onto the lifting hook for 0 2 seconds The connections at point
350. f a model contact pair interactions describe contact between two surfaces or between a single surface and itself e General contact can be defined in the model or history part of the input file contact pairs are defined in the history part of the input file e Surfaces used with the general contact algorithm can span multiple unattached bodies More than two surface facets can share a common edge In contrast all surfaces used with the contact pair algorithm must be continuous and simply connected e Surfaces are defined using the SURFACE option Individual nodes can be included in a contact pair by using the TYPE NODE parameter on the SURFACE option Analytical rigid surfaces are assigned to a rigid body by using the ANALYTICAL SURFACE parameter on the RIGID BODY option The parameters TY PE SEGMENTS CYLINDRICAL or REVOLUTION on the SURFACE option specify the type of analytical rigid surface 12 93 SUMMARY e In Abaqus Explicit single sided surfaces on shell membrane or rigid elements must be defined so that the normal directions do not flip as the surface is traversed e Abaqus Explicit does not smooth rigid surfaces they are faceted like the underlying elements Coarse meshing of discrete rigid surfaces can produce noisy solutions with the contact pair algorithm The general contact algorithm does include some numerical rounding of features e Tie constraints are a useful means of mesh refinement in Abaqus e Abaqus Ex
351. f damping is important to obtain accurate results However damping 1s approximate in the sense that it models the energy absorbing characteristics of the structure without attempting to model the physical mechanisms that cause them Therefore it is difficult to determine the damping data required for a simulation Occasionally you may have data available from dynamic tests but often you will have to work with data gleaned from references or experience In such cases you should be very cautious in interpreting the results and you should use parametric studies to assess the sensitivity of the simulation to damping values MESH DESIGN FOR DYNAMICS 7 3 Element selection Virtually all of the elements in Abaqus can be used in dynamic analyses In general the rules for selecting the elements are the same as those for static stimulations However for simulations of impact and blast loading first order elements should be used They have a lumped mass formulation which is better able to model the effect of stress waves than the consistent mass formulation used in the second order elements 7 4 Mesh design for dynamics When you are designing meshes for dynamic simulations you need to consider the mode shapes that will be excited in the response and use a mesh that is able to represent those mode shapes adequately This means that a mesh that is adequate for a static simulation may be unsuitable for calculating the dynamic response to loading that
352. f the hole and use a uniform pressure e The magnitude of the applied uniform pressure will be 50 MPa 30 kN 2 x 0 015 m x 0 02 m After examining the static response of the lug you will modify the model and use Abaqus Explicit to study the transient dynamic effects resulting from sudden loading of the lug 4 3 1 Coordinate system In your model define the global 1 axis to lie along the length of the lug the global 2 axis to be vertical and the global 3 axis to lie in the thickness direction Place the origin of the global coordinate system x 0 y 0 z 0 at the center of the hole on the z 0 face see Figure 4 14 4 12 EXAMPLE CONNECTING LUG 4 3 2 Mesh design You need to consider the type of element that will be used before you start building the mesh for a particular problem A suitable mesh design that uses quadratic elements may very well be unsuitable if you change to linear reduced integration elements For this example use 20 node hexahedral elements with reduced integration C3D20R With the element type selected you can design the mesh for the connecting lug The most important decision regarding the mesh design for this application is how many elements to use around the circumference of the lug s hole A possible mesh for the connecting lug is shown in Figure 4 15 you should build your model to be similar to it Figure 4 15 Suggested mesh of C3D20R elements for the connecting lug model
353. f the model Frequencies of structural significance are typically two to four orders of magnitude less than the highest frequency of the model In this example the stable time increment ranges between 8 4 x 10 ms to 8 8 x 10 ms see the status file circuit sta 12 81 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST A3 N 403 NSET BOTCHIP ALL A3 N 403 NSET CHIPS x1 E3 a A3 ANTIALIASING N 403 NSET CHIPS 1 3 1 0 0 5 r ath Pa ll Ky A 0 0 hi q 1 py ae 7 J 1 53 Vertical Acceleration m s 0 0 1 0 2 0 3 0 4 0 5 0 6 0 x1 E 3 Time s Figure 12 62 Comparison of acceleration output with and without filtering which corresponds to a sample rate of about 1 MHz this sample rate has been rounded down for this discussion even though it means that the value is not conservative Recalling the Sampling Theorem the highest frequency that can be described by a given sample rate is half that rate therefore the highest frequency of this model is about 500 kHz and typical structural frequencies could be as high as 2 3 kHz more than 2 orders of magnitude less than the highest model frequency While the output recorded every increment contains a lot of undesirable solution noise in the 3 to 500 kHz range it is guaranteed to be good not aliased data which can be filtered later with a postprocessing operation if necessary Next consider the data recorded every 0 07 ms without any filtering Recall
354. fine sets using the NSET and ELSET options in the input file The name of a set 1s specified with either the NSET or ELSET parameter The data lines list the nodes or elements that are included in the set Each data line can contain up to 16 numbers and there can be as many data lines as required For example the node set LHEND see Figure 4 16 can be defined as NSET NSET LHEND 3241 3243 3245 3247 3249 3251 3253 3255 3257 8241 8245 8249 8253 8257 13241 13243 13245 13247 13249 13251 13253 13255 13257 18241 18245 18249 18253 18257 23241 23243 23245 23247 23249 23251 23253 23255 23257 If you are adding a node or element set to the input file with an editor and the identification numbers follow a regular pattern the GENERATE parameter allows a range of nodes to be included by specifying the beginning node number ending node number and the increment in node numbers For example the node set LHEND could be defined as follows NSET NSET LHEND GENERATE 3241 3257 2 8241 8257 13241 13257 18241 18257 23241 23257 N ANA Sets can also be created by referring to other sets If the preprocessor that you used did not create the element set BUILTIN or the node set HOLEBOT that are shown in Figure 4 16 add them to your input file using an editor they will be essential in limiting the output during the simulation You should also create the element set PRESS shown in Figure 4 16 Remember to use
355. forming a channel in Abaqus Explicit 13 8 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit 13 5 1 Preprocessing rerunning the model with Abaqus Explicit Before starting save a copy of channel inpas channel freq inp Make all subsequent changes to the channel freq inp file channel freq inp is also available in the Forming a channel with Abaqus Standard Section A 13 In this section you will modify the input file in order to perform a frequency extraction of the blank using Abaqus Standard Determining an appropriate step time Loading rates Section 13 2 discusses the procedures for determining the appropriate step time for a quasi static process We can determine an approximate lower bound on step time duration if we know the lowest natural frequency the fundamental frequency of the blank One way to obtain such information is to run a frequency analysis in Abaqus Standard In this forming analysis the punch deforms the blank into a shape similar to the lowest mode Therefore it is important that the time for the forming stage is greater than or equal to the time period for the lowest mode if you wish to model structural as opposed to localized deformation To perform a natural frequency extraction 1 Modify the MATERIAL option block to include the DENSITY suboption DENSITY 7800 1 2 Delete all data associated with the die holder and punch SURFACE RIGID BODY CONTACT PAIR etc These rigid parts
356. frequently during the simulation without using excessive disk space Remove the existing output requests from your input file and add the following output options which ensure that only selected output is saved during the nonlinear analysis To reduce the size of the output database file the FREQUENCY parameter is used on the OQUTPUT FIELD option in this simulation field output is written every second increment Thus the FREQUENCY parameter is set to 2 on the OUTPUT option OUTPUT FIELD FREQUENCY 2 VARIABLE PRESELECT The parameter VARIABLE PRESELECT indicates that a preselected set of the most commonly used field variables for a given type of analysis will be written to the output database odb file If you are simply interested in the final results set the FREQUENCY parameter equal to a large number Results are always stored at the end of each step regardless of the value of the FREQUENCY parameter therefore using a large value causes only the final results to be saved Request that the displacements of the nodes at the midspan be saved to the output database file These results will be used later to demonstrate the X Y plotting capability in Abaqus Viewer Use the default FREQUENCY value FREQUENCY 1 for this history output request for the output database file Here the NODE OUTPUT option must appear immediately after the history output request Remember to use the NSET or ELSET parameters when limiting the output being requ
357. g constraints would affect the solution only in the immediate vicinity of the constrained end The torsional stiffness of a beam with a solid cross section depends on the shear modulus G of the material and the torsion constant J of the beam section The torsion constant depends on the shape and the warping characteristics of the beam cross section Torsional loads that produce large amounts of inelastic deformation in the cross section cannot be modeled accurately with this approach Closed thin walled cross sections Beams that have closed thin walled non circular cross sections BOX or HEX have significant torsional stiffness and thus behave in a manner similar to solid sections Abaqus assumes that warping in these sections is also unconstrained The thin walled nature of the cross section allows Abaqus to consider the shear strains to be constant through the wall thickness The thin walled assumption is generally valid provided that the wall thickness is 1 10 a typical beam cross section dimension Examples of typical cross section dimensions for thin walled cross sections include 5 FORMULATION AND INTEGRATION e The diameter of a pipe section e The length of an edge of a box section e The typical edge length of an arbitrary section Open thin walled cross sections Open thin walled cross sections are very flexible in torsion when warping is unconstrained and the primary source of torsional stiffness in such structures is t
358. ge rotations but only small strains The general purpose shells allow the shell thickness to change with the element deformation All of the other shell elements assume small strains and no change in shell thickness even though the element s nodes may undergo finite rotations Triangular and quadrilateral elements with linear and quadratic interpolation are available Both linear and quadratic axisymmetric shell elements are available All of the quadrilateral shell elements except for S4 and the triangular shell element S3 S3R use reduced integration The S4 element and the other triangular shell elements use full integration Table 3 1 summarizes the shell elements available in Abaqus Standard All the shell elements in Abaqus Explicit are general purpose Finite membrane strain and small membrane strain formulations are available Triangular and quadrilateral elements are FINITE ELEMENTS Table 3 1 Three classes of shell elements in Abaqus Standard General Purpose Shells Thin Only Shells Thick Only Shells S4 S4R S3 S3R SAX1 SAX2 STRI3 STRI65 S4R5 S8R S8RT SAX2T SC6R SC8R S8R5 S9R5 SAXA available with linear interpolation A linear axisymmetric shell element is also available Table 3 2 summarizes the shell elements available in Abaqus Explicit Table 3 2 Two classes of shell elements in Abaqus Explicit Finite Strain Shells Small Strain Shells S4 S4R S3 S3R SAX1 S4RS S4RSW S3RS For most
359. ge the render style to facilitate your selection Click Done in the prompt area Click Plot in the XY Data from ODB Field Output dialog box to plot the nodal displacement as a function of time The history of the oscillation as shown in Figure 4 40 indicates that the displacements are small relative to the structure s dimensions Thus this problem could have been solved adequately using small deformation theory This would have reduced the computational cost of the simulation without significantly affecting the results Nonlinear geometric effects are discussed further in Chapter 8 Nonlinearity We are also interested in the stress history of the connecting lug The area of the lug near the built in end is of particular interest because the peak stresses expected to occur there may cause yielding in the material To generate a plot of Mises stress versus time 1 Plot the deformed shape of the lug again 4 45 EXAMPLE CONNECTING LUG Select this node Y a Figure 4 39 Selected node at the bottom of the hole Displacement D50 40 60 i li 1 ll f li 1 li L Oo 1 0 2 0 3 0 40 5 0 1 3 Time Figure 4 40 Displacement of a node at the bottom of the hole Select the Variables tab in the XY Data from ODB Field Output dialog box Deselect U2 as the variable for t
360. gh disk space and memory available to complete the analysis However it is possible to combine the datacheck and analysis phases of the simulation by using the command abaqus job frame interactive If a simulation is expected to take a substantial amount of time it is convenient to run it in the background by omitting the interactive parameter abaqus job frame The above commands apply for the standard Abaqus installation on a workstation However Abaqus jobs may be run in batch queues on some computers If you have any questions ask your systems administrator how to run Abaqus on your system 2 3 8 Results After the analysis is completed the data file frame dat will contain the tables of results requested with the NODE PRINT and EL PRINT options The tables of results follow the output from the datacheck analysis The results from the overhead hoist simulation follow Element output Two dimensional overhead hoist frame STEP 1 INCREMENT 1 10kN central load TIME COMPLETED IN THIS STEP 0 00 STEP 1 STATIC ANALYSIS 10kN central load FIXED TIME INCREMENTS TIME INCREMENT IS 2 220E 16 TIME PERIOD IS 2 220E 16 LINEAR EQUATION SOLVER TYPE DIRECT SPARSE THIS IS A LINEAR PERTURBATION STEP ALL LOADS ARE DEFINED AS CHANGE IN LOAD TO THE REFERENCE STATE 2 26 PROCESS NOTE 1 2 3 4 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST MEMORY ESTIMATE FLOATING PT MINIMUM MEMORY MEMORY TO OPERATIONS RE
361. ght service cargo crane is shown in Figure 6 11 You have been asked to determine the static deflections of the crane when it carries a load of 10 kN You should also identify the critical members and joints in the structure 1 e those with the highest stresses and loads Because this 1s a static analysis you will analyze the cargo crane using Abaqus Standard The crane consists of two truss structures joined together by cross bracing The two main members in each truss structure are steel box beams box cross sections Each truss structure is stiffened by internal bracing which 1s welded to the main members The cross bracing connecting the two truss 6 11 5 EXAMPLE CARGO CRANE Figure 6 11 Sketch of a light service cargo crane structures is bolted to the truss structures These connections can transmit little if any moment and therefore are treated as pinned joints Both the internal bracing and cross bracing use steel box beams with smaller cross sections than the main members of the truss structures The two truss structures are connected at their ends at point E in such a way that allows independent movement in the 3 direction and all of the rotations while constraining the displacements in the 1 and 2 directions to be the same The crane is welded firmly to a massive structure at points A B C and D The dimensions of the crane are shown in Figure 6 12 In the following figures truss A is the structure consisting of membe
362. gree of freedom should be constrained using the BOUNDARY option A shear force that does not act through the beam s shear center produces torsion The twisting moment is equal to the shear force multiplied by its eccentricity with respect to the shear center Often the centroid and the shear center do not coincide in open thin walled beam sections see Figure 6 10 If the nodes are not located at the shear center of the cross section the section may twist under loading 6 10 6 3 6 4 EXAMPLE CARGO CRANE F d es f Figure 6 10 Approximate locations of shear centers s and centroids c for a number of beam cross sections Selecting beam elements e First order shear deformable beam elements B21 B31 should be used in any simulation that includes contact e Ifthe transverse shear deformation is important use Timoshenko quadratic beam elements B22 B32 e If the structure is either very rigid or very flexible the hybrid beam elements B21H B32H etc available in Abaqus Standard should be used in geometrically nonlinear simulations e The Euler Bernoulli cubic beams B23 B33 available in Abaqus Standard are very accurate for simulations that include distributed loading such as dynamic vibration analyses e Structures with open thin walled cross sections should be modeled with the elements that use open section warping theory B310S B32OS available in Abaqus Standard Example cargo crane A li
363. gure 12 16 Dimensions in m of the components in the forming simulation elements are used so that better resolution of the deformation through the thickness of the blank will be obtained The node and element numbers for the mesh shown in Figure 12 18 are from the model of this problem given in Forming a channel with Abaqus Standard Section A 13 These node and element numbers are used in the discussion that follows Tools The tools are modeled with analytical rigid surfaces 12 5 3 Preprocessing creating the model The steps that follow assume that you have access to the full input file for this example This input file channel inp is provided in Forming a channel with Abaqus Standard Section A 13 in the online HTML version of this manual Instructions on how to fetch and run the script are given in Appendix A Example Files If you wish to create the entire model using Abaqus CAE please refer to Abaqus Standard 2 D example forming a channel Section 12 6 of Getting Started with Abaqus Interactive Edition 12 18 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL Figure 12 17 Mesh Node and element numbers increase by 1 Figure 12 18 Node and element numbers for the blank 12 19 5 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL 12 5 4 Reviewing the input file the model data We first review the model definition including the node and element definitions and section and material propert
364. gy D S dii aa ee ee E S A K S E E S 2 00 4 00 6 00 x10 Time Figure 13 11 Kinetic energy history for forming analysis attempt 2 The response of the kinetic energy is clearly related to the forming of the blank the value of kinetic energy peaks in the middle of the second step corresponding to the time when the punch velocity is the greatest Thus the kinetic energy is appropriate and reasonable The internal energy for attempt 2 shown in Figure 13 12 shows a smooth increase from zero up to the final value Again the ratio of kinetic energy to internal energy is quite small and appears to be acceptable Figure 13 13 compares the internal energy in the two forming attempts 13 5 3 Discussion of the two forming attempts Our initial criteria for evaluating the acceptability of the results was that the kinetic energy should be small compared to the internal energy What we found was that even for the most severe case attempt 1 this condition seems to have been met adequately The addition of a smooth step amplitude curve helped reduce the oscillations in the kinetic energy yielding a satisfactory quasi static response 13 16 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit o a PR 3 B 8 8 Internal Energy gt 8 S 2 00 4 00 6 00 p10 Time Figure 13 12 Internal energy history for forming analysis attempt 2 IE Attempt 1 IE Attempt 2 x10 2 00 1 60 Internal Energy
365. h com tw Thailand WorleyParsons Pte Ltd Singapore Tel 65 6735 8444 abaqus sg worleyparsons com Turkey A Ztech Ltd Istanbul Tel 90 216 361 8850 info a ztech com tr Complete contact information is available at http www simulia com locations locations html Contents 1 Introduction The Abaqus products Getting started with Abaqus Abaqus documentation Getting help Support A quick review of the finite element method 2 Abaqus Basics Components of an Abaqus analysis model Format of the input file Example creating a model of an overhead hoist Comparison of implicit and explicit procedures Summary 3 Finite Elements and Rigid Bodies Finite elements Rigid bodies Summary 4 Using Continuum Elements Element formulation and integration Selecting continuum elements Example connecting lug Mesh convergence Related Abaqus examples Suggested reading Summary 5 Using Shell Elements Element geometry Shell formulation thick or thin Shell material directions Selecting shell elements Example skew plate Related Abaqus examples CONTENTS 1 1 1 2 1 3 1 4 1 5 1 6 Zal Lie 2 2 4 25 3 1 3 2 3 3 4 1 4 2 4 3 4 4 4 5 4 6 4 7 5 1 32 53 5 4 5 5 5 6 CONTENTS Suggested reading sM Summary 5 8 6 Using Beam Elements Beam cross section geometry 6 1 Formulation and integration 6 2 Selecting beam elements 6 3 Example cargo crane 6 4 Related Abaqus examples 6 5 Suggested
366. h time dependent material response creep swelling viscoelasticity and two layer viscoplasticity when inertia effects can be neglected For more information on quasi static analysis in Abaqus Standard see Quasi static analysis Section 6 2 5 of the Abaqus Analysis User s Manual 13 1 Analogy for explicit dynamics To provide you with a more intuitive understanding of the differences between a slow quasi static loading case and a rapid loading case we use the analogy illustrated in Figure 13 1 The figure shows two cases of an elevator full of passengers In the slow case the door opens and you walk in To make room the occupants adjacent to the door slowly push their neighbors who push their neighbors and so on This disturbance passes through the elevator until the people next to the walls indicate that they cannot move A series of waves pass through the elevator until everyone has reached a new equilibrium position If you increase your speed slightly you will shove your neighbors more forcefully than before but in the end everyone will end up in the same position as in the slow case In the fast case the door opens and you run into the elevator at high speed permitting the occupants no time to rearrange themselves to accommodate you You will injure the two people directly in front of the door while the other occupants will be unaffected 13 1 LOADING RATES Fast Case Figure 13 1 Analogy for slow and fast load
367. hat we expect as a quasi static solution it is usually desirable to increase the loading time to 10 times the period of the lowest mode to be certain that the solution is truly quasi static To improve the results even further the velocity of the rigid cylinder could be ramped up gradually for example using a SMOOTH STEP amplitude definition thereby easing the initial impact 13 2 3 Metal forming problems Artificially increasing the speed of forming events is necessary to obtain an economical solution but how large a speedup can we impose and still obtain an acceptable static solution If the deformation of the sheet metal blank corresponds to the deformed shape of the lowest mode the time period of the lowest structural mode can be used as a guideline for forming speed However in forming processes the rigid dies and punches can constrain the blank in such a way that its deformation may not relate to the structural modes In such cases a general recommendation is to limit punch speeds to less than 1 of the sheet metal wave speed For typical processes the punch speed is on the order of 1 m s while the wave speed of steel is approximately 5000 m s This recommendation therefore suggests a factor of 50 as an upper bound on the speedup of the punch velocity The suggested approach to determining an acceptable punch velocity involves running a series of analyses at various punch speeds in the range of 3 to 50 m s Perform the analyses in the or
368. havior see Figure 10 14 Y A Figure 10 14 Contour of equivalent plastic strain PEEQ It is clear from the plot that there is gross yielding in the lug where it is attached to its parent structure The maximum plastic strain reported in the contour legend is about 10 However this value may contain errors from the extrapolation process Use the query tool O to check the integration point values of PEEQ in the elements with the largest plastic strains You will find that the largest equivalent plastic strains in the model are about 0 067 at the integration points This does not necessarily indicate a large extrapolation error since there are strain gradients present in the vicinity of the peak plastic deformation 10 23 5 EXAMPLE CONNECTING LUG WITH PLASTICITY Creating a variable variable stress strain plot The X Y plotting capability in Abaqus Viewer was introduced earlier in this manual In this section you will learn how to create X Y plots showing the variation of one variable as a function of another You will use the stress and strain data saved to the output database odb file to create a stress strain plot for one of the integration points in an element adjacent to the constrained end of the lug In the model used in this discussion the stress strain data were saved for element 206 You may have specified a different element number in your model if you did use that element number in place of 206 i
369. he Abaqus Analysis User s Manual for details on checking the validity of using shell theory Transverse shear force and strain are available for general purpose and thick only shell elements For three dimensional elements estimates of transverse shear stress are provided The calculation of 5 7 SHELL MATERIAL DIRECTIONS these stresses neglects coupling between bending and twisting deformation and assumes small spatial gradients of material properties and bending moments 5 3 Shell material directions Shell elements unlike continuum elements use material directions local to each element Anisotropic material data such as that for fiber reinforced composites and element output variables such as stress and strain are defined in terms of these local material directions In large displacement analyses the local material axes on a shell surface rotate with the average motion of the material at each integration point 5 3 1 Default local material directions The local material 1 and 2 directions lie in the plane of the shell The default local 1 direction is the projection of the global 1 axis onto the shell surface If the global 1 axis is normal to the shell surface the local 1 direction is the projection of the global 3 axis onto the shell surface The local 2 direction is perpendicular to the local 1 direction in the surface of the shell so that the local 1 direction local 2 direction and the positive normal to the surface form
370. he FREQUENCY parameter is omitted data are written every increment Restart files can become very large for large models so it is often useful to include the OVERLAY parameter to control the size of the restart file This parameter allows data to be overwritten on the restart file during a step 11 4 3 Reading a restart file When restarting a simulation from the end of a previous analysis use the READ parameter on the RESTART option You can also use the STEP and INC parameters to specify the particular point in the simulation s load history from which to restart the analysis When performing a restart simulation the RESTART option should appear immediately after the HEADING option No model data need appear in this restart input file since the model data for the analysis will be read from the restart file Only node set definitions element set definitions amplitude definitions and additional history data can be modified in the restart input file 11 17 RESTART ANALYSIS Continuing an interrupted run The new analysis continues directly from the specified step and increment of the previous analysis If the given step and increment do not correspond to the end of the previous analysis Abaqus will simulate all of the remaining previously defined load history data before trying to simulate any new load history data provided in the input file Therefore if an analysis was interrupted by a computer malfunction the following input file
371. he X Y data plot 3 Change the Position field to Integration Point 4 Click the arrow next to S Stress components and toggle on Mises as the stress variable for the X Y data Select the Elements Nodes tab Choose Pick from viewport as the selection method for identifying the element for which you want X Y data 4 46 EXAMPLE CONNECTING LUG 6 Click Edit Selection In the viewport select one of the elements near the built in end of the lug as shown in Figure 4 41 Click Done in the prompt area oa Figure 4 41 Selected element near the built in end of the lug hidden 7 Click Plot in the XY Data from ODB Field Output dialog box to plot the Mises stress at the selected element as a function of time The peak Mises stress is on the order of 550 MPa as shown in Figure 4 42 This value is larger than the typical yield strength of steel Thus the material would have yielded before experiencing such a large stress Material nonlinearity is discussed further in Chapter 10 Materials Mises stress Ou L L i L 1 ll No 1 0 20 3 0 40 5 0 x1 E 3 Time Figure 4 42 Mises stress near the built in end of the lug 4 47 MESH CONVERGENCE 4 4 Mesh convergence It is important that you use a sufficiently refined mesh to ensure that the results from your Aba
372. he boundary conditions constraints loads and output required and can be given in any order that is convenient Boundary conditions Boundary conditions are applied to those parts of the model where the displacements are known Such parts may be constrained to remain fixed have zero displacement during the simulation or may have specified nonzero displacements In either situation the constraints are applied directly to the nodes of the model 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST In some cases a node may be constrained completely and thus cannot move in any direction for example node 101 in our case In other cases a node is constrained in some directions but is free to move in others For example node 103 is fixed in the vertical direction but is free to move in the horizontal direction The directions in which a node is able to move are called degrees of freedom dof In the case of our two dimensional hoist each node can move in the global 1 and 2 directions therefore there are two degrees of freedom at each node If the hoist could move out of plane the problem would be three dimensional and each node would have three degrees of freedom Nodes attached to beam and shell elements have additional degrees of freedom representing the components of rotation and thus may have up to six degrees of freedom The labeling convention used for the degrees of freedom in Abaqus is as follows 1 Translation in the 1 direction
373. he computed response is stable during the step The user should ensure that a valid response has been obtained by carefully checking the energy history and other response variables 9 3 4 Mass scaling to control time incrementation Since the mass density influences the stability limit under some circumstances scaling the mass density can potentially increase the efficiency of an analysis For example because of the complex discretization of many models there are often regions containing very small or poorly shaped elements that control the stability limit These controlling elements are often few in number and may exist in localized areas By increasing the mass of only these controlling elements the stability limit can be increased significantly while the effect on the overall dynamic behavior of the model may be negligible The automatic mass scaling features in Abaqus Explicit can keep offending elements from hindering the stability limit There are two fundamental approaches used in mass scaling defining a scaling factor directly or defining a desired element by element stable time increment for the elements whose mass is to be scaled These two approaches described in detail in Mass scaling Section 11 6 1 of the Abaqus 9 8 EXAMPLE STRESS WAVE PROPAGATION IN A BAR Analysis User s Manual permit additional user control over the stability limit However use caution when employing mass scaling since significantly changing t
374. he constraint of the axial warping strains Constraining the warping of open thin walled beams introduces axial stresses that can affect the beam s response to other loading types Abaqus Standard has shear deformable beam elements B31OS and B32OS which include the warping effects in open thin walled sections These elements must be used when modeling structures with open thin walled cross sections such as a channel defined as an ARBITRARY section or an I section that are subjected to significant torsional loading The variation of the warping induced axial deformation over the beam s cross section is defined by the section s warping function The magnitude of this function is treated as an extra degree of freedom 7 in the open section beam elements Constraining this degree of freedom prevents warping at the nodes at which the constraints are applied So that the warping amplitude can be different in each branch the junction between open section beams in a frame structure generally should be modeled with separate nodes for each branch see Figure 6 9 Use separate nodes for the members connected at this location Constrain dof s 1 6 to be equal at the connection but keep the warping degree of freedom 7 independent and constrain it separately if necessary Figure 6 9 Connecting open section beams However if the connection is designed to prevent warping all branches should share a common node and the warping de
375. he mass of the model may change the physics of the problem 9 3 5 Effect of material on stability limit The material model affects the stability limit through its effect on the dilatational wave speed In a linear material the wave speed is constant therefore the only changes in the stability limit during the analysis result from changes in the smallest element dimension during the analysis In a nonlinear material such as a metal with plasticity the wave speed changes as the material yields and the stiffness of the material changes Abaqus Explicit monitors the effective wave speeds in the model throughout the analysis and the current material state in each element is used for stability estimates After yielding the stiffness decreases reducing the wave speed and consequently increasing the stability limit 9 3 6 Effect of mesh on stability limit Since the stability limit is roughly proportional to the shortest element dimension it 1s advantageous to keep the element size as large as possible Unfortunately for accurate analyses a fine mesh 1s often necessary To obtain the highest possible stability limit while using the required level of mesh refinement the best approach 1s to have a mesh that is as uniform as possible Since the stability limit is based on the smallest element dimension in the model even a single small or poorly shaped element can reduce the stability limit drastically For diagnostic purposes Abaqus Explicit provid
376. he nodes would have been written in the local coordinate system Check that the sum of the reaction forces and reaction moments with the corresponding applied loads is zero The nonzero reaction force in the 3 direction equilibrates the vertical force of the pressure load 20 kPa x 1 0 m x 0 4 m In addition to the reaction forces the pressure load causes self equilibrating reaction moments at the constrained rotational degrees of freedom The table of displacements which is not shown here shows that the mid span deflection across the plate is 5 3 cm which is approximately 5 of the plate s length By running this as a linear analysis we assume the displacements to be small It 1s questionable whether these displacements are truly small relative to the dimensions of the structure nonlinear effects may be important requiring further investigation In this case we need to perform a geometrically nonlinear analysis which is discussed in Chapter 8 Nonlinearity 5 20 5 5 8 EXAMPLE SKEW PLATE Postprocessing This section discusses postprocessing with Abaqus Viewer Both contour and symbol plots are useful for visualizing shell analysis results Since contour plotting was discussed in detail in Chapter 4 Using Continuum Elements we use symbol plots here Start Abaqus Viewer by typing the following command at the operating system prompt abaqus viewer odb skew By default Abaqus Viewer plots the undeformed shape of the
377. he output variable ALLAE is the accumulated artificial strain energy This discussion on hourglass control applies equally to shell elements Since energy is dissipated as plastic deformation as the plate deforms the total internal energy is much greater than the elastic strain energy alone Therefore it is most meaningful in this analysis to compare the artificial strain energy to an energy quantity that includes the dissipated energy as well as the elastic strain energy Such a variable is the total internal energy ALLIE which is a summation of all internal energy quantities The artificial strain energy is approximately 2 of the total internal energy indicating that hourglassing is not a problem One thing we can notice from the deformed shape is that the central stiffener is subject to almost pure in plane bending Using only two first order reduced integration elements through the depth of the stiffener is not sufficient to model in plane bending behavior While the solution from this coarse mesh appears to be adequate since there is little hourglassing for completeness we will study how the solution changes when we refine the mesh of the stiffener Use caution when you refine the mesh since mesh refinement will increase the solution time by increasing the number of elements and decreasing the element size An input file for a model with a refined stiffener mesh is included in Blast loading on a stiffened plate Section A 9 blast _ refin
378. he performance of Abaqus the tests are multiple element tests of simple geometries or simplified versions of real problems The NAFEMS benchmark problems are included in this manual Abaqus DOCUMENTATION Abaqus Verification Manual This manual contains basic test cases providing verification of each individual program feature procedures output options MPCs etc against exact calculations and other published results It may be useful to run these problems when learning to use a new capability In addition the supplied input data files provide good starting points to check the behavior of elements materials etc Abaqus Theory Manual This manual contains detailed precise discussions of all theoretical aspects of Abaqus It is written to be understood by users with an engineering background Abaqus Keywords Reference Manual This manual contains a complete description of all the input options that are available in Abaqus Standard Abaqus Explicit and Abaqus CFD Abaqus User Subroutines Reference Manual This manual contains a complete description of all the user subroutines available for use in Abaqus analyses It also discusses the utility routines that can be used when writing user subroutines Abaqus Glossary This manual defines technical terms as they apply to the Abaqus Unified FEA Product Suite Abaqus Release Notes This manual contains brief descriptions of the new features available in the latest release of the Abaqus
379. he plot appearance to obtain a plot similar to Figure 12 64 In Figure 12 64 it is clear that the postprocessing filter in Abaqus Viewer does not suffer from the time delay that occurs when filtering 1s performed while the analysis is running This is because the Abaqus Viewer filters are bidirectional which means that the filtering is applied first in a forward pass which introduces some time delay and then in a backward pass which removes the time delay As a consequence of the bidirectional filtering in Abaqus Viewer the filtering 1s essentially applied twice which results in additional attenuation of the filtered signal compared to the attenuation achieved with a single pass filter This is why the local peaks in the acceleration curve filtered in Abaqus Viewer are a bit lower than those in the curve filtered by Abaqus Explicit 12 85 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST A3 all butterworth cutoff_476Hz order2 33 ANTIALIASING N 403 NSET BOTCHIP LARGEINC A3_ANTIALIASING N 403 NSET CHIPS Vertical Acceleration m s 20 x1 E 3 Figure 12 64 Comparison of acceleration filtered in Abaqus Explicit and Abaqus Viewer To develop a better understanding of the Abaqus Viewer filtering capabilities return to the Operate on XY Data dialog box and filter the acceleration data with other filter options For example try different cutoff frequencies Can you confirm that the cutoff frequency of 2 4 kHz assoc
380. he ratio of its initial bulk modulus Ko to its initial shear modulus 4o Poisson s ratio v also provides a measure of compressibility since it is defined as _ 3 Ko to 2 6 Ko po 2 Table 10 2 provides some representative values Table 10 2 Relationship between compressibility and Poisson s ratio 0 452 ee S If no value is given for the material compressibility by default Abaqus Explicit assumes Ko 19 20 corresponding to Poisson s ratio of 0 475 Since typical unfilled elastomers have Kg ig ratios in the range of 1 000 to 10 000 v 0 4995 to v 0 49995 and filled elastomers have K 19 ratios in the range of 50 to 200 v 0 490 to v 0 497 this default provides much more compressibility than is available in most elastomers However if the elastomer 1s relatively unconfined this softer modeling of the material s bulk behavior usually provides quite accurate results Unfortunately in cases where the material is highly confined such as when it is in contact with stiff metal parts and has a very small 10 52 HYPERELASTICITY amount of free surface especially when the loading is highly compressive it may not be feasible to obtain accurate results with Abaqus Explicit If you are defining the compressibility rather than accepting the default value in Abaqus Explicit an upper limit of 100 is suggested for the ratio of Ko jo Larger ratios introduce high frequency noise into the dynamic solution
381. he stress in the truss and the reaction force at the constrained end of the truss In this case the rod shown in Figure 1 3 will be modeled with two truss elements In Abaqus truss elements can carry axial loads only The discretized model is shown in Figure 1 4 together with the node and element labels A QUICK REVIEW OF THE FINITE ELEMENT METHOD Element 1 Node a Element 2 Node c Figure 1 4 Discretized model of the truss problem Free body diagrams for each node in the model are shown in Figure 1 5 In general each node will carry an external load applied to the model P and internal loads I caused by stresses in the elements attached to that node For a model to be in static equilibrium the net force acting on each node must be zero 1 e the internal and external loads at each node must balance each other For node a this equilibrium equation can be obtained as follows R h D p eo Node a b b _ C C P lt _ _o _ gt Node b Node c Figure 1 5 Free body diagram for each node Assuming that the change in length of the rod is small the strain in element 1 is given by 11 T where u and u are the displacements at nodes a and b respectively and L is the original length of the element Assuming that the material is elastic the stress in the rod is given by the strain multiplied by the Young s modulus E 011 Bey 5 A QUICK REVIEW OF THE FINITE ELEMENT METHOD The axia
382. he table of stresses in the data file skew dat An excerpt from the table is shown below THE FOLLOWING TABLE IS PRINTED FOR ALL ELEMENTS WITH TYPE S8R5 AT THE INTEGRATION POINTS ELEMENT PT SEC FOOT S11 S22 12 PT NOTE 1 1 1 OR 4 2759E 07 9 3051E 06 6 7584E 06 1 1 3 OR 4 2759E 07 9 3051E 06 6 7584E 06 1 2 1 OR 7 4724E 07 2 7832E 06 1 0599E 07 1 2 3 OR 7 4724E 07 2 7832E 06 1 0599E 07 1 3 1 OR 7 3273E 07 2 8832E 07 2 1403E 07 1 3 3 OR 7 3273E 07 2 8832E 07 2 1403E 07 1 4 1 OR 8 2885E 07 1 8951E 07 1 4786E 07 1 4 3 OR 8 2885E 07 1 8951E 07 1 4786E 07 114 1 1 OR 8 2885E 07 1 8951E 07 1 4786E 07 114 1 3 OR 8 2885E 07 1 8951E 07 1 4786E 07 114 2 1 OR 7 3273E 07 2 8832E 07 2 1403E 07 114 2 3 OR 7 3273E 07 2 8832E 07 2 1403E 07 114 3 1 OR 7 4724E 07 2 7832E 06 1 0599E 07 114 3 3 OR 7 4724E 07 2 7832E 06 1 0599E 07 114 4 1 OR 4 2759E 07 9 3051E 06 6 7584E 06 114 4 3 OR 4 2759E 07 9 3051E 06 6 7584E 06 MAXIMUM 2 3826E 08 1 0326E 08 7 0025E 07 ELEMENT 4 4 4 MINIMUM 2 3826E 08 1 0326E 08 7 0025E 07 ELEMENT 4 4 4 OR ORIENTATION USED FOR THIS ELEMENT 5 19 5 EXAMPLE SKEW PLATE The second column SEC PT section point identifies the location in the element where the stress was calculated Section point lies on the SNEG surface of the shell and section point 3 lies on the SPOS surface The letters OR appear in the FOOTNOTE column indicating that an ORIENTATION option has been used for the element the stresse
383. hese terms are quite small and the regular symmetric solver works well unless the contact surface has high curvature For higher coefficients of friction the unsymmetric solver is invoked automatically because it will improve the convergence rate The unsymmetric solver requires twice as much computer memory and scratch disk space as the symmetric solver The unsymmetric solver can also be selected by including the UNSYMM YES parameter on the STEP option Large values of u generally do not cause any difficulties in Abaqus Explicit 12 4 INTERACTION BETWEEN SURFACES Figure 12 3 Exponential decay friction model 12 2 4 Other contact interaction options The other contact interaction models available in Abaqus depend on the analysis product and the algorithm used and may include adhesive contact behavior softened contact behavior fasteners for example spot welds and viscous contact damping These options are not discussed in this guide Details about them can be found in the Abaqus Analysis User s Manual 12 2 5 Surface based constraints Tie constraints are used to tie together two surfaces for the duration of a simulation Each node on the slave surface is constrained to have the same motion as the point on the master surface to which it is closest For a structural analysis this means the translational and optionally the rotational degrees of freedom are constrained Abaqus uses the undeformed configuration of the model to
384. hey will generally generate too much unnecessary output 4 20 EXAMPLE CONNECTING LUG You were asked to determine the deflection of the connecting lug when the load is applied A simple method for obtaining this result is to print out all the displacements in the model However it is likely that the location on the lug with the largest deflection is probably going to be on the bottom of the hole where the load is applied Furthermore only the displacement in the 2 direction U2 is going to be of interest You should have created a node set HOLEBOT containing those nodes Use that set to limit the requested displacements to just those five nodes at the bottom of the hole and to limit the output to just the vertical displacements NODE PRINT NSET HOLEBOT U2 It is good practice to check that the reaction forces at the constraints balance the applied loads All the reaction forces at a node can be printed by specifying the variable RF We again use the node set LHEND to limit the output to those nodes that are constrained NODE PRINT NSET LHEND TOTAL YES SUMMARY NO RF You can define several NODE PRINT and EL PRINT options The parameter TOTALS YES causes the sum of the reaction forces at all the nodes in the node set to be printed The SUMMARY NO parameter prevents the minimum and maximum values in the table from being printed The following commands print the stress tensor variable S and the Mises stress variable MIS
385. hile it is running The message file contains the details of the load incrementation and iterations Results can be saved at the end of each increment so that the evolution of the structure s response can be visualized in Abaqus Viewer Results can also be plotted in the form of X Y graphs 8 28 TYPES OF PROBLEMS SUITED FOR Abaqus Explicit 9 Nonlinear Explicit Dynamics In previous chapters you explored the basics of explicit dynamics procedures in this chapter you will examine this topic in greater detail The explicit dynamics procedure can be an effective tool for solving a wide variety of nonlinear solid and structural mechanics problems It is often complementary to an implicit solver such as Abaqus Standard From a user standpoint the distinguishing characteristics of the explicit and implicit methods are e Explicit methods require a small time increment size that depends solely on the highest natural frequencies of the model and is independent of the type and duration of loading Simulations generally take on the order of 10 000 to 1 000 000 increments but the computational cost per increment is relatively small e Implicit methods do not place an inherent limitation on the time increment size increment size 1s generally determined from accuracy and convergence considerations Implicit simulations typically take orders of magnitude fewer increments than explicit simulations However since a global set of equations must be so
386. his section you will use the contour plotting capability of Abaqus Viewer to display the von Mises stress and equivalent plastic strain distributions in the plate Use the model with the refined stiffener mesh to create the plots To generate contour plots of the von Mises stress and equivalent plastic strain 1 From the list of variable types on the left side of the Field Output toolbar select Primary 10 45 5 EXAMPLE BLAST LOADING ON A STIFFENED PLATE 50 00 40 00 30 00 20 00 Original mm Refined Displacement mm 10 00 0 00 0 00 0 01 0 02 0 03 0 04 0 05 Time s Figure 10 31 Central node displacement history for the original and refined meshes 2 From the list of output variables in the center of the toolbar select S The stress invariants and components are available in the next list to the right Select the Mises stress invariant 3 From the main menu bar select Result Section Points 4 In the Section Points dialog box that appears select Top and bottom as the active locations and click OK 5 Select Plot Contours On Deformed Shape or use the IN tool from the toolbox Abaqus plots the contours of the von Mises stress on both the top and bottom faces of each shell element To see this more clearly rotate the model in the viewport The view that you set earlier for the animation exercise should be changed so that the stress distribution is clearer Y 6 Change the view back to
387. i 0 00 2 00 4 00 6 00 b10 Time Figure 13 13 Comparison of internal energies for the two attempts of the forming analysis The additional requirements that the histories of kinetic energy and internal energy must be appropriate and reasonable are very useful and necessary but they also increase the subjectivity of 13 17 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit evaluating the results Enforcing these requirements in general for more complex forming processes may be difficult because these requirements demand some intuition regarding the behavior of the forming process Results of the forming analysis Now that we are satisfied that the quasi static solution for the forming analysis is adequate we can study some of the other results of interest Figure 13 14 shows a comparison of the Mises stress in the blank obtained with Abaqus Standard and Abaqus Explicit S Mises S Mises Avg 75 Avg 75 4 778e 08 2 419e 06 Figure 13 14 Contour plot of Mises stress in Abaqus Standard left and Abaqus Explicit right channel forming analyses The plot shows that the peak stresses in the Abaqus Standard and Abaqus Explicit analyses are within 1 of each other and that the overall stress contours of the blank are very similar To further examine the validity of the quasi static analysis results you should compare the equivalent plastic strain results and final deformed shapes from the two an
388. ialog box appears 3 Set the Arrowhead option to use filled arrowheads in the triad 4 Click OK to apply the settings and to close the dialog box 5 Use the predefined views available in the Views toolbar to display the plate as shown in Figure 5 17 In this figure perspective is turned off To turn off perspective click the tool in the View Options toolbar 5 25 5 EXAMPLE SKEW PLATE Tip If the Views toolbar is not visible select View Toolbars Views from the main menu bar By default the material 1 direction is colored blue the material 2 direction is colored yellow and if it is present the material 3 direction is colored red pE w ur de lt g lt v T N X hT I at v y r p3 w i i An S WW x i y Ww A xX x 4 ex 7N w KY rA ay Ne 7 4 ead XS w y Bd e wk aan EOK ar Aor ar on te or AA LY x Ar tur w A Ww Ur 4 ON et Pl as Od Ol ba 4 Cr r Cow r Ce A ON eT Ue SN oN Ne W Uw ae et a Se Ne r AY yr X x re Cee NA D Y Pa a ei v dw iv wr Ar A Cr w cal x w we A N RA SA ad XN y bd a y a ot X wx e e ae tv Ww A A Y Ww tw ar tw tw tw 4m ma On ENEN pes bi z w ae at p e yw Ar r Ur a wN Ww re Cr we Oy Wa x ae ET N Wer A Ye Or Cr amp Ne Ne veg ee Nee We X Y W uv aw y
389. iated with the built in anti aliasing filter with a time increment size of 0 07 was appropriate Does increasing the cutoff frequency to 6 kHz 7 kHz or even 10 kHz produce significantly different results You should find that a moderate increase in the cutoff frequency does not have a significant effect on the results implying that we probably have not missed physically meaningful frequency content when we filtered with a cutoff frequency of 2 4 kHz Compare the results of filtering the acceleration data with Butterworth and Chebyshev Type I filters The Chebyshev filter requires a ripple factor parameter rippleF actor which indicates how much oscillation you will allow in exchange for an improved filter response see Filtering output and operating on output in Abaqus Explicit in Output to the output database Section 4 1 3 of the Abaqus Analysis User s Manual for more information For the Chebyshev Type I filter a ripple factor of 0 071 will result in a very flat pass band with a ripple that is only 0 5 You may not notice much difference between the filters when the cutoff frequency is 5 kHz but what about when the cutoff frequency is 2 kHz What happens when you increase the order of the Chebyshev Type I filter Compare your results to those shown in Figure 12 65 12 86 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST A3 all chebyshev1 cutoff_2kHz order2 A3 all chebyshev1 cutoff_2kHz order6 A3 all butterworth cutoff
390. ic elements in models with such geometries because they show much less sensitivity to mesh distortion In a severely distorted mesh however simply changing the element type will generally not produce accurate results The mesh distortion should be minimized as much as possible to improve the accuracy of the results 5 SELECTING CONTINUUM ELEMENTS 4 1 4 Hybrid elements A hybrid element formulation is available for just about every type of continuum element in Abaqus Standard including all reduced integration and incompatible mode elements Hybrid elements are not available in Abaqus Explicit Elements using this formulation have the letter H in their names Hybrid elements are used when the material behavior is incompressible Poisson s ratio 0 5 or very close to incompressible Poisson s ratio gt 0 475 Rubber is an example of a material with incompressible material behavior An incompressible material response cannot be modeled with regular elements except in the case of plane stress because the pressure stress in the element is indeterminate Consider an element under uniform hydrostatic pressure Figure 4 13 Uniform pressure Figure 4 13 Element under hydrostatic pressure If the material is incompressible its volume cannot change under this loading Therefore the pressure stress cannot be computed from the displacements of the nodes and thus a pure displacement formulation is inadequate for any element w
391. ickness of beams and shells 12 Temperature at other points through the thickness of beams and shells Directions 1 2 and 3 correspond to the global 1 2 and 3 directions respectively unless a local coordinate system has been defined at the nodes Axisymmetric elements are the exception with the displacement and rotation degrees of freedom referred to as follows l Translation in the r direction 2 Translation in the z direction 6 Rotation in the r z plane Directions r radial and z axial correspond to the global 1 and 2 directions respectively unless a local coordinate system has been defined at the nodes See Chapter 5 Using Shell Elements for a discussion of defining a local coordinate system at the nodes In this guide our attention is restricted to structural applications Therefore only elements with translational and rotational degrees of freedom are discussed For information on other types of elements for example heat transfer elements consult the Abaqus Analysis User s Manual By default Abaqus CAE uses the alphabetical option z y z for labeling the view orientation triad In general this manual adopts the numerical option 1 2 3 to permit direct correspondence with degree of freedom and output labeling For more information on labeling of axes see Customizing the view triad Section 5 4 of the Abaqus CAE User s Manual Number of nodes order of interpolation Displacements rotations temp
392. ient to apply the constraints directly to a node set containing all the nodes Thus in the lug model we prefer to create the node set LHEND to specify the constraints BOUNDARY LHEND ENCASTRE If you think that you defined the boundary conditions incorrectly you can display them in Abaqus Viewer and compare them with the boundary conditions shown in Figure 4 19 The postprocessing instructions given at the end of Postprocessing Section 2 3 9 discuss how to do this Loading The lug carries a pressure of 50 MPa distributed around the bottom half of the hole Pressure loads can be defined conveniently using the preprocessor by selecting the element faces to which the load is applied In the connecting lug input file these loads will appear as a DLOAD option block For example the DLOAD option block for the connecting lug may look like DLOAD 1 P6 5 E 07 2 P6 5 E 07 3 P6 5 E 07 4 P6 5 E 07 13 P6 5 E 07 1015 P6 5 E 07 1016 P6 5 E 07 4 19 5 EXAMPLE CONNECTING LUG The format of each data line is lt element or element set name gt lt load ID gt lt load magnitude gt In this case the load ID consists of the letter P followed by the number of the element face to which pressure is applied The face numbers depend on the connectivity of the element and are defined for each element type in the Abaqus Analysis User s Manual For the three dimensional hexahedral elements used in this example
393. ies Model description The input file starts with a relevant description of the simulation and model in the HEADING option HEADING Analysis of the forming of a channel SI units N kg m s Nodal coordinates and element connectivity Check that the preprocessor used the correct element type for the blank Provide a meaningful element set name such as BLANK for the elements The ELEMENT option in this model follows ELEMENT TYPE CPE4R ELSET BLANK The model definition also specifies the creation of node sets so that parts of the model can be constrained and moved easily These nodes are located on the centerline of the blank and have symmetric constraints into a node set called CENTER NSET NSET CENTER 1 102 203 304 405 The node along the middle of the sheet at the left hand side of the model underneath the punch is included in node set MIDLEFT NSET NSET MIDLEFT 203 Again the node numbers in these option blocks are for the model in Figure 12 18 your node numbers may be different Two element sets BLANK_B and BLANK_T will be defined that contain the lower and upper rows of elements in the blank These will be used to define the contact surfaces on the blank ELSET ELSET BLANK B GENERATE 1 100 1 ELSET ELSET BLANK T GENERATE 301 400 1 12 20 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL Section and material properties for the blank The blank is made from a high strength steel elastic m
394. ified in an Abaqus Standard analysis cannot be imported into an Abaqus Explicit analysis and vice versa see Transferring results between Abaqus Explicit and Abaqus Standard Section 9 2 2 of the Abaqus Analysis User s Manual 12 12 Related Abaqus examples e Indentation of a crushable foam plate Section 3 2 10 of the Abaqus Benchmarks Manual e Pressure penetration analysis of an air duct kiss seal Section 1 1 16 of the Abaqus Example Problems Manual e Deep drawing of a cylindrical cup Section 1 3 4 of the Abaqus Example Problems Manual 12 13 Suggested reading The following references provide additional information on contact analysis with finite element methods They allow the interested user to explore the topic in more depth General texts on contact analysis e Belytschko T W K Liu and B Moran Nonlinear Finite Elements for Continua and Structures Wiley amp Sons 2000 e Crisfield M A Non linear Finite Element Analysis of Solids and Structures Volume IT Advanced Topics Wiley amp Sons 1997 e Johnson K L Contact Mechanics Cambridge 1985 e Oden J T and G F Carey Finite Elements Special Problems in Solid Mechanics Prentice Hall 1984 12 92 SUMMARY General text on digital signal proccesing e Stearns S D and R A David Signal Processing Algorithms in MATLAB Prentice Hall P T R 1996 12 14 Summary e Contact analyses require a careful logical app
395. ify Reaction Force RF2 as the Y axis label and Total Time as the X axis label 5 Click Dismiss to close the dialog box The punch force shown in Figure 12 23 rapidly increases to about 160 kN during Step 2 which runs from a total time of 1 0 to 2 0 History plot of the stabilization and internal energies It is important to verify that the presence of contact stabilization does not significantly alter the physics of the problem One way to assess this requirement is to compare the energy dissipation due to stabilization ALLSD against the internal energy of the structure ALLIE Ideally the amount of stabilization energy should be a small fraction of the internal energy Figure 12 24 shows the variation of the stabilization and internal energies It is clear that the dissipated stabilization energy is indeed small x1 E3 1 5 ALLIE Whole Model ALLSD Whole Model 0 0 0 0 Figure 12 24 Stabilization and internal energies 12 32 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL Plotting contours on surfaces Abaqus Viewer includes a number of features designed specifically for postprocessing contact analyses The Display Group feature can be used to collect surfaces into display groups similar to element and node sets To display contact surface normal vectors 1 2 Plot the undeformed model shape In the Results Tree expand the Surface Sets container Select the surfaces named BLANK T and P
396. igid body motion of the components before contact conditions constrain them and sudden changes in contact conditions which lead to severe discontinuity iterations as Abaqus Standard tries to establish the exact condition of all contact surfaces Therefore wherever possible take precautions to avoid these situations Removing rigid body motion is not particularly difficult Simply ensure that there are enough constraints to prevent all rigid body motions of all the components in the model This approach may mean using boundary conditions initially to get the components into contact instead of applying loads directly Using this approach may require more steps than originally anticipated but the solution of the problem should proceed more smoothly Alternatively contact controls may be used to stabilize rigid body motion automatically With this approach Abaqus Standard applies viscous damping to the slave nodes of the contact pair Care must be taken however to ensure that the viscous damping does not significantly alter the physics of the problem as will be the case if the dissipated stabilization energy and contact damping stresses are sufficiently small The simulation will consist of two steps Since the simulation involves material geometric and boundary nonlinearities general steps must be used In addition the forming process is quasi static thus we can ignore inertia effects throughout the simulation Rather than use additional steps
397. igure 4 43 Different meshes for the connecting lug problem 4 48 MESH CONVERGENCE We consider the influence of the mesh density on three particular results from this model e The displacement of the bottom of the hole e The peak Mises stress at the stress concentration on the bottom surface of the hole e The peak Mises stress where the lug is attached to the parent structure The locations where the results are compared are shown in Figure 4 44 Mises 3 13 ae7eto8 attachment 2 200e 08 1 933e 08 _ 1 667e 08 gt m a von Mises stress on bottom surface of hole 43 771e 08 von Mises stress at 3 000e 08 6 000e 07 E 8 872e 06 2 Displacement of bottom of hole q Step Step 1 sea 1 Step Time 2 2200E 16 3 Primary Var S Mi Deformed Var U Defotiati ion Scale Factor 2 968e 01 Figure 4 44 Locations where results are compared in the mesh refinement study The results for each of the four mesh densities are compared in Table 4 3 along with the CPU time required to run each simulation Table 4 3 Results of mesh refinement study Displacement of Stress at Stress at Relative D n of hole Do of hole ee a time Coarse 3 07E 4 O7E 4 256 E6 E6 3126 12 E6 083 83 4 49 MESH CONVERGENCE The coarse mesh predicts less accurate displacements at the bottom of hole but the normal fine and very fine meshes all predict similar results The normal mesh 1s therefore co
398. igure 7 1 Mass spring system This mass spring system has a natural frequency in radians time given by w 1 m If the mass is moved and then released it will oscillate at this frequency If the force is applied at this frequency the amplitude of the displacement will increase dramatically a phenomenon known as resonance Real structures have a large number of natural frequencies It is important to design structures in such a way that the frequencies at which they may be loaded are not close to the natural frequencies The natural frequencies can be determined by considering the dynamic response of the unloaded structure P 0 in the dynamic equilibrium equation The equation of motion is then Mu I 0 For an undamped system J Ku so Mu Ku 0 Solutions to this equation have the form oe Substituting this into the equation of motion yields the eigenvalue problem K AM where w This system has n eigenvalues where n is the number of degrees of freedom in the finite element model Let A be the jth eigenvalue Its square root w is the natural frequency of the jth mode of the structure and is the corresponding jth eigenvector The eigenvector is also known as the mode shape because it is the deformed shape of the structure as it vibrates in the jth mode 1 2 INTRODUCTION In Abaqus the FREQUENCY procedure is used to extract the modes and frequencies of the structure This procedure is
399. igure 7 7 2 pe Step Step 1 Frequency extraction of the first 30 modes 1 Mode 1 Value 1773 4 Freq 6 7023 cycles time Deformed Var U Deformation Scale Factor 8 000e 01 3 Figure 7 7 Mode 1 4 Select the third mode frame 3 in Step 1 from the Frame Selector dialog box Afterward close the dialog box Abaqus Viewer displays the third mode shape shown in Figure 7 8 7 17 5 EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING 2 Pa Step Step 1 Frequency extraction of the first 30 modes 1 Mode 3 Value 7647 5 Freq 13 918 cycles time Deformed Var U Deformation Scale Factor 8 000e 01 3 Figure 7 8 Mode 3 Note A complete list of the available frames is given in the Step Frame dialog box Result Step Frame This dialog box offers an alternative means to switching between frames Animation of results You will animate the analysis results First create a scale factor animation of the third eigenmode Then create a time history animation of the transient results To create a scale factor animation of an eigenmode lt O 1 From the main menu bar select Animate Scale Factor or use the tool in the toolbox Abaqus Viewer displays the third mode shape and steps through different deformation scale factors ranging from 0 to 1 Abaqus Viewer also displays the movie player controls on the right side of the context bar 2 In the context bar click i to pause the animation 7 18 EXAMPLE
400. image From the main menu bar select Options Superimpose or use the aly tool in the toolbox to change the edge style of the superimposed 1 e undeformed image From the Superimpose Plot Options dialog box click the Color amp Style tab In the Color amp Style tabbed page select the dashed edge style Click OK to close the Superimpose Plot Options dialog box and to apply the change The plot is shown in Figure 2 12 The undeformed model shape appears with a dashed edge style Figure 2 12 Undeformed and deformed model shapes Checking the model with Abaqus Viewer You can use Abaqus Viewer to check that the model is correct before running the simulation You have already learned how to draw plots of the model and to display the node and element numbers These are useful tools for checking that Abaqus is using the correct mesh The boundary conditions applied to the overhead hoist model can also be displayed and checked 2 33 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST To display boundary conditions on the undeformed model o Click the i tool in the toolbox to disable multiple plot states in the viewport Display the undeformed model shape if it 1s not displayed already From the main menu bar select View ODB Display Options 1 2 3 4 In the ODB Display Options dialog box click the Entity Display tab 5 Toggle on Show boundary conditions 6 Click OK Abaqus Viewer displays symbols
401. ime specifies the proportion of load applied in the first increment The initial load increment is given by Alama x Load magnitude Total The choice of initial time increment can be critical in certain nonlinear simulations in Abaqus Standard but for most analyses an initial increment size that is 5 to 10 of the total step time is usually sufficient In static simulations the total step time is usually set to 1 0 for convenience unless for example rate dependent material effects or dashpots are included in the model With a total step time of 1 0 the proportion of load applied is always equal to the current step time 1 e 50 of the total load is applied when the step time is 0 5 Although you must specify the initial increment size in Abaqus Standard Abaqus Standard automatically controls the size of the subsequent increments This automatic control of the increment size is suitable for the majority of nonlinear simulations performed with Abaqus Standard although further controls on the increment size are available Abaqus Standard will terminate an analysis if excessive cutbacks caused by convergence problems reduce the increment size below the minimum value The default minimum allowable time increment ATmin is 10 times the total step time By default Abaqus Standard has no upper limit on the increment size AT magz other than the total step time Depending on your Abaqus Standard simulation you may want to specify different mi
402. imulations that you want to perform when planning your computer resources 8 2 3 Automatic incrementation control in Abaqus Standard Abaqus Standard automatically adjusts the size of the load increments so that it solves nonlinear problems easily and efficiently You only need to suggest the size of the first increment in each step of your simulation Thereafter Abaqus Standard automatically adjusts the size of the increments If you do not provide a suggested initial increment size Abaqus Standard will try to apply all of the loads defined in the step in the first increment In highly nonlinear problems Abaqus Standard will have to reduce the increment size repeatedly resulting in wasted CPU time Generally it is to your advantage to provide a reasonable initial increment size see Modifications to the input file the history data Section 8 4 1 for an example only in very mildly nonlinear problems can all of the loads in a step be applied in a single increment The number of iterations needed to find a converged solution for a load increment will vary depending on the degree of nonlinearity in the system By default if the solution appears to diverge Abaqus Standard abandons the increment and starts again with the increment size set to 25 of its previous value An attempt is then made at finding a converged solution with this smaller load increment If the increment still fails to converge Abaqus Standard reduces the increment size again
403. imum compressive nominal strain is about 56 Because the nominal strains in the model remained within the range where the Abaqus hyperelasticity model has a good fit to the material data you can be fairly confident that the response predicted by the mount is reasonable from a material modeling viewpoint 10 8 Mesh design for large distortions We know that the element distortions in the corners of the rubber mount are undesirable The results in these areas are unreliable and if the load were increased the analysis might fail These problems can be corrected by using a better mesh design The mesh shown in Figure 10 56 is an example of an alternate mesh design that might be used to reduce element distortion in the bottom left corner of the rubber model 10 77 5 MESH DESIGN FOR LARGE DISTORTIONS ee NN H Ha a a Figure 10 56 Modified mesh to minimize element distortions in the bottom left corner of the rubber model during the simulation of r Cl The issues surrounding the mesh distortion in the opposite corner are addressed in Techniques for reducing volumetric locking Section 10 9 The elements in the bottom left hand corne
404. in Abaqus You can use any number of different materials in your simulation Each material definition starts with a MATERIAL option The NAME parameter identifies the name associated with the material being defined This name is used to assign the material definition to specific elements in the model The material definition is one of the few situations in which the position of option blocks in the Abaqus input file is important All of the option blocks defining specific aspects of a material s behavior such as its elastic modulus or density must follow the MATERIAL option directly Furthermore the material option blocks defining the behavior of a particular material cannot be interrupted by other nonmaterial options Abaqus issues an error message if it cannot associate a material behavior option block such as ELASTIC with a prior MATERIAL option For example consider a material description such as an elastic plastic metal subjected to gravitational loads that requires several material behavior option blocks to supply Abaqus with the necessary data In addition to the elastic and plastic property option blocks Abaqus needs the material s density to calculate the gravitational loads Thus the complete material description would be MATERIAL NAME STEEL ELASTIC t Elastic properties 2 1E11 0 3 PLASTIC lt Plastic properties 2 0E8 0 0 3 0H8 0 2 DENSITY lt Density 7800 0 A non material option block be
405. in a shell element name indicates the number of nodes in the element except for the case of axisymmetric shells for which the first number indicates the order of interpolation Two types of shell elements are available in Abaqus conventional shell elements and continuum shell elements Conventional shell elements discretize a reference surface by defining the element s planar dimensions its surface normal and its initial curvature Continuum shell elements on the other hand resemble three dimensional solid elements in that they discretize an entire three dimensional body yet are formulated so that their kinematic and constitutive behavior is similar to conventional shell elements In this manual only conventional shell elements are discussed Henceforth we will refer to them simply as shell elements For more information on continuum shell elements see Shell elements overview Section 29 6 1 of the Abaqus Analysis User s Manual The use of shell elements is discussed in detail in Chapter 5 Using Shell Elements Shell element library In Abaqus Standard general three dimensional shell elements are available with three different formulations general purpose thin only and thick only The general purpose shells and the axisymmetric shells with asymmetric deformation account for finite membrane strains and arbitrarily large rotations The three dimensional thick and thin element types provide for arbitrarily lar
406. in the global coordinate system Define the nodes for the rigid surface so that it is large enough to keep the deformable bodies from falling off any of its edges Use a 0 1 mm vertical clearance from the bottom corner of the foam packaging to ensure that there is no initial overclosure of the contact surfaces Element properties Give each element set appropriate section properties Include the appropriate MATERIAL parameter on each section option so that each set of elements 1s linked to a material definition We have named the foam packaging material FOAM and we will define it in the next section SOLID SECTION ELSET PACK MATERIAL FOAM CONTROLS HGLASS SECTION CONTROLS NAME HGLASS HOURGLASS ENHANCED For the circuit board it is most meaningful to output stress results in the longitudinal and lateral directions aligned with the edges of the board Therefore we need to specify local material directions for the circuit board mesh We can use the same local coordinate system that we previously defined using the SYSTEM option The desired material directions can be achieved using the ORIENTATION option with the DEFINITION COORDINATES parameter On the first data line specify the x y and z coordinates of two points a and b respectively to define the local coordinate system On the second data line specify an additional rotation of 90 about the local 2 or y axis The name of the ORIENTATION is then referred to on the SHELL SECTION
407. in the viewport Thus begin by creating and saving display groups for each region of interest 4 35 5 EXAMPLE CONNECTING LUG To create and save a display group containing the elements at the built in end 1 In the Results Tree double click Display Groups 2 Choose Elements from the Item list and Pick from viewport as the selection method 3 4 In the prompt area set the selection method to by angle and click the built in face of the lug Restore the option to select entities closest to the screen Click Done when all the elements at the built in face of the lug are highlighted in the viewport In the Create Display Group dialog box click Save Selection As Save the display group as built in elements To create and save a display group containing the nodes at the built in end 1 2 In the Create Display Group dialog box choose Nodes from the Item list and Pick from viewport as the selection method In the prompt area set the selection method to by angle and click the built in face of the lug Click Done when all the nodes on the built in face of the lug are highlighted in the viewport In the Create Display Group dialog box click Save Selection As Save the display group as built in nodes To create and save a display group containing the nodes at the bottom of the hole 1 2 In the Create Display Group dialog box click Edit Selection to select a different group of nodes In the prompt area
408. in the Free Body Cut Manager 4 34 EXAMPLE CONNECTING LUG 11 From the Free Body Plot Options dialog box select the Force tab in the Color amp Style tabbed page Click the resultant color sample to change the color of the resultant force arrow 12 Once you have selected a new color for the resultant force arrow click OK in the Free Body Plot Options dialog box and click Dismiss in the Free Body Cut Manager The free body cut is displayed in the viewport as shown in Figure 4 34 why o j Figure 4 34 Free body cut displayed on the connecting lug Generating tabular data reports for subsets of the model Tabular output data were generated earlier for this model using printed output requests However for complicated models it is convenient to write these data for selected regions of the model using Abaqus Viewer This is achieved using display groups in conjunction with the report generation feature For the connecting lug problem we will generate the following tabular data reports e Stresses in the elements at the built in end of the lug to determine the maximum stress in the lug e Reaction forces at the built in end of the lug to check that the reaction forces at the constraints balance the applied loads e Vertical displacements at the bottom of the hole to determine the deflection of the lug when the load is applied Each of these reports will be generated using display groups whose contents are selected
409. inear reduced integration elements see Table 4 2 are within an acceptable range for many applications The results suggest that at least four elements should be used through the thickness when modeling any structures carrying bending loads with this type of element When a single linear reduced integration element is used through the thickness of the beam all the integration points lie on the neutral axis and the model is unable to resist bending loads These cases are marked with a in Table 4 2 Linear reduced integration elements are very tolerant of distortion therefore use a fine mesh of these elements in any simulation where the distortion levels may be very high The quadratic reduced integration elements available in Abaqus Standard also have hourglass modes However the modes are almost impossible to propagate in a normal mesh and are rarely a problem if the mesh is sufficiently fine The 1 x 6 mesh of C3D20R elements fails to converge because of hourglassing unless two elements are used through the width but the more refined meshes do not fail even when only one element is used through the width Quadratic reduced integration elements are not susceptible to locking even when subjected to complicated states of stress Therefore these elements are generally the best choice for most general stress displacement simulations except in large displacement simulations involving very large strains and in some types of contact analyses J I
410. inetic energy of the deforming material should not exceed a small fraction typically 5 to 10 of the internal energy throughout most of the simulation Using the AMPLITUDE option with the DEFINITION SMOOTH STEP parameter is the most efficient way to prescribe displacements in a quasi static analysis Import the model from Abaqus Explicit to Abaqus Standard to perform an efficient springback analysis 13 29 Appendix A EXAMPLE FILES Appendix A Example Files This appendix contains a list of complete input files for the examples contained in this guide You can get a copy of any of these input files with the command abaqus fetch job file name where file name does not include the extension inp A 1 Overhead hoist frame e frame inp e frame xpl inp A 2 Connecting lug e lug inp e lug xpl inp A 3 Skew plate e skew inp A 4 Cargo crane e crane inp A 5 Cargo crane dynamic loading e dynamics inp e dynamics xpl inp A 6 Nonlinear skew plate e skew_nl inp e skew _nl xpl inp A 7 Stress wave propagation in a bar e wave 50x10x10 inp e wave 25x5x5 inp 5 Appendix A EXAMPLE FILES e wave 50x5x5 inp e wave 50x10x5 inp A 8 Connecting lug with plasticity e lug plas inp e lug plas hard inp A 9 Blast loading on a stiffened plate e blast_base inp e blast _damp inp e blast _long inp e blast _refined inp e blast _rate inp A 10 Axisymmetric mount e mount inp A 11 Test fit of hyperelasti
411. ing cases The same thinking is true for quasi static analyses The speed of the analysis often can be increased substantially without severely degrading the quality of the quasi static solution the end result of the slow case and a somewhat accelerated case are nearly the same However if the analysis speed is increased to a point at which inertial effects dominate the solution tends to localize and the results are quite different from the quasi static solution 13 2 Loading rates The actual time taken for a physical process is called its natural time Generally it is safe to assume that performing an analysis in the natural time for a quasi static process will produce accurate static results After all if the real life event actually occurs in a natural time scale in which velocities are zero at the conclusion a dynamic analysis should be able to capture the fact that the analysis has in fact achieved a steady state You can increase the loading rate so that the same physical event occurs in less time as long as the solution remains nearly the same as the true static solution and dynamic effects remain insignificant 13 2 1 Smooth amplitude curves For accuracy and efficiency quasi static analyses require the application of loading that is as smooth as possible Sudden jerky movements cause stress waves which can induce noisy or inaccurate solutions Applying the load in the smoothest possible manner requires that the acceleration change
412. ining a vector as part of the element property definition The orientations can be plotted in Abaqus Viewer e The beam cross section can be offset from the nodes that define the beam This procedure is useful in modeling stiffeners on shells e The linear and quadratic beams include the effects of shear deformation The cubic beams in Abaqus Standard do not account for shear flexibility The open section beam elements in Abaqus Standard correctly model the effects of torsion and warping including warping constraints in thin walled open sections e Multi point constraints constraint equations and connectors can be used to connect degrees of freedom at nodes to model pinned connections rigid links etc e Bending moment type plots allow the results of one dimensional elements such as beams to be visualized easily e Display options allow you to render beam profiles for enhanced graphical representations of undeformed and deformed plots e Hard copies of Abaqus Viewer plots can be obtained in PostScript PS Encapsulated PostScript EPS Tag Image File Format TIFF Portable Network Graphics PNG and Scalable Vector Graphics SVG formats 6 30 INTRODUCTION T Linear Dynamics A static analysis is sufficient if you are interested in the long term response ofa structure to applied loads However if the duration of the applied load is short such as in an earthquake or if the loading is dynamic in nature such as
413. input file the history data The history definition is substantially different from that in the static analysis Therefore delete the entire static step and add a new history section as discussed below Two steps are required for this analysis The first step calculates the natural frequencies and mode shapes of the structure The second step then uses these data to calculate the transient dynamic response of the hoist If you want to model any nonlinearities in this simulation you must use the DYNAMIC procedure In this analysis we will assume that everything is linear Step 1 Modes and frequencies The FREQUENCY procedure is used to calculate natural frequencies and mode shapes Abaqus offers the Lanczos and the subspace iteration eigenvalue extraction methods The Lanczos method is the default method it is generally faster when a large number of eigenmodes is required for a system with many degrees of freedom The subspace iteration method may be faster when only a few less than 20 eigenmodes are needed We use the default Lanczos eigensolver in this analysis The number of modes required 1s specified on the data line of the FREQUENCY option Alternatively it is possible to specify the minimum and maximum frequencies of interest so that the step will complete once Abaqus has found all of the eigenvalues inside the specified range A shift point may also be specified so that eigenvalues nearest the shift point will be extracted By
414. integration procedures For both the implicit and the explicit time integration procedures equilibrium is defined in terms of the external applied forces P the internal element forces I and the nodal accelerations M P I where M is the mass matrix Both procedures solve for nodal accelerations and use the same element calculations to determine the internal element forces The biggest difference between the two procedures lies in the manner in which the nodal accelerations are computed In the implicit procedure a set of linear equations is solved by a direct solution method The computational cost of solving this set of equations is high when compared to the relatively low cost of the nodal calculations with the explicit method Abaqus Standard uses automatic incrementation based on the full Newton iterative solution method Newton s method seeks to satisfy dynamic equilibrium at the end of the increment at time t At and to compute displacements at the same time The time increment At is relatively large compared to that used in the explicit method because the implicit scheme is unconditionally stable For a nonlinear problem each increment typically requires several iterations to obtain a solution within the prescribed tolerances Each Newton iteration solves for a correction c to the incremental displacements Au Each iteration requires the solution of a set of simultaneous equations K c P I Mjii EXPLICIT DYN
415. ion You can use these results to create X Y plots In particular you will plot the vertical displacement history of the nodes located at the edges of the plate midspan To create X Y plots of the midspan displacements 1 file First display only the nodes in the node set named PART 1 1 MIDSPAN in the Results Tree expand the Node Sets container underneath the output database file named skew_n1 odb Click mouse button 3 on the set named PART 1 1 MIDSPAN and select Replace from the menu that appears Use the Common Plot Options dialog box to show the node labels i e numbers to determine which nodes are located at the edges of the plate midspan In the Results Tree expand the History Output container for the output database named skew nl odb Locate the output labeled as follows Spatial displacement U3 at Node xxx in NSET MIDSPAN Each of these curves represents the vertical motion of one of the midspan nodes Tip Filter the container according to U3 to facilitate your selection Select using Ctrl Click the vertical motion of the two midspan edge nodes Use the node labels to determine which curves you need to select Click mouse button 3 and select Plot from the menu that appears Abaqus reads the data for both curves from the output database file and plots a graph similar to the one shown in Figure 8 14 For clarity the second curve has been changed to a dashed line and the default gri
416. ion of the legend open the Chart Legend Options dialog box and switch to the Area tabbed page In the Position region of this page toggle on Inset and click Dismiss Drag the legend in the viewport so that it fits within the grid as shown in Figure 10 29 We can see that once the load has been removed and the plate vibrates freely the kinetic energy increases as the strain energy decreases When the plate is at its maximum deflection and therefore has its maximum strain energy it is almost entirely at rest causing the kinetic energy to be at a minimum The plastic strain energy rises to a plateau and then rises again From the plot of kinetic energy we can see that the second rise in plastic strain energy occurs when the plate has rebounded from 10 43 5 EXAMPLE BLAST LOADING ON A STIFFENED PLATE 3 x10 50 00 40 00 30 00 Energy J 20 00 10 00 0 00 0 01 0 02 0 03 0 04 0 05 Time s Figure 10 29 Energy quantities as a function of time its maximum displacement and is moving back in the opposite direction We are therefore seeing plastic deformation on the rebound after the blast pulse Even though there is no indication that hourglassing is a problem in this analysis study the artificial strain energy to make sure As discussed in Chapter 4 Using Continuum Elements artificial strain energy or hourglass stiffness is the energy used to control hourglass deformation and t
417. ipe hitting a rigid wall inelastic buckling collapse of a thin walled elbow explosive loading of an elastic viscoplastic thin ring consolidation under a footing buckling of a composite shell with a hole and deep drawing of a metal sheet It is generally useful to look for relevant examples in this manual and to review them when embarking on a new class of problem When you want to use a feature that you have not used before you should look up one or more examples that use that feature Then use the example to familiarize yourself with the correct usage of the capability To find an example that uses a certain feature search the online documentation or use the abaqus findkeyword utility see Querying the keyword problem database Section 3 2 13 of the Abaqus Analysis User s Manual for more information All the input files associated with the examples are provided as part of the Abaqus installation The abaqus fetch utility is used to extract sample Abaqus input files from the compressed archive files provided with the release see Fetching sample input files Section 3 2 14 of the Abaqus Analysis User s Manual for more information You can fetch any of the example files so that you can run the simulations yourself and review the results You can also access the input files through the hyperlinks in the Abaqus Example Problems Manual Abaqus Benchmarks Manual This manual contains benchmark problems and analyses used to evaluate t
418. is typically coincident with the shell s midsurface However many situations arise in which it is more convenient to define the reference surface as offset from the shell s midsurface For example surfaces created in CAD packages usually represent either the top or bottom surface of the shell body In this case it may be easier to define the reference surface to be coincident with the CAD surface and therefore offset from the shell s midsurface 3 11 FINITE ELEMENTS 3 1 Shell offsets can also be used to define a more precise surface geometry for contact problems where shell thickness is important By default shell offset and thickness are accounted for in contact constraints in Abaqus Explicit The effect of offset and thickness in contact can be suppressed if required Shell offsets can also be useful when modeling a shell with continuously varying thickness In this case defining the nodes at the shell midplane can be difficult If one surface is smooth while the other is rough as in some aircraft structures it is easiest to use shell offsets to define the nodes at the smooth surface Offsets can be introduced by using the OFFSET parameter on the SHELL SECTION and SHELL GENERAL SECTION options The offset value is defined as a fraction of the shell thickness measured from the shell s midsurface to the shell s reference surface The degrees of freedom for the shell are associated with the reference surface All kine
419. issipated Erp is the frictional energy dissipated Ex 1s the kinetic energy Ergpg is the internal heat energy Ew is the work done by the externally applied loads and Epw Ecw and Emw are the work done by contact penalties by constraint penalties and by propelling added mass respectively Hy pr is the external heat energy through external fluxes The sum of these energy components is Etotai Which should be constant In the numerical model is only approximately constant generally with an error of less than 1 To illustrate energy balance with a simple example consider the uniaxial tensile test shown in Figure 13 6 The energy history for the quasi static test would appear as shown in Figure 13 7 Ifa simulation is quasi static the work applied by the external forces is nearly equal to the internal energy of the system The viscously dissipated energy is generally small unless viscoelastic materials discrete dashpots or material damping are used We have already established that the inertial forces are negligible in a quasi static analysis because the velocity of the material in the model is very small The corollary to both of these conditions 1s that the kinetic energy is also small As a general rule the kinetic energy of the deforming material should not exceed a small fraction typically 5 to 10 of its internal energy throughout most of the process When comparing the energies remember that Abaqus Explicit reports a global e
420. istortions flash formation and contact interaction with the dies An example of a quasi static forming simulation is presented in Chapter 13 Quasi Static Analysis with Abaqus Explicit Materials with degradation and failure Material degradation and failure often lead to severe convergence difficulties in implicit analysis programs but Abaqus Explicit models such materials well An example of material degradation is the concrete cracking model in which tensile cracking causes the material stiffness to become negative An example of material failure is the ductile failure model for metals in which material stiffness can degrade until it reduces to zero At this time the failed elements are removed from the model entirely Each of these types of analyses can include temperature and heat transfer effects 9 2 Explicit dynamic finite element methods This section contains an algorithmic description of the Abaqus Explicit solver as well as a comparison between implicit and explicit time integration and a discussion of the advantages of the explicit dynamics method 9 2 1 Explicit time integration Abaqus Explicit uses a central difference rule to integrate the equations of motion explicitly through time using the kinematic conditions at one increment to calculate the kinematic conditions at the next EXPLICIT DYNAMIC FINITE ELEMENT METHODS increment At the beginning of the increment the program solves for dynamic equilibrium which
421. ith incompressible material behavior Hybrid elements include an additional degree of freedom that determines the pressure stress in the element directly The nodal displacements are used only to calculate the deviatoric shear strains and stresses A more detailed description of the analysis of rubber materials is given in Chapter 10 Materials 4 2 Selecting continuum elements The correct choice of element for a particular simulation is vital if accurate results are to be obtained at a reasonable cost You will undoubtedly develop your own guidelines for selecting elements for your own particular applications as you become more experienced in using Abaqus However as you begin to use Abaqus the guidelines given here may be helpful The following recommendations apply to both Abaqus Standard and Abaqus Explicit 4 10 EXAMPLE CONNECTING LUG e Minimize the mesh distortion as much as possible Coarse meshes with distorted linear elements can give very poor results e Use a fine mesh of linear reduced integration elements CAX4R CPE4R CPS4R C3D8R etc for simulations involving very large mesh distortions large strain analysis e In three dimensions use hexahedral brick shaped elements wherever possible They give the best results for the minimum cost Complex geometries can be difficult to mesh completely with hexahedrons therefore wedge and tetrahedral elements may be necessary The linear versions of these element
422. ith output filtering In this section you will add real time filters to the history output requests for the circuit board drop test analysis While Abaqus Explicit does allow you to create user defined output filters Butterworth Chebyshev Type I and Chebyshev Type II based on criteria that you specify in this example we will use the built in anti aliasing filter The built in anti aliasing filter is designed to give you the best un aliased representation of the results recorded at the output rate you specify on the output request 12 79 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST To do this Abaqus Explicit internally applies a low pass second order Butterworth filter with a cutoff frequency set to one sixth of the sampling rate For more information see Overview of filtering Abaqus history output in the Dassault Systemes Knowledge Base at www 3ds com support knowledge base or the SIMULIA Online Support System which is accessible through the My Support page at www simulia com For more information on defining your own real time filters see Filtering output and operating on output in Abaqus Explicit in Output to the output database Section 4 1 3 of the Abaqus Analysis User s Manual Modifying the history output requests When Abaqus writes nodal history output to the output database it gives each data object a name that indicates the recorded output variable the filter used if any the node number and the n
423. ither of the other two elements whose normals are printed in the data file as shown below 6 19 5 EXAMPLE CARGO CRANE NORMAL DEFINITIONS ELEMENT NODE NORMAL ELEMENT NODE NORMAL 100 101 0 1820 0 9831 2 0481E 02 101 101 0 1820 0 9831 2 0481E 02 101 102 0 1820 0 9831 2 0481E 02 102 102 0 1820 0 9831 2 0481E 02 102 103 0 1820 0 9831 2 0481E 02 103 103 0 1820 0 9831 2 0481E 02 103 104 0 1820 0 9831 2 0504E 02 104 105 6 1600E 02 0 9981 6 9312E 03 In this table element 113 shows no normal for either of its nodes node 102 and node 105 Thus the normal shown for node 102 above in the NODE DEFINITIONS table was the average of the normals from elements 101 102 and 113 Using the Abaqus logic for averaging normals we could have predicted that the normals at the nodes of element 113 would be averaged with the normals for the adjacent elements For this problem the important part of the averaging logic is that normals that subtend an angle less than 20 with the reference normal are averaged with the reference normal to define a new reference normal In the case of the normals at node 102 the original reference normal is the normal for elements 101 and 102 Since the normal for element 113 at node 102 subtends an angle less than 20 with the original reference normal it is averaged with the normals for elements 101 and 102 at node 102 to define the new reference normal at that node On the other hand since the normal for element 112 subt
424. l 1972 Summary There are three sources of nonlinearity in structural problems material geometric and boundary contact Any combination of these may be present in an Abaqus analysis Geometric nonlinearity occurs whenever the magnitude of the displacements affects the response of the structure It includes the effects of large displacements and rotations snap through and load stiffening In Abaqus Standard nonlinear problems are solved iteratively using the Newton Raphson method A nonlinear problem will require many times the computer resources required by a linear problem Abaqus Explicit does not need to iterate to obtain a solution however the computational cost may be affected by reductions in the stable time increment due to large changes in geometry A nonlinear analysis step is split into a number of increments Abaqus Standard iterates to find the approximate static equilibrium obtained at the end of each new load increment Abaqus Standard controls the load incrementation by using convergence controls throughout the simulation Abaqus Explicit determines a solution by advancing the kinematic state from one increment to the next using a smaller time increment than what is commonly used in implicit analyses The size of the increment is limited by the stable time increment By default time incrementation is completely automated in Abaqus Explicit The status file allows the progress of an analysis to be monitored w
425. l class of discontinuous constraint allowing forces to be transmitted from one part of the model to another The constraint 1s discontinuous because it is applied only when the two surfaces are in contact When the two surfaces separate no constraint is applied The analysis has to be able to detect when two surfaces are in contact and apply the contact constraints accordingly Similarly the analysis must be able to detect when two surfaces separate and remove the contact constraints 12 1 Overview of contact capabilities in Abaqus Contact simulations in Abaqus Standard can either be surface based or contact element based Contact simulations in Abaqus Explicit are surface based only In this manual surface based contact 1s discussed Surface based contact can utilize either the general automatic contact algorithm or the contact pair algorithm The general contact algorithm allows for a highly automated contact definition where contact is based on an automatically generated all inclusive surface definition Conversely the contact pair algorithm requires you to explicitly pair surfaces that may potentially come into contact Both algorithms require specification of contact properties between surfaces for example friction The discussion of contact in this manual addresses the contact pair approach and general contact in Abaqus Standard and general contact in Abaqus Explicit 12 2 Interaction between surfaces The interaction betwee
426. l force acting on the end node is equivalent to the stress in the rod multiplied by its cross sectional area A Thus a relationship between internal force material properties and displacements is obtained EA I 011A Esi A a u Equilibrium at node a can therefore be written as EA aay aa Equilibrium at node b must take into account the internal forces acting from both elements joined at that node The internal force from element is now acting in the opposite direction and so becomes negative The resulting equation is EA EA By a a ue u 0 For node c the equilibrium equation is EA P a uw 0 For implicit methods the equilibrium equations need to be solved simultaneously to obtain the displacements of all the nodes This requirement is best achieved by matrix techniques therefore write the internal and external force contributions as matrices If the properties and dimensions of the two elements are the same the equilibrium equations can be simplified as follows P 1 1 0 u a EA P y f 9 f u 0 Fo 0 1 1 uo In general it may be that the element stiffnesses the A L terms are different from element to element therefore write the element stiffnesses as K and Ko for the two elements in the model We are interested in obtaining the solution to the equilibrium equation in which the externally applied forces P are in equilibrium with the internally generated forces I
427. lacement in the vertical direction as follows In the Contour Plot Options dialog box click Defaults to reset the minimum and maximum contour values and the number of intervals to their default values before proceeding To contour the displacement of the connecting lug in the 2 direction 1 From the list of variable types on the left side of the Field Output toolbar select Primary if it is not already selected Tip You can click T on the left side of the Field Output toolbar to make your selections from the Field Output dialog box instead of the toolbar If you use the dialog box you must click Apply or OK for Abaqus Viewer to display your selections in the viewport 2 From the list of available output variables in the center of the toolbar select output variable U 3 From the list of available components and invariants on the right side of the Field Output toolbar select U2 What is the maximum displacement value in the negative 2 direction Displaying a subset of the model By default Abaqus Viewer displays your entire model however you can choose to display a subset of your model called a display group This subset can contain any combination of part instances geometry cells faces or edges elements nodes and surfaces from the current model or output database For the connecting lug model you will create a display group consisting of the elements at the bottom of the hole Since a pressure load was applied to this region
428. lanes of elements in the z direction are incremented by 1000 Figure 4 18 Element numbers in the plane z 0 4 3 4 Reviewing the input file the model data The model data including the node and element definitions set definitions and section and material properties are discussed in the following sections 4 15 5 EXAMPLE CONNECTING LUG Model description An Abaqus input file always starts with the HEADING option Often the description given in this option by the preprocessor is not very informative although it might give the date and time when the file was generated You should provide a suitable title on the data lines of this option so that someone looking at this file can tell what is being modeled and what units you used The HEADING option block used in lug inp appears below HEADING Linear Elastic Steel Connecting Lug S I Units N kg m 8 Nodal coordinates and element connectivity In input files created by a preprocessor the model s nodal coordinates usually are in one large NODE option block with the coordinates specified for each node individually The element definitions generated by the preprocessor usually are contained in several ELEMENT option blocks Typically each block contains elements that have the same element section and material properties In the connecting lug model only one element type is used and all the elements have the same properties Therefore there will probably be a single
429. ld at the top of the dialog box Your cursor should be at the end of the text field Multiply the data object in the text field by the magnitude of the applied load by entering 5500 Save the multiplied data object by clicking Save As at the bottom of the dialog box The Save XY Data As dialog box appears 6 In the Name text field type FORCEDEF and click OK to close the dialog box 7 To view the force displacement plot click Plot Expression at the bottom of the Operate on XY Data dialog box You have now created a curve with the force deflection characteristic of the mount the axis labels do not reflect this since you did not change the actual variable plotted To get the stiffness you need to differentiate the curve FORCEDEF You can do this by using the differentiate operator in the Operate on XY Data dialog box 10 70 EXAMPLE AXISYMMETRIC MOUNT To obtain the stiffness 1 In the Operate on XY Data dialog box clear the current expression 2 From the Operators listed click differentiate X differentiate appears in the text field at the top of the dialog box 3 In the XY Data field double click FORCEDEF The expression differentiate FORCEDEF appears in the text field 4 Save the differentiated data object by clicking Save As at the bottom of the dialog box The Save XY Data As dialog box appears 5 In the Name text field type STIFF and click OK to close the dialog box 6 To plot the
430. ld that the section of pipe will be subjected to axial tension when in service Start by considering a load magnitude of 4 MN The lowest vibrational mode of the pipe will be a sine wave deformation in any direction transverse to the pipe axis because of the symmetry of the structure s cross section You will use three dimensional beam elements to model the pipe section The analysis requires a natural frequency extraction Thus you will use Abaqus Standard as your analysis product 11 9 5 EXAMPLE VIBRATION OF A PIPING SYSTEM 11 3 1 Coordinate system The default global coordinate system is used Place the origin at the left end of the pipe section and make the axis of the pipe and the global 1 axis coincident as shown in Figure 11 8 11 3 2 Mesh design Model the pipe section with a uniformly spaced mesh of 30 second order pipe elements PIPE32 The node and element numbers of the model used in this discussion are shown in Figure 11 9 Element 30 er 1 Neng Figure 11 9 Node and element numbers both increase by 1 from left to right 11 3 3 Preprocessing creating the model You can create the mesh for this example using your preprocessor or if you prefer you can use the Abaqus mesh generation options shown in Vibration of a piping system Section A 12 If you wish to create the entire model using Abaqus CAE please refer to Example vibration of a piping system Section 11 3 of Getting Started with Abaqus In
431. le to identify the problems with the heavily filtered data if we did not have appropriate data for comparison In general it is best to use a minimal amount of filtering in Abaqus Explicit so that the output database contains a rich un aliased representation for the solution recorded at a reasonable number of time points rather than at every increment If additional filtering is necessary it can be done as a postprocessing operation in Abaqus Viewer Filtering acceleration history in Abaqus Viewer In this section we will use Abaqus Viewer to filter the acceleration history data written to the output database Filtering as a postprocessing operation in Abaqus Viewer has several advantages over the real time filtering available in Abaqus Explicit In the Abaqus Viewer you can quickly filter 12 84 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST X Y data and plot the results You can easily compare the filtered results to the unfiltered results to verify that the filter produced the desired effect Using this technique you can quickly iterate to find appropriate filter parameters In addition the Abaqus Viewer filters do not suffer from the time delay that is unavoidable when filtering 1s applied during the analysis Keep in mind however that postprocessing filters cannot compensate for poor analysis history output if the data has been aliased or if physically meaningful frequencies have been removed no postprocessing operation can reco
432. lements Typically the number of nodes in an element is clearly identified in its name The 8 node brick element as you have seen is called C3D8 and the 8 node general shell element is called S8R The beam element family uses a slightly different convention the order of interpolation is identified in the name Thus a first order three dimensional beam element is called B31 whereas a second order three dimensional beam element is called B32 A similar convention is used for axisymmetric shell and membrane elements Formulation An element s formulation refers to the mathematical theory used to define the element s behavior In the absence of adaptive meshing all of the stress displacement elements in Abaqus are based on the Lagrangian or material description of behavior the material associated with an element remains associated with the element throughout the analysis and material cannot flow across element boundaries In the alternative Eulerian or spatial description elements are fixed in space as the material flows through them Eulerian methods are used commonly in fluid mechanics simulations Abaqus Standard uses Eulerian elements to model convective heat transfer Adaptive meshing combines the features of pure Lagrangian and Eulerian analyses and allows the motion of the element to be independent of the material Eulerian elements and adaptive meshing are not discussed in this guide 3 4 FINITE ELEMENTS To accommodate differe
433. lent nodal forces for applied pressures on first order elements always have a consistent sign and magnitude therefore there is no ambiguity about the contact state that a given distribution of nodal forces represents If you are using the node to surface formulation and your geometry is complicated and requires the use of an automatic mesh generator the modified second order tetrahedral elements C3D10M in Abaqus Standard should be used These elements are designed to be used in complex contact simulations regular second order tetrahedral elements C3D10 have zero contact force at their corner nodes leading to poor predictions of the contact pressures The modified second order tetrahedral elements can calculate the contact pressures accurately Regular second order elements can generally be used without difficulty with the surface to surface formulation 12 3 7 Contact algorithm Understanding the algorithm Abaqus Standard uses to solve contact problems will help you understand the diagnostic output in the message file and carry out contact simulations successfully The contact algorithm in Abaqus Standard which is shown in Figure 12 10 is built around the Newton Raphson technique discussed in Chapter 8 Nonlinearity Abaqus Standard examines the state of all contact interactions at the start of each increment to establish whether slave nodes are open or closed If a node is closed Abaqus Standard determines whether it is sliding o
434. lindrical panel with a circular hole Section 1 2 2 of the Abaqus Example Problems Manual e Unstable static problem reinforced plate under compressive loads Section 1 2 5 of the Abaqus Example Problems Manual e Large rotation of a one degree of freedom system Section 1 3 5 of the Abaqus Benchmarks Manual e Vibration of a cable under tension Section 1 4 3 of the Abaqus Benchmarks Manual 8 6 Suggested reading The following references provide additional information on nonlinear finite element methods They allow the interested user to explore the topic in more depth General texts on nonlinear finite element analysis e Belytschko T W K Liu and B Moran Nonlinear Finite Elements for Continua and Structures Wiley amp Sons 2000 e Bonet J and R D Wood Nonlinear Continuum Mechanics for Finite Element Analysis Cambridge 1997 e Cook R D D S Malkus and M E Plesha Concepts and Applications of Finite Element Analysis Wiley amp Sons 1989 8 27 SUMMARY 8 7 e Crisfield M A Non linear Finite Element Analysis of Solids and Structures Volume I Essentials Wiley amp Sons 1991 e Crisfield M A Non linear Finite Element Analysis of Solids and Structures Volume IT Advanced Topics Wiley amp Sons 1997 e E Hinton editor NAFEMS Introduction to Nonlinear Finite Element Analysis NAFEMS Ltd 1992 e Oden J T Finite Elements of Nonlinear Continua McGraw Hil
435. linear analysis of a cantilever beam Section 2 1 2 of the Abaqus Benchmarks Manual 6 28 SUMMARY 182 N m 265 N m Figure 6 21 Bending moment diagram moment about beam 1 axis for elements in display group MainA The locations with the highest stress created by the bending of the elements are indicated 6 6 Suggested reading Basic beam theory e Timoshenko S Strength of Materials Part II Krieger Publishing Co 1958 e Oden J T and E A Ripperger Mechanics of Elastic Structures McGraw Hill 1981 Basic computational beam theory e Cook R D D S Malkus and M E Plesha Concepts and Applications of Finite Element Analysis John Wiley amp Sons 1989 e Hughes T J R The Finite Element Method Prentice Hall Inc 1987 6 7 Summary e The behavior of beam elements can be determined by numerical integration of the section either BEAM SECTION or BEAM GENERAL SECTION or can be given directly in terms of area moments of inertia and torsional constant BEAM GENERAL SECTION e When BEAM GENERAL SECTION is used with numerical integration the calculations are done once at the start of the simulation and elastic behavior is assumed 6 29 SUMMARY e Abaqus includes a number of standard cross section shapes Other shapes provided they are thin walled can be modeled using SECTION ARBITRARY e The orientation of the cross section must be defined either by specifying a third node or by def
436. linear and nonlinear static analyses as well as dynamic analyses An introduction to CFD analysis and modeling fluid structure interaction is also included Other types of simulations such as heat transfer and mass diffusion are not covered 1 2 1 How to use this guide Each of the chapters in this guide introduces one or more topics relevant to using Abaqus Standard and Abaqus Explicit Throughout the manual the term Abaqus is used to refer collectively to both Abaqus Standard and Abaqus Explicit the individual product names are used when information applies to only one product Most chapters contain a short discussion of the topic or topics being considered and one or two tutorial examples You should work through the examples carefully since they contain a great deal of practical advice on using Abaqus The capabilities of Abaqus Standard and Abaqus Explicit are introduced gradually in these examples You may create input files using a text editor however using an interactive pre processor facilitates model creation for these examples Full versions of the input files that you create in each example are in Appendix A Example Files If you have access to Abaqus CAE you can use the companion manual Getting Started with Abaqus Interactive Edition to perform all preprocessing and analysis steps using detailed Abaqus CAE tutorials This chapter is a short introduction to Abaqus and this guide Chapter 2 Abaqus Basics which is ce
437. lled boundary conditions would be applied around the edge of the sink where it is attached to the worktop The response of the sink to a number of different loading conditions may be of interest and has to be simulated For example a simulation may need to be performed to ensure that the sink does not break if someone stands on it Step 4 would therefore be a linear perturbation step analyzing the static response of the sink to a local pressure load Remember that the results from Step 4 will be perturbations from the state of the sink after the forming process do not be surprised for example if the displacement of the center of the sink in this step is say only 2 mm but you know that the sink deformed much more than that since the start of the forming simulation This hypothetical 2 mm deflection is just the additional deformation from the sink s final configuration after the forming process 1 e the end of Step 3 caused by the weight of the person The total deflection measured from the undeformed sheet s configuration is the sum of this 2 mm and the deflection at the end of Step 3 The sink may also be fitted with a waste disposal unit so its steady state dynamic response to a harmonic load at certain frequencies must be simulated Step 5 would therefore be a second linear perturbation step using the STEADY STATE DYNAMICS DIRECT procedure with a load applied at the point of attachment of the disposal unit The base state for this step i
438. lled the Abaqus output database file and has the extension odb e Printed tables of results written to the Abaqus data dat file e Restart data used to continue the analysis written to the Abaqus restart res file e Results stored in binary files for subsequent postprocessing with third party software written to the Abaqus results il file You will use the first two of these in the overhead hoist simulation By default an output database file which includes a preselected set of the most commonly used output variables for a given type of analysis 1s created A list of preselected variables for default output database output is given in the Abaqus Analysis User s Manual You do not need EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST to add any output requests to accept these defaults For this example the default output database output includes the deformed configuration and the applied nodal loads Selected results also can be written in tabular form to the Abaqus data file By default no printout is written to the Abaqus data file The NODE PRINT option controls the printing of nodal results for example displacements and reaction forces while the EL PRINT option controls the printing of element results A comprehensive list of the output variables available is given in the Abaqus Analysis User s Manual The data lines for either of these options list the output to appear in the columns of the table Each data lin
439. lot 1 In the Results Tree double click XY Data The Create XY Data dialog box appears 2 Select Operate on XY data and click Continue The Operate on XY Data dialog box appears Expand the Name field to see the full name of each curve 3 From the Operators listed select combine X X combine appears in the text field at the top of the dialog box 4 In the XY Data field select the stress and strain curves 10 25 5 EXAMPLE CONNECTING LUG WITH PLASTICITY Click Add to Expression The expression combine E11 MISES appears in the text field In this expression E11 will determine the X values and MISES will determine the Y values in the combined plot Save the combined data object by clicking Save As at the bottom of the dialog box The Save XY Data As dialog box appears In the Name text field type SVE11 and click OK to close the dialog box To view the combined stress strain plot click Plot Expression at the bottom of the dialog box Click Cancel to close the dialog box Click X in the prompt area to cancel the current procedure This X Y plot would be clearer if the limits on the X and Y axes were changed To customize the stress strain curve 1 2 Double click either axis to open the Axis Options dialog box Set the maximum value of the X axis E11 strain to 0 09 the maximum value of the Y axis MISES stress to 500 MPa and the minimum value to 0 0 MPa Switch
440. lution and toggle off Print date 6 Click OK to apply your selections and to close the dialog box 7 In the Print dialog box click OK Abaqus Viewer creates a PostScript file of the current image and saves it in your working directory as beam ps You can print this file using your system s command for printing PostScript files Displacement summary Write a summary of the displacements of all nodes in display group MainA to a file named crane rpt The peak displacement at the tip of the crane in the 2 direction is 0 0188 m Section forces and moments Abaqus can provide output for structural elements in terms of forces and moments acting on the cross section at a given point These section forces and moments are defined in the local beam coordinate system Toggle off the rendering of beam profiles then contour the section moment 6 27 5 RELATED Abaqus EXAMPLES 6 5 about the beam l axis in the elements in display group MainA For clarity reset the view so that the elements are displayed in the 1 2 plane To create a bending moment type contour plot 1 2 From the list of variable types on the left side of the Field Output toolbar select Primary From the list of output variables in the center of the toolbar select SM Abaqus Viewer automatically selects SM1 the first component name in the list on the right side of the Field Output toolbar and displays a contour plot of the bending moment about the beam
441. lved in each increment the cost per increment of an implicit method is far greater than that of an explicit method Knowing these characteristics of the two procedures can help you decide which methodology 1s appropriate for your problems 9 1 Types of problems suited for Abaqus Explicit Before discussing how the explicit dynamics procedure works it is helpful to understand what classes of problems are well suited to Abaqus Explicit Throughout this manual we have incorporated pertinent examples of the following classes of problems commonly performed in Abaqus Explicit High speed dynamic events The explicit dynamics method was originally developed to analyze high speed dynamic events that can be extremely costly to analyze using implicit programs such as Abaqus Standard As an example of such a simulation the effect of a short duration blast load on a steel plate is analyzed in Chapter 10 Materials Since the load is applied rapidly and is very severe the response of the structure changes rapidly Accurate tracking of stress waves through the plate is important for capturing the dynamic response Since stress waves are associated with the highest frequencies of the system obtaining an accurate solution requires many small time increments Complex contact problems Contact conditions are formulated more easily using an explicit dynamics method than using an implicit method The result is that Abaqus Explicit can readily analyze
442. ly to identify the regions of high stress and then refining the mesh in these regions The latter procedure is carried out easily using preprocessors like Abaqus CAE where the complete numerical model 1 e material properties boundary conditions loads etc can be defined based on the geometry of the structure It is simple to mesh the geometry coarsely for the initial simulation and then to refine the mesh in the appropriate regions as indicated by the results from the coarse simulation Abaqus provides an advanced feature called submodeling that allows you to obtain more detailed and accurate results in a region of interest in the structure The solution from a coarse mesh of the entire structure is used to drive a detailed local analysis that uses a fine mesh in this region of interest This topic is beyond the scope of this guide See Submodeling overview Section 10 2 1 of the Abaqus Analysis User s Manual for further details 4 5 Related Abaqus examples If you are interested in learning more about using continuum elements in Abaqus you should examine the following problems e Geometrically nonlinear analysis of a cantilever beam Section 2 1 2 of the Abaqus Benchmarks Manual e Spherical cavity in an infinite medium Section 2 2 4 of the Abaqus Benchmarks Manual e Performance of continuum and shell elements for linear analysis of bending problems Section 2 3 5 of the Abaqus Benchmarks M
443. lysis type Abaqus can carry out many different types of simulations but this guide only covers the two most common static and dynamic stress analyses In a static analysis the long term response of the structure to the applied loads is obtained In other cases the dynamic response of a structure to the loads may be of interest for example the effect of a sudden load on a component such as occurs during an impact or the response of a building in an earthquake Output requests An Abaqus simulation can generate a large amount of output To avoid using excessive disk space you can limit the output to that required for interpreting the results 2 2 Format of the input file The input file is the means of communication between the preprocessor usually Abaqus CAE and the analysis product Abaqus Standard or Abaqus Explicit It contains a complete description of the numerical model The input file is a text file that has an intuitive keyword based format so it 1s easy to modify using a text editor if necessary if a preprocessor such as Abaqus CAE is used modifications should be made using it Indeed small analyses can be specified easily by typing the input file directly The example of an overhead hoist shown in Figure 2 1 is used to illustrate the basic format of the Abaqus input file The hoist is a simple pin jointed truss model that is constrained at the left hand end and mounted on rollers at the right hand end The members can rotat
444. m shown in Figure 8 4 that deflects under an applied load until it hits a stop 8 2 SOURCES OF NONLINEARITY Stress Ultimate tensile stress Initial yield stress M aterial Failure Slope is Young s modulus E Strain Figure 8 2 Stress strain curve for an elastic plastic material under uniaxial tension Stress Strain Figure 8 3 Stress strain curve for a rubber type material AS Figure 8 4 Cantilever beam hitting a stop 5 SOURCES OF NONLINEARITY The vertical deflection of the tip is linearly related to the load if the deflection is small until it contacts the stop There is then a sudden change in the boundary condition at the tip of the beam preventing any further vertical deflection and so the response of the beam is no longer linear Boundary nonlinearities are extremely discontinuous when contact occurs during a simulation there is a large and instantaneous change in the response of the structure Another example of boundary nonlinearity is blowing a sheet of material into a mold The sheet expands relatively easily under the applied pressure until it begins to contact the mold From then on the pressure must be increased to continue forming the sheet because of the change in boundary conditions Boundary nonlinearity is covered in Chapter 12 Contact 8 1 3 Geometric nonlinearity The third source of nonlinearity is related to changes in the geometry of the
445. m the list of variable types on the left side of the Field Output toolbar and select PEEQ from the list of output variables PEEQ is an integrated measure of plastic strain A nonintegrated measure of plastic strain is PEMAG PEEQ and PEMAG are equal for proportional loading 6 Use the tool to zoom into any region of interest in the blank as shown in Figure 12 22 The maximum plastic strain is approximately 21 Compare this with the failure strain of the material to determine if the material will tear during the forming process History plots of the reaction forces on the blank and punch The solid line in Figure 12 23 shows the variation of the reaction force RF2 at the punch s rigid body reference node 12 30 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL 3 053e 02 0 000e 00 Figure 12 22 Contours of the scalar plastic strain variable PEEQ in one corner of the blank x1 E6 0 00 0 05 Force 0 10 0 15 0 0 0 5 1 0 1 5 2 0 Figure 12 23 Force on punch 12 31 5 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL To create a history plot of the reaction force 1 In the Results Tree expand the History Output container Double click Reaction force RF1 PI PART 1 1 Node xxx in NSET NOUT A history plot of the reaction force in the 1 direction appears 2 Open the Axis Options dialog box to label the axes 3 Switch to the Title tabbed page 4 Spec
446. main in effect for all subsequent contour plots until you change them or reset them to their default values 4 29 5 EXAMPLE CONNECTING LUG S Mises Avg 75 4 000e 08 3 622e 08 3 244e 08 2 867e 08 2 489e 08 2 111e 08 1 733e 08 1 356e 08 9 778e 07 6 000e 07 8 879e 06 Step Step 1 Increment 1 Step Time 2 2200E 16 Primary Var S Mises z x Deformed Var U Deformation Scale Factor 2 968e 01 Figure 4 31 Customized plot of Mises stress Displaying contour results on interior surfaces You can cut your model such that interior surfaces are made visible For example you may want to examine the stress distribution in the interior of a part View cuts can be created for such purposes Here a simple planar cut is made through the lug to view the Mises stress distribution through the thickness of the part To create a view cut 1 From the main menu bar select Tools View Cut Create 2 In the dialog box that appears accept the default name and shape Enter 0 0 0 as the Origin of the plane 1 e a point through which the plane will pass 1 0 1 as the Normal axis to the plane and 0 1 0 as Axis 2 of the plane 3 Click OK to close the dialog box and to make the view cut The view appears as shown in Figure 4 32 From the main menu bar select Tools View Cut Manager to open the View Cut Manager By default the regions on and below the cut 4 30 EXAMPLE CONNECTING LUG
447. mate strength Yield point Hardening Necking Nominal stress Young s modulus E Failure Unloading curve Parallel to Young s modulus Nominal strain Figure 10 2 Nominal stress strain behavior of an elastic plastic material in a tensile test The deformation of the metal prior to reaching the yield point creates only elastic strains which are fully recovered if the applied load 1s removed However once the stress in the metal exceeds the yield stress permanent inelastic deformation begins to occur The strains associated with this permanent deformation are called plastic strains Both elastic and plastic strains accumulate as the metal deforms in the post yield region The stiffness of a metal typically decreases dramatically once the material yields see Figure 10 2 A ductile metal that has yielded will recover its initial elastic stiffness when the applied load is removed see Figure 10 2 Often the plastic deformation of the material increases its yield stress for subsequent loadings this behavior is called work hardening Another important feature of metal plasticity 1s that the inelastic deformation is associated with nearly incompressible material behavior Modeling this effect places some severe restrictions on the type of elements that can be used in elastic plastic simulations A metal deforming plastically under a tensile load may experience highly localized extension and thinning
448. matic quantities including the element s area are calculated there Large offset values for curved shells may lead to a surface integration error affecting the stiffness mass and rotary inertia for the shell section For stability purposes Abaqus Explicit also automatically augments the rotary inertia used for shell elements on the order of the offset squared which may result in errors in the dynamics for large offsets When large offsets from the shell s midsurface are necessary use multi point constraints or rigid body constraints instead Element output variables The element output variables for shells are defined in terms of local material directions that lie on the surface of each shell element In all large displacement simulations these axes rotate with the element s deformation You can also define a local material coordinate system that rotates with the element s deformation in a large displacement analysis 4 Beam elements Beam elements are used to model components in which one dimension the length is significantly greater than the other two dimensions and only the stress in the direction along the axis of the beam is significant Beam element names in Abaqus begin with the letter B The next character indicates the dimensionality of the element 2 for two dimensional beams and 3 for three dimensional beams The third character indicates the interpolation used 1 for linear interpolation 2
449. matically chooses appropriate load increments and convergence tolerances and continually adjusts them during the analysis to ensure that an accurate solution is obtained efficiently The Abaqus products Abaqus consists of three main analysis products Abaqus Standard Abaqus Explicit and Abaqus CFD Several add on analysis options are available to further extend the capabilities of Abaqus Standard and Abaqus Explicit The Abaqus Aqua option works with Abaqus Standard and Abaqus Explicit The Abaqus Design and Abaqus AMS options work with Abaqus Standard Abaqus Foundation is an optional subset of Abaqus Standard Abaqus CAE is the complete Abaqus environment that includes capabilities for creating Abaqus models interactively submitting and monitoring Abaqus jobs and evaluating results Abaqus Viewer is a subset of Abaqus CAE that includes just the postprocessing functionality In addition the Abaqus Interface for Moldflow and the Abaqus Interface for MSC ADAMS are interfaces to Moldflow and ADAMS Flex respectively Abaqus also provides translators that convert geometry from third party CAD systems to models for Abaqus CAE convert entities from third party preprocessors to input for Abaqus analyses and that convert output from Abaqus analyses to entities for third party postprocessors The relationship between these products 1s shown in Figure 1 1 Abaqus Standard Abaqus Standard is a general purpose analysis product that can solve a wide range
450. mber of elements with no dependence on element dimensions thus these requirements increase by a factor of 8 Whereas predicting the cost increase with mesh refinement for the explicit method is rather straightforward cost is more difficult to predict when using the implicit method The difficulty arises from the problem dependent relationship between element connectivity and solution cost a relationship that does not exist in the explicit method Using the implicit method experience shows that for many problems the computational cost is roughly proportional to the square of the number of degrees of freedom Consider the same example of a three dimensional model with uniform square elements Refining the mesh by a factor of two in all three directions increases the number of degrees of freedom by approximately 2 causing the computational cost to increase by a factor of roughly 2 or 64 The disk space and memory requirements increase in the same manner although the actual increase is difficult to predict The explicit method shows great cost savings over the implicit method as the model size increases as long as the mesh is relatively uniform Figure 2 16 illustrates the comparison of cost versus model size using the explicit and implicit methods For this problem the number of degrees of freedom scales with the number of elements explicit Cost Oe implicit Number of degrees of freedom Figure 2 16 Cost versus mod
451. mbering shown in Figure 2 6 The coordinates of nodes are defined using the NODE option Each data line of this option block has the form lt node number gt lt x1 coordinate gt lt x coordinate gt lt x3 coordinate gt The nodes for the hoist model are defined as follows NODE 101 0 0 0 102 1 0 0 103 2 O 0 104 0 5 0 866 O 105 1 5 0 866 O Element connectivity The members of the overhead hoist are modeled with truss elements The format of each data line for a truss element is lt element number gt lt node l gt lt node 2 gt where node 1 and node 2 are at the ends of the element see Figure 2 5 For example element 16 connects nodes 103 and 105 see Figure 2 6 so the data line defining this element is 16 103 105 The TYPE parameter on the ELEMENT option must be used to specify the kind of element being defined In this case you will use T2D2 truss elements One of the most useful features in Abaqus is the availability of node and element sets that are referred to by name By using the ELSET parameter on the ELEMENT option all of the elements defined in the option block are added to an element set called FRAME A set name can have as many as 80 characters and must start with a letter Since element section properties are assigned through element set names all elements in the model must belong to at least one element set The complete ELEMENT option block for the overhead hoist
452. mbination of the mass and stiffness matrices C aM B6K where a and are user defined constants Although the assumption that the damping is proportional to the mass and stiffness matrices has no rigorous physical basis in practice the damping distribution rarely is known in sufficient detail to warrant any other more complicated model In general this model ceases to be reliable for heavily damped systems that is above approximately 10 of critical damping As with the other forms of damping you can define precisely the Rayleigh damping of each mode of the system For a given mode i the damping ratio and the Rayleigh damping values and are related through Q Bw l 2W 2 The RAYLEIGH parameter on the MODAL DAMPING option indicates that Rayleigh damping is to be used For example to define a 0 2525 and 8 2 9 x 10 for modes 1 10 and a 0 2727 and 8 3 03 x 10 for modes 11 20 the following lines would be included in the step definition MODAL DAMPING RAYLEIGH 1 10 0 2525 2 9E 3 11 20 0 2727 3 03E 3 Composite damping In composite damping a fraction of critical damping is defined for each material and a composite damping value is found for the whole structure This option is useful when many different materials are present in the structure Composite damping is not discussed further in this guide 7 2 2 Choosing damping values In most linear dynamic problems the proper specification o
453. mbols in the Common Plot Options dialog box In the Variable tabbed page of the Report Field Output dialog box change the position to Unique Nodal Toggle off S Stress components and select RF1 RF2 and RF3 from the list of available RF Reaction force variables 8 In the Data region at the bottom of the Setup tabbed page toggle on Column totals 11 12 13 Click Apply 10 In the Results Tree click mouse button 3 on nodes at hole bottom underneath the Display Groups container In the menu that appears select Plot to make it the current display group In the Variable tabbed page of the Report Field Output dialog box toggle off RF Reaction force and select U2 from the list of available U Spatial displacement variables In the Data region at the bottom of the Setup tabbed page toggle off Column totals Click OK 4 37 5 EXAMPLE CONNECTING LUG Open the file Lug rpt in a text editor A portion of the table of element stresses is shown below The element data are given at the element integration points The integration point associated with a given element is noted under the column labeled Int Pt The bottom of the table contains information on the maximum and minimum stress values in this group of elements The results indicate that the maximum Mises stress at the built in end is approximately 330 MPa Your results may differ slightly if your mesh is not identical to the one used here Field Output Report
454. me at the element s integration points to remain constant In certain classes of elements the addition of these incompressibility constraints makes the element overconstrained When these elements cannot resolve all of these constraints they suffer from volumetric locking which causes their response to be too stiff Volumetric locking is indicated by a rapid variation of hydrostatic pressure stress from element to element or integration point to integration point The fully integrated second order solid elements available in Abaqus Standard are very susceptible to volumetric locking when modeling incompressible material behavior and therefore should not be used in elastic plastic simulations The fully integrated first order solid elements in Abaqus Standard do not suffer from volumetric locking because Abaqus actually uses a constant volume strain in these elements Thus they can be used safely in plasticity problems Reduced integration solid elements have fewer integration points at which the incompressibility constraints must be satisfied Therefore they are not overconstrained and can be used for most elastic plastic simulations The second order reduced integration elements in Abaqus Standard should be used with caution if the strains exceed 20 40 because at this magnitude they can suffer from volumetric locking This effect can be reduced with mesh refinement 10 10 EXAMPLE CONNECTING LUG WITH PLASTICITY If you have to use f
455. ment specifies a value of 15 for alpha damping and 0 for the remaining damping quantities These values produce a reasonable trade off in the values of critical damping at low and high frequencies of the structure For the three lowest natural frequencies the effective value of is greater than 0 05 but as was shown in Figure 7 10 the first two modes do not contribute significantly to the response For the remaining modes the value of is less than 0 05 The variation of as a function of natural frequency is shown in Figure 7 12 0 20 Critical damping 0 05 0 00 0 100 200 300 400 500 600 Frequency rad sec Figure 7 12 Effect of damping on the results 3 Repeat the previous step for the main member section properties 1 24 COMPARISON WITH DIRECT TIME INTEGRATION Delete both analysis steps 5 Create an single explicit dynamics step and specify a time period of 0 5 s In addition edit the step to use linear geometry by setting NLGEOM NO on the STEP option this will result in a linear analysis For your simulation the option block defining the explicit dynamics step should look similar to the following STEP NLGEOM NO Direct integration transient dynamic analysis DYNAMIC EXPLICIT t O55 BULK VISCOSITY 0 06 1 2 Redefine the tip load The CLOAD option block for this simulation 1s CLOAD AMPLITUDE BOUNCE 104 2 1 0E4 Redefine node set TIP to include only node 104
456. mesh detail The MASS elements are positioned as shown in Figure 12 52 The mesh for the packaging is too coarse near the impacting corner to provide highly accurate results However the mesh is adequate for a low cost preliminary study Element set PARTS Element set CHIPS contains elements on e contains all mass the circuit board Z 10 135 elements each with a connected to the mass of 0 005 kg chips Element set BOTPART contains only the bottom most of these elements Node set CHIPS contains corresponding nodes Figure 12 52 Position of mass elements on circuit board Numbers in parentheses are x y coordinates in millimeters based on a local origin at the bottom left hand corner of the circuit board 12 62 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST 12 10 3 Node and element sets The steps that follow assume that you have access to the full input file for this example This input file circuit inp is provided in Circuit board drop test Section A 15 in the online HTML version of this manual Instructions on how to fetch and run the script are given in Appendix A Example Files Figure 12 52 and Figure 12 53 show all of the sets necessary to apply the element properties loads initial conditions and boundary conditions as well as to request output for postprocessing Element set BOARD contains all circuit board elements Node set BOARD contains all circuit board nodes El
457. method has great cost savings over the implicit method as the model size increases e The stability limit is the maximum time increment that can be used to advance the kinematic state and still remain accurate 9 29 SUMMARY e Abaqus Explicit automatically controls the time increment size throughout the analysis to maintain stability e As the material stiffness increases the stability limit decreases as the material density increases the stability limit increases e Fora mesh with a single material the stability limit is roughly proportional to the smallest element dimension e Generally mass proportional damping is used in Abaqus Explicit to damp low frequency oscillations and stiffness proportional damping is used to damp high frequency oscillations e In some situations an Abaqus Explicit analysis may become unstable The example problems in this chapter describe how to recognize and rectify instabilities 9 30 DEFINING MATERIALS IN Abaqus 10 Materials The material library in Abaqus allows most engineering materials to be modeled including metals plastics rubbers foams composites granular soils rocks and plain and reinforced concrete This guide discusses only three of the most commonly used material models linear elasticity metal plasticity and rubber elasticity All of the material models are discussed in detail in Part V Materials of the Abaqus Analysis User s Manual 10 1 Defining materials
458. metrically It is easier to define the orientation of the beam section geometry for this model than it was for the cargo crane model in the earlier chapters because the pipe section is symmetric Define the approximate nj direction as the vector 0 0 1 0 In this model the actual n vector will coincide with this approximate vector BEAM SECTION ELSET PIPE MATERIAL STEEL SECTION PIPE 0 09 0 02 0 0 0 0 1 0 Material data The option blocks defining the material behavior of the steel pipe in your model are included in the following lines MATERIAL NAME STEEL ELASTIC 200 E9 0 3 You must define the density of the steel material 7800 kg m because eigenmodes and eigenfrequencies are being extracted in this simulation and a mass matrix is needed for this procedure Therefore the following option block must follow the ELASTIC option block DENSITY 7800 11 11 5 EXAMPLE VIBRATION OF A PIPING SYSTEM 11 3 5 Reviewing the input file the history data In this simulation you need to investigate the eigenmodes and eigenfrequencies of the steel pipe section when a 4 MN tensile load is applied Therefore the load history data will be split into two steps Step 1 General step Apply a 4 MN tensile force Step 2 Linear perturbation step Calculate modes and frequencies The actual magnitude of time in these steps will have no effect on the results unless the model includes damping or rate dependent material pro
459. mode These one element simulations are very easy to perform in Abaqus CAE Please consult the Abaqus CAE User s Manual for details Stability of the material model 10 7 It is common for the material model determined from the test data to be unstable at certain strain magnitudes Abaqus performs a stability check to determine the strain magnitudes where unstable behavior will occur and prints a warning message in the data dat file You should check this information carefully since your simulation may not converge if any part of the model experiences strains beyond the stability limits The stability checks are done for specific deformations so it is possible for the material to be unstable at the strain levels indicated if the deformation is more complex Likewise it is possible for the material to become unstable at lower strain levels if the deformation is more complex In Abaqus Standard your simulation may not converge if a part of the model exceeds the stability limits See Hyperelastic behavior of rubberlike materials Section 22 5 1 of the Abaqus Analysis User s Manual for suggestions on improving the accuracy and stability of the test data fit Example axisymmetric mount You have been asked to find the axial stiffness of the rubber mount shown in Figure 10 39 and to identify any areas of high maximum principal stress that might limit the fatigue life of the mount The mount is bonded at both ends to steel plates
460. model see Figure 2 6 is shown below ELEMENT TYPE T2D2 ELSET FRAME 11 101 102 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST 12 102 103 13 101 104 14 102 104 15 102 105 16 103 105 17 104 105 Element section properties Each element must refer to an element section property The appropriate element section option for each element and the additional geometric data if any needed for each element are described in the Abaqus Analysis User s Manual For the T2D2 element you must use the SOLID SECTION option and give one data line with the cross sectional area of the element If you leave the data line blank the cross sectional area 1s assumed to be 1 0 In this case all the members are circular bars that are 5 mm in diameter Their cross sectional area is 1 963 x 10 m The MATERIAL parameter which is required for most element section options refers to the name of a material property definition that is to be used with the elements The name can have up to 80 characters and must begin with a letter In this example all of the elements have the same section properties and are made of the same material Typically there will be several different element section properties in an analysis for example different components in a model may be made of different materials The elements are associated with material properties through element sets For the overhead hoist model the elements are added to an eleme
461. mouse until the cursor is over the desired item Select Point to an item and then click mouse button 1 Shift Click Press and hold the Shift key click mouse button 1 and then release the Shift key Ctrl Click Press and hold the Ctrl key click mouse button 1 and then release the Ctrl key Abaqus Viewer is designed for use with a 3 button mouse Accordingly this manual refers to mouse buttons 1 2 and 3 as shown in Figure 1 2 However you can use Abaqus Viewer with a 2 button mouse as follows e The two mouse buttons are equivalent to mouse buttons 1 and 3 on a 3 button mouse e Pressing both mouse buttons simultaneously is equivalent to pressing mouse button 2 on a 3 button mouse Tip You are instructed to click mouse button 2 in procedures throughout this manual Make sure that you configure mouse button 2 or the wheel button to act as a middle button click Abaqus documentation The documentation for Abaqus is extensive and complete The following documentation and publications are available from SIMULIA through the Abaqus online HTML documentation and in PDF format For more information on accessing the online HTML manuals refer to the discussion of execution procedures in the Abaqus Analysis User s Manual For more information on printing the manuals refer to Printing from a PDF book Section 5 3 of Using Abaqus Online Documentation Abaqus Analysis User s Manual This manual contains a com
462. mping in the highest element mode is given by the following equation LE bi bs min 0 Enot Cd e where 1s the fraction of critical damping The linear term alone represents 6 of critical damping whereas the quadratic term is usually much smaller 9 25 5 DAMPING OF DYNAMIC OSCILLATIONS 9 5 2 Viscous pressure Viscous pressure loads are commonly used in structural problems and quasi static problems to damp out the low frequency dynamic effects thus allowing static equilibrium to be reached in a minimal number of increments These loads are applied as distributed loads DLOAD defined by the following formula P U0 n where p is the pressure applied to the body c is the viscosity given on the data line as the magnitude of the load v is the velocity vector of the point on the surface where the viscous pressure is being applied and n is the unit outward normal vector to the surface at the same point For typical structural problems it is not desirable to absorb all of the energy Typically c is set equal to a small percentage perhaps 1 or 2 percent of the quantity pcg as an effective way of minimizing ongoing dynamic effects 9 5 3 Material damping The material model itself may provide damping in the form of plastic dissipation or viscoelasticity For many applications such damping may be adequate Another option is to use Rayleigh damping defined using the DAMPING option which is part of the MATE
463. ms require a large number of increments The explicit solution method has proven valuable in solving quasi static problems as well Abaqus Explicit solves certain types of static problems more readily than Abaqus Standard does One advantage of the explicit procedure over the implicit procedure is the greater ease with which it resolves complicated contact problems In addition as models become very large the explicit procedure requires fewer system resources than the implicit procedure Refer to Comparison of implicit and explicit procedures Section 2 4 for a detailed comparison of the implicit and explicit procedures Applying the explicit dynamic procedure to quasi static problems requires some special considerations Since a static solution is by definition a long time solution it 1s often computationally impractical to simulate an event in its natural time scale which would require an excessive number of small time increments To obtain an economical solution the event must be accelerated in some way The problem is that as the event is accelerated the state of static equilibrium evolves into a state of dynamic equilibrium in which inertial forces become more dominant The goal is to model the process in the shortest time period in which inertial forces remain insignificant Quasi static analyses can also be conducted in Abaqus Standard Quasi static stress analysis in Abaqus Standard is used to analyze linear or nonlinear problems wit
464. n The expression full integration refers to the number of Gauss points required to integrate the polynomial terms in an element s stiffness matrix exactly when the element has a regular shape For hexahedral and quadrilateral elements a regular shape means that the edges are straight and meet at right angles and that any edge nodes are at the midpoint of the edge Fully integrated linear elements use two integration points in each direction Thus the three dimensional element C3D8 uses a 2 x 2 x 2 array of integration points in the element Fully integrated quadratic elements available only in Abaqus Standard use three integration points in each direction The locations of the integration points in fully integrated two dimensional quadrilateral elements are shown in Figure 4 2 4 2 ELEMENT FORMULATION AND INTEGRATION Linear element Quadratic element e g CPS4 e g CPS8 Figure 4 2 Integration points in fully integrated two dimensional quadrilateral elements Several different finite element meshes were used in Abaqus Standard simulations of the cantilever beam problem as shown in Figure 4 3 The simulations use either linear or quadratic fully integrated elements and illustrate the effects of both the order of the element first versus second and the mesh density on the accuracy of the results 8 x 24 Figure 4 3 Meshes used for the cantilever beam simulations The ratios of the tip displacemen
465. n 100 000 customers in 80 countries A pioneer in the 3D software market since 1981 Dassault Systemes develops and markets PLM application software and services that support industrial processes and provide a 3D vision of the entire lifecycle of products from conception to maintenance to recycling The Dassault Systemes portfolio consists of CATIA for designing the virtual product SolidWorks for 3D mechanical design DELMIA for virtual production SIMULIA for virtual testing ENOVIA for global collaborative lifecycle management and 3DVIA for online 3D lifelike experiences Dassault Systemes shares are listed on Euronext Paris 13065 DSU PA and Dassault Systemes ADRs may be traded on the US Over The Counter OTC market DASTY For more information visit www 3ds com BS DASSAULT SUYUSTEMES www 3ds com Abaqus the 3DS logo SIMULIA CATIA SolidWorks DELMIA ENOVIA 3DVIA and Unified FEA are trademarks or registered trademarks of Dassault Syst mes or its subsidiaries in the US and or other countries Other company product and service names may be trademarks or service marks of their respective owners Dassault Systemes 2012
466. n Abaqus Explicit the three analysis options are DYNAMIC EXPLICIT DYNAMIC TEMPERATURE DISPLACEMENT EXPLICIT and ANNEAL The DYNAMIC TEMPERATURE DISPLACEMENT procedure simulates the fully coupled thermal mechanical response of a body while the ANNEAL procedure simulates the relaxation of stresses and plastic strains that occurs as metals are heated to a high temperature In this simulation we want to determine the dynamic response of the structure over a period of 0 01 s Thus we will use DYNAMIC EXPLICIT Replace the STATIC option block with the following DYNAMIC EXPLICIT 0 01 Modifying the output requests Because this is a dynamic analysis in which the transient response of the frame is of interest it 1s helpful to have the displacements of the center point written as history output Displacement history output can be requested only for a node set Thus you will create a node set that contains the node at the center of the bottom of the truss Then you will add displacements to the history output requests Create a set named CENTER using the NSET option as follows NSET NSET CENTER 102 Place this option block in the model data portion of your input file e g after the node definitions Replace the existing output requests with the following OUTPUT FIELD VARIABLE PRESELECT OUTPUT HISTORY VARIABLE PRESELECT FREQUENCY 1 NODE OUTPUT NSET CENTER U Submitting the new input file for analysis Perform
467. n contacting surfaces consists of two components one normal to the surfaces and one tangential to the surfaces The tangential component consists of the relative motion sliding of the surfaces and possibly frictional shear stresses Each contact interaction can refer to a contact property that specifies a model for the interaction between the contacting surfaces There are several contact interaction models available in Abaqus the default model is frictionless contact with no bonding 12 1 5 INTERACTION BETWEEN SURFACES 12 2 1 Behavior normal to the surfaces The distance separating two surfaces is called the clearance The contact constraint is applied in Abaqus when the clearance between two surfaces becomes zero There is no limit in the contact formulation on the magnitude of contact pressure that can be transmitted between the surfaces The surfaces separate when the contact pressure between them becomes zero or negative and the constraint is removed This behavior referred to as hard contact is the default contact behavior in Abaqus and is summarized in the contact pressure clearance relationship shown in Figure 12 1 Contact pressure Contact clearance Figure 12 1 Contact pressure clearance relationship for hard contact By default hard contact is directly enforced when using contact pairs in Abaqus Standard The dramatic change in contact pressure that occurs when a contact condition changes from open
468. n how to use the data in these files to assess Abaqus s progress on your simulations There may be situations where you decide based on information in these files to terminate your analysis early A more likely scenario is that you may need to use these files to learn what caused Abaqus to terminate your analysis prematurely 1 e what caused the convergence problems Status file The status file 1s particularly useful for monitoring the progress of a nonlinear simulation while the job is running The output below shows the status file for this nonlinear skewed plate example SUMMARY OF JOB INFORMATION STEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC OF DOF IF DISCON ITERS ITERS TIME TIME LPF TIME LPF MONITOR RIKS ITERS FREQ 1 1 1 0 4 4 0 100 0 100 0 1000 1 2 1 0 2 2 0 200 0 200 0 1000 1 3 1 0 2 2 0 350 0 350 0 1500 1 4 1 0 2 2 0 575 0 575 0 2250 1 5 1 0 3 3 0 913 0 913 0 3375 1 6 1 0 2 2 1 00 1 00 0 08750 The status file contains a separate line for every converged increment in the simulation The first column shows the step number 1in this case there is only one step The second column gives the 8 16 EXAMPLE NONLINEAR SKEW PLATE increment number The sixth column shows the number of iterations Abaqus needed to obtain a converged solution in each increment for example Abaqus needed 4 iterations in increment 1 The eighth column shows the total step time completed and the ninth column shows the increment size AT This ex
469. n mode is plotted it is a rigid body mode Advance the plot to the second mode of the blank Superimpose the undeformed model shape on the deformed model shape The frequency analysis shows that the blank has a fundamental frequency of 140 Hz corresponding to a period of 0 00714 s Figure 13 8 shows the displaced shape of the second mode We now know that the shortest step time for the forming analysis is 0 00714 s 2 G Figure 13 8 Second mode of the blank from the Abaqus Standard frequency analysis Creating the Abaqus Explicit forming analysis The goal of the forming process is to quasi statically form a channel with a punch displacement of 0 03 m In selecting loading rates for quasi static analyses it is recommended that you begin with faster loading rates and decrease the loading rates as necessary to converge on a quasi static solution more quickly However if you wish to increase the likelihood of a quasi static result in your first analysis attempt you should consider step times that are a factor of 10 to 50 times slower than that corresponding to the fundamental frequency In this analysis you will start with a time period of 0 007 s for the forming analysis step which is based on the frequency analysis 13 10 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit performed in Abaqus Standard which shows that the blank has a fundamental frequency of 140 Hz corresponding to a time period of 0 00714 s This time period corresp
470. n the input examples that follow Also use data from an integration point that is closest to the top surface of the lug but not adjacent to the constrained nodes Thus you will need to identify the element s label as well as its nodal connectivity to determine which integration point to use To determine the integration point number 1 In the Display Group toolbar select the Create Display Group iso tool in the Create Display Group dialog box select Elements as the item and Element sets as the method From the list of available element sets select EL206 and toggle on Highlight items in viewport to confirm its selection Click Replace 2 Plot the undeformed shape of this element with the node labels made visible Click the auto fit tool to obtain a plot similar to Figure 10 185 3 Use the Query tool to obtain the nodal connectivity for this corner element select Element and click the element in the viewport The nodal connectivity will be printed to the message area you are interested in only the first four nodes 4 Compare the nodal connectivity list with the undeformed model shape plot to determine which is the 1 2 3 4 face on your C3D20R element as defined in Three dimensional solid element library Section 28 1 4 of the Abaqus Analysis User s Manual For example in Figure 10 15 the 2841 3241 3245 2845 face corresponds to the 1 2 3 4 face After comparing these you will find we are interested in the
471. nal analytical rigid surface e Use TYPE CYLINDRICAL to define a three dimensional analytical rigid surface that is extruded infinitely in the out of plane direction e Use TYPE REVOLUTION to define a three dimensional analytical rigid surface of revolution The following is an example input for the two dimensional analytical rigid surface named SRIGID shown in Figure 12 7 SURFACE TYPE SEGMENTS NAME SRIGID START 5 0 0 0 LINE 10 0 0 0 CIRCL 15 0 5 0 10 0 5 0 where the rigid body is defined by RIGID BODY ANALYTICAL SURFACE SRIGID REF NODE 10000 Segment that defi lt gt you define 22 E direction Surface that is generated TYPE REVOLUTION TYPE CYLINDER Figure 12 7 Analytical rigid surfaces Discretized rigid surfaces are based on the underlying elements that make up a rigid body thus they can be more geometrically complex than analytical rigid surfaces Discretized rigid surfaces are defined using the SURFACE option in exactly the same manner as surfaces on deformable bodies 12 3 2 Contact interactions With the contact pair approach you define possible contact between two surfaces in an Abaqus Standard simulation by giving the surface names on the CONTACT PAIR option When you define a contact pair you must decide whether the magnitude of the relative sliding will be small or finite The default is the more general finite sliding formulation The small sliding formulation is appropriat
472. ncompatible mode elements The incompatible mode elements available primarily in Abaqus Standard are an attempt to overcome the problems of shear locking in fully integrated first order elements Since shear locking is caused by the inability of the element s displacement field to model the kinematics associated with bending additional degrees of freedom which enhance the element s deformation gradient are introduced into the first order element These enhancements to the deformation gradient allow a first order element to have a linear variation of the deformation gradient across the element s domain as shown in Figure 4 9 a The standard element formulation results in a constant deformation gradient across the element as shown in Figure 4 9 b resulting in the nonzero shear stress associated with shear locking These enhancements to the deformation gradient are entirely internal to an element and are not associated with nodes positioned along the element edges Unlike incompatible mode formulations that enhance the displacement field directly the formulation used in Abaqus does not result in overlapping material or a hole along the boundary between two elements as shown in Figure 4 10 Furthermore the formulation used in Abaqus is extended easily to nonlinear finite strain simulations something which is not as easy with the enhanced displacement field elements 5 ELEMENT FORMULATION AND INTEGRATION b Figure 4 9 Variati
473. ned completely by a maximum of six degrees of freedom at the rigid body reference node In Abaqus Explicit rigid bodies are particularly effective for modeling relatively stiff parts of a structure for which tracking stress waves and distributions is not important Element stable time increment estimates in the stiff region can result in a very small global time increment Since rigid bodies and elements that are part of a rigid body do not affect the global time increment using a rigid body instead of a deformable finite element representation in a stiff region can result in a much larger global time increment without significantly affecting the overall accuracy of the solution Rigid bodies defined with analytical rigid surfaces in Abaqus are slightly cheaper in terms of computational cost than discrete rigid bodies and may yield smoother results In Abaqus Explicit for example contact with analytical rigid surfaces tends to be less noisy than contact with discrete rigid bodies because analytical rigid surfaces can be smooth whereas discrete rigid bodies are inherently faceted However the shapes that can be defined with analytical rigid surfaces are limited 3 2 2 Components of a rigid body To create a discrete rigid body use the RIGID BODY option as the property reference for the elements forming the rigid body Use the REF NODE parameter to assign a rigid body reference node to the rigid body A rigid body reference node has both transl
474. nen RT _ Rene y Figure 10 52 Undeformed model shape of the rubber mount oe N In this figure the axisymmetric model is displayed as a planar two dimensional shape You can producing a three dimensional visual effect by sweeping the model through a specified angle In addition you can also mirror results about selected planes such as symmetry planes to render results on a full three dimensional representation of the model These are visualization aids only Any numerical representation of the results such as the contour legend indicates only the portion of the model that was analyzed Since in this problem the symmetry plane does not necessarily coincide with one of the global coordinate system planes a local system will be defined to facilitate the mirroring operation To define a local coordinate system for postprocessing 1 2 From the main menu bar select Tools Coordinate System Create In the Create Coordinate System dialog box enter rectangular as the name and click Continue Select the node at the top left corner of the model as the origin the node at the top right corner as the point on the X axis and the node at the bottom left corner as the point in the X Y plane To mirror and sweep the cross section 1 From the main menu bar selec
475. neously and is held constant for 3 88 x 10 s Then the load is suddenly removed and held constant at zero The AMPLITUDE option is used to define the time variation of loads and boundary conditions On the data lines following the AMPLITUDE option pairs of data are given in the form lt time gt lt amplitude gt lt time gt lt amplitude gt etc Up to four data pairs can be entered on each data line Abaqus considers the amplitude to be held constant following the last amplitude value given The following AMPLITUDE option block defines the amplitude for the blast load AMPLITUDE NAME BLAST 0 1 3 88E 5 1 3 89E 5 0 3 90E 5 0 9 4 3 Reviewing the input file the history data We will now review the history data associated with this problem including the step definition loading bulk viscosity and output requests EXAMPLE STRESS WAVE PROPAGATION IN A BAR Step definition The step definition indicates that this is an explicit dynamics analysis with a duration of 2 0 x 10 s You can also include a descriptive title for the step STEP Blast loading DYNAMIC EXPLICIT 2 0E 4 Loading Apply the pressure load with a value of 1 0 x 10 Pa to the free face of the bar which you previously defined to be in an element set called ELOAD The pressure load at any given time is the magnitude specified under the DLOAD option times the value interpolated from the amplitude curve To apply the load correctly you ne
476. neral contact interactions is the more general finite sliding formulation Small sliding is appropriate if the relative motion of the two surfaces is less than a small proportion of the characteristic length of an element face The small sliding formulation is selected by including the SMALL SLIDING parameter on the CONTACT PAIR option Using the small sliding formulation when applicable results in a more efficient analysis 12 9 Modeling considerations in Abaqus Explicit We now discuss the following modeling considerations correct definition of surfaces overconstraints mesh refinement and initial overclosures 12 9 1 Correct surface definitions Certain rules must be followed when defining surfaces for use with each of the contact algorithms The general contact algorithm has fewer restrictions on the types of surfaces that can be involved in contact however two dimensional and node based surfaces can be used only with the contact pair algorithm Continuous surfaces Surfaces used with the general contact algorithm can span multiple unattached bodies More than two surface facets can share a common edge In contrast all surfaces used with the contact pair algorithm must be continuous and simply connected The continuity requirement has the following implications for what constitutes a valid or invalid surface definition for the contact pair algorithm e Intwo dimensions the surface must be either a simple nonintersecting curve with two
477. nergy balance which includes the kinetic energy of any rigid bodies with mass Since only the deformable bodies are of interest when evaluating the results the kinetic energy of the rigid bodies should be subtracted from Erota When evaluating the energy balance For example if you are simulating a transport problem with rolling rigid dies the kinetic energy of the rigid bodies may be a significant portion of the total kinetic energy of the model In such cases you must subtract the kinetic energy associated with rigid body motions before a meaningful comparison with internal energy can be made 13 7 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit 13 5 In this example you will solve the channel forming problem from Chapter 12 Contact using Abaqus Explicit You will then compare the results from the Abaqus Standard and Abaqus Explicit analyses You will make modifications to the model created for the Abaqus Standard analysis so that you are able to run it in Abaqus Explicit These modifications include adding density to the material model and changing the steps Before running the Abaqus Explicit analysis you will use the frequency extraction procedure in Abaqus Standard to determine the time period required to obtain a proper quasi static response I Figure 13 6 Uniaxial tensile test E energy on ee ee S TOT KE v FD Figure 13 7 Energy history for quasi static tensile test time Example
478. ness e the radius of curvature and e the wavelength of the highest vibration mode of interest Abaqus shell elements assume that plane sections perpendicular to the shell midsurface remain plane Do not be confused into thinking that the thickness must be less than 1 10 of the element dimensions A highly refined mesh may contain shell elements whose thickness is greater than their in plane dimensions although this is not generally recommended continuum elements may be more suitable in such a case Element geometry Two types of shell elements are available in Abaqus conventional shell elements and continuum shell elements Conventional shell elements discretize a reference surface by defining the element s planar dimensions its surface normal and its initial curvature The nodes of a conventional shell element however do not define the shell thickness the thickness 1s defined through section properties Continuum shell elements on the other hand resemble three dimensional solid elements in that they discretize an entire three dimensional body yet are formulated so that their kinematic and constitutive behavior is similar to conventional shell elements Continuum shell elements are more accurate in contact modeling than conventional shell elements since they employ two sided contact taking into account changes in thickness For thin shell applications however conventional shell elements provide superior performance In this manual
479. ness of the pipe and thus increased the vibrational frequencies of the pipe section This lowest natural frequency is within the frequency range of the harmonic loads therefore resonance of the pipe may be a problem when it is used with this loading You therefore need to continue the simulation and apply additional tensile load to the pipe section until you find the magnitude that raises the natural frequency of the pipe section to an acceptable level Rather than repeating the analysis and increasing the applied axial load you can use the restart capability in Abaqus to continue the load history of a prior simulation in a new analysis 11 4 Restart analysis Multistep simulations need not be defined in a single job Indeed it is usually desirable to run a complex simulation in stages This allows you to examine the results and confirm that the analysis is performing as expected before continuing with the next stage The Abaqus restart analysis capability allows a simulation to be restarted and the model s response to additional load history to be calculated The restart analysis capability is discussed in detail in Restarting an analysis Section 9 1 1 of the Abaqus Analysis User s Manual 11 16 RESTART ANALYSIS 11 4 1 The restart and state files The Abaqus Standard restart res file and the Abaqus Explicit state abq file contain the information necessary to continue a previous analysis In Abaqus Explicit the pa
480. nimum and or maximum allowable increment sizes For example if you know that your simulation may have trouble obtaining a solution if too large a load increment is applied perhaps because the model may undergo plastic deformation you may want to decrease AT maz If the increment converges in fewer than five iterations this indicates that the solution is being found fairly easily Therefore Abaqus Standard automatically increases the increment size by 50 if two consecutive increments require fewer than five iterations to obtain a converged solution Details of the automatic load incrementation scheme are given in the message file as shown in more detail in Results Section 8 4 3 8 11 5 INCLUDING NONLINEARITY IN AN Abaqus ANALYSIS 8 3 Including nonlinearity in an Abaqus analysis We now discuss how to account for nonlinearity in an Abaqus analysis The main focus is on geometric nonlinearity 8 3 1 Geometric nonlinearity Incorporating the effects of geometric nonlinearity in an analysis requires only minor changes to an Abaqus Standard model You need to make sure the step definition considers geometrically nonlinear effects by setting the NLGEOM parameter equal to YES on the STEP option This is the default setting in Abaqus Explicit You also need to set time incrementation parameters as discussed in Automatic incrementation control in Abaqus Standard Section 8 2 3 The following input describes a static analysis in whi
481. ns to make the model behave as if the whole component were being modeled You may also have to adjust the applied loads to reflect the portion of the structure actually being modeled Consider the portal frame in Figure 10 41 The frame is symmetric about the vertical line shown in the figure To maintain symmetry in the model any nodes on the symmetry line must be constrained from translating in the 1 direction and from rotating about the 2 or 3 axes degrees of freedom 5 and 6 Therefore the symmetry constraints are BOUNDARY lt node gt 1 lt node gt 5 6 In the frame problem the load is applied along the model s symmetry plane therefore only half of the total value should be applied to the portion you are modeling In axisymmetric analyses using axisymmetric elements such as this rubber mount example we need model only the cross section of the component The element formulation automatically includes the effects of axial symmetry 10 57 5 EXAMPLE AXISYMMETRIC MOUNT Mirror symmetry Axisymmetry Repetitive symmetry 7 Cyclic symmetry Figure 10 40 Various forms of symmetry Point load P applied Applied on center line load P 2 r a XSYMM 7 boundary condition ae Base built in 2 t 3 l ENCASTRE boundary condition Figure 10 41 Symmetric portal frame 10 7 2 Coordinate system The model in this example uses the default r z 1 2 axisymmetric coordinate system in this sim
482. nt library Section 28 1 3 of the Abaqus Analysis User s Manual Element properties The SOLID SECTION option defines the material and any additional geometric data associated with a set of continuum elements For three dimensional and axisymmetric elements no additional geometric information is required the nodal coordinates completely define the element geometry For plane stress and plane strain elements the thickness of the elements must be specified on the data line For example if the elements are 0 2 m thick the element property definition would be the following SOLID SECTION ELSET lt element setname gt MATERIAL lt material name gt 0 2 Formulation and integration Alternative formulations available for the continuum family of elements in Abaqus Standard include an incompatible mode formulation the last or second to last letter in the element name is I and a hybrid element formulation the last letter in the element name is H both of which are discussed in detail later in this guide In Abaqus Standard you can choose between full and reduced integration for quadrilateral and hexahedral brick elements In Abaqus Explicit you can choose between full and reduced integration for hexahedral brick elements however only reduced integration is available for quadrilateral first order elements Both the formulation and type of integration can have a significant effect on the accuracy of solid elements as discussed in El
483. nt results stored at nodes such as nodal forces The relative size of the arrows indicates the relative magnitude of the results and the vectors are oriented along the global direction of the results The symbol plot legend shows how each arrow color corresponds to a specific range of values You can plot results for the resultant of variables such as displacement U reaction force RF etc or you can plot individual components of these variables Before proceeding suppress the visibility of the element normals To generate a symbol plot of the displacement 1 From the list of variable types on the left side of the Field Output toolbar select Symbol 2 From the list of output variables in the center of the toolbar select U 3 From the list of vector quantities and selected components select U3 Abaqus Viewer displays a symbol plot of the displacement vector resultant on the deformed model shape 4 The default shaded render style obscures the arrows An unobstructed view of the arrows can be obtained by changing the render style to Wireframe using the Common Plot Options dialog box If the element normals are still visible you should turn them off at this time 5 The symbol plot can also be based on the undeformed model shape From the main menu bar select Ploot Symbols On Undeformed Shape 5 22 5 EXAMPLE SKEW PLATE A symbol plot on the undeformed model shape appears as shown in Figure 5 14 Figure 5 14 Symb
484. nt set called FRAME Element set FRAME is then used as the value of the ELSET parameter on the element section option Add the following option block to your input file SOLID SECTION ELSET FRAME MATERIAL STEEL diameter 5mm gt area 1 963E 5 sq m 1 963E 5 A Any line in the input file that begins l with is treated as a comment Cross sectional area of truss elements Materials One of the features that makes Abaqus a truly general purpose finite element program is that almost any material model can be used with any element Once the mesh has been created material models can be associated as appropriate with the elements in the mesh Abaqus has a large number of material models many of which include nonlinear behavior In this overhead hoist example we use the simplest form of material behavior linear elasticity In Chapter 10 Materials two of the most common forms of nonlinear material behavior are considered metal plasticity and rubber elasticity A discussion of all the material models available in Abaqus can be found in the Abaqus Analysis User s Manual 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST Linear elasticity is appropriate for many materials at small strains particularly for metals up to their yield point It is characterized by a linear relationship between stress and strain Hooke s law as shown in Figure 2 7 Stress Young s modulus E Strain Figure 2 7 Linear
485. nt types of behavior some element families in Abaqus include elements with several different formulations For example the shell element family has three classes one suitable for general purpose shell analysis another for thin shells and yet another for thick shells These shell element formulations are explained in Chapter 5 Using Shell Elements Some Abaqus Standard element families have a standard formulation as well as some alternative formulations Elements with alternative formulations are identified by an additional character at the end of the element name For example the continuum beam and truss element families include members with a hybrid formulation in which the pressure continuum elements or axial force beam and truss elements is treated as an additional unknown these elements are identified by the letter H at the end of the name C3D8H or B31H Some element formulations allow coupled field problems to be solved For example elements whose names begin with the letter C and end with the letter T such as C3D8T possess both mechanical and thermal degrees of freedom and are intended for coupled thermal mechanical simulations Several of the most commonly used element formulations are discussed later in this guide Integration Abaqus uses numerical techniques to integrate various quantities over the volume of each element Using Gaussian quadrature for most elements Abaqus evaluates the material response at
486. ntered around a simple example covers the basics of using Abaqus By the end of Chapter 2 Abaqus Basics you will know the fundamentals of how to prepare a model for an Abaqus simulation check the data run the analysis job and view the results Chapter 3 Finite Elements and Rigid Bodies presents an overview of the main element families available in Abaqus The use of continuum solid elements shell elements and beam elements is discussed in Chapter 4 Using Continuum Elements Chapter 5 Using Shell Elements and Chapter 6 Using Beam Elements respectively Linear dynamic analyses are discussed in Chapter 7 Linear Dynamics Chapter 8 Nonlinearity introduces the concept of nonlinearity in general and geometric nonlinearity in particular and contains the first nonlinear Abaqus simulation Nonlinear dynamic analyses are discussed in Chapter 9 Nonlinear Explicit Dynamics and material nonlinearity 1s introduced in Chapter 10 Materials Chapter 11 Multiple Step Analysis introduces the concept of multistep simulations and Chapter 12 Contact discusses the many issues that arise in contact analyses Using Abaqus Explicit to solve quasi static problems is presented in Chapter 13 Quasi Static Analysis with Abaqus Explicit The illustrative example is a sheet metal forming simulation which requires importing between Abaqus Explicit and Abaqus Standard to perform the forming
487. nternal energy alone is not adequate to confirm the quality You should also evaluate the two energies independently to determine whether they are reasonable This part of the evaluation 13 13 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit takes on increased importance when accurate springback stress results are needed because an accurate springback stress solution is highly dependent on accurate plasticity results Even if the kinetic energy is fairly small if it contains large oscillations the model could be experiencing significant plasticity Generally we expect smooth loading to produce smooth results if the loading 1s smooth but the energy results are oscillatory the results may be inadequate Since an energy ratio is incapable of showing such behavior you should also study the kinetic energy history itself to see whether it is smooth or noisy If the kinetic energy does not indicate quasi static behavior it can be useful to look at velocity histories at some nodes to get an understanding of the model s behavior in various regions Such velocity histories can indicate which regions of the model are oscillating and causing the high kinetic energies Evaluating the results Enter Abaqus Viewer and open the output database created by this job channel xp1 odb Plot the whole model kinetic ALLKE and internal ALLIE energies History plots of the kinetic and internal energies for the whole model appear as shown in Figure 13 9
488. nts in a numerically integrated shell You can specify any odd number of section points through the shell thickness with the SHELL SECTION option By default Abaqus uses five section points through the thickness of a homogeneous Shell which is sufficient for most nonlinear design problems However you should use more section points in some complicated simulations especially when you anticipate reversed plastic bending nine is normally sufficient in this case For linear problems three section points provide exact integration through the thickness However the SHELL GENERAL SECTION option is more efficient for linear elastic shells If you use the SHELL GENERAL SECTION option the material behavior must be linear elastic as the stiffness of the cross section 1s calculated only once at the beginning of the simulation In this case all calculations are done in terms of the resultant forces and moments across the entire cross section If you request stress or strain output Abaqus provides default output for the bottom surface the midplane and the top surface ELEMENT GEOMETRY 5 1 2 Shell normals and shell surfaces The connectivity of the shell element defines the direction of the positive normal as shown in Figure 5 2 n n 4 face SPOS 3 1 3 1 face SNEG 2 Three dimensional shells 2 n 2 Axisymmetric shells Figure 5 2 Positive normals for shells For axisymmetric shell elements the positive normal direction is defined b
489. nverged as far as the displacements are concerned The convergence of the results is plotted in Figure 4 45 Stress at attachment ne 3 o a O 14 oo _ as oa Stress on hole r y Aa N ELA e T a a z 1 2 f _ O if g e 4 Displacement of hole t E 1 0 20 40 60 80 100 120 Relative Mesh Density Figure 4 45 Convergence of results in mesh refinement study All the results are normalized with respect to the values predicted by the coarse mesh The peak stress on the bottom of the hole converges much more slowly than the displacements because stress and strain are calculated from the displacement gradients thus a much finer mesh is required to predict accurate displacement gradients than is needed to calculate accurate displacements Mesh refinement significantly changes the stress calculated at the attachment of the connecting lug it continues to increase with continued mesh refinement A stress singularity exists at the corner of the lug where it attaches to the parent structure Theoretically the stress is infinite at this location therefore increasing the mesh density will not produce a converged stress value at this location This singularity occurs because of the idealizations used in the finite element model The connection between the lug and the parent structure has been modeled as a sharp corner and the parent structure has been modeled as rigid These idealizations lead to the stress singularity In reality the
490. nvergence difficulties that may be encountered when solving problems involving a nonlinear material response using implicit methods We will now focus on solving a problem involving plasticity using explicit dynamics As will become evident shortly convergence difficulties are not an issue in this case since iteration is not required for explicit methods In this example you will assess the response of a stiffened square plate subjected to a blast loading in Abaqus Explicit The plate is firmly clamped on all four sides and has three equally spaced stiffeners welded to it The plate is constructed of 25 mm thick steel and is 2 m square The stiffeners are made from 12 5 mm thick plate and have a depth of 100 mm Figure 10 18 shows the plate geometry and material properties in more detail Since the plate thickness is significantly smaller than any other global dimensions shell elements can be used to model the plate The purpose of this example is to determine the response of the plate and to see how it changes as the sophistication of the material model increases Initially we analyze the behavior with the standard elastic plastic material model Subsequently we study the effects of including material damping and rate dependent material properties 10 5 1 Coordinate system This model uses the default rectangular coordinate system with the plate lying in the 1 3 plane Since the plate thickness is significantly smaller than any other global dim
491. o where Lis the current length lo is the original length and e is the true strain or logarithmic strain The stress measure that is the conjugate to the true strain is called the true stress and is defined as and OC A where F is the force in the material and A is the current area A ductile metal subjected to finite deformations will have the same stress strain behavior in tension and compression if true stress 1s plotted against true strain 10 2 3 Defining plasticity in Abaqus When defining plasticity data in Abaqus you must use true stress and true strain Abaqus requires these values to interpret the data correctly Quite often material test data are supplied using values of nominal stress and strain In such situations you must use the expressions presented below to convert the plastic material data from nominal stress strain values to true stress strain values The relationship between true strain and nominal strain is established by expressing the nominal Strain as l i l l l nS tne w lo lo bo Adding unity to both sides of this expression and taking the natural log of both sides provides the relationship between the true strain and the nominal strain 10 4 PLASTICITY IN DUCTILE METALS e ln 1 Enom The relationship between true stress and nominal stress is formed by considering the incompressible nature of the plastic deformation and assuming the elasticity is also incompressible so loo LA
492. o bending therefore they are useful for modeling pin jointed frames Moreover truss elements can be used as an approximation for cables or strings for example in a tennis racket Trusses are also sometimes used to represent reinforcement within other elements The overhead hoist model in Chapter 2 Abaqus Basics uses truss elements All truss element names begin with the letter T The next two characters indicate the dimensionality of the element 2D for two dimensional trusses and 3D for three dimensional trusses The final character represents the number of nodes in the element Truss element library Linear and quadratic trusses are available in two and three dimensions Quadratic trusses are not available in Abaqus Explicit Degrees of freedom Truss elements have only translational degrees of freedom at each node Three dimensional truss elements have degrees of freedom 1 2 and 3 while two dimensional truss elements have degrees of freedom 1 and 2 Element properties The SOLID SECTION option is used to specify the name of the material property definition associated with the given set of truss elements The cross sectional area is given on the data line SOLID SECTION ELSET lt element set name gt MATERIAL lt material gt lt cross sectional area gt 3 14 RIGID BODIES Formulation and integration In addition to the standard formulation a hybrid truss element formulation is available in A
493. o illustrate the problem of determining the proper loading rate consider the deformation of a side intrusion beam in a car door by a rigid cylinder as shown in Figure 13 3 The actual test is quasi static The response of the beam varies greatly with the loading rate At an extremely high impact velocity of 400 m s the deformation in the beam is highly localized as shown in Figure 13 4 To obtain a better quasi static solution consider the lowest mode The frequency of the lowest mode is approximately 250 Hz which corresponds to a period of 4 milliseconds The natural frequencies can easily be calculated using the FREQUENCY procedure in Abaqus Standard To deform the beam by the desired 0 2 m in 4 milliseconds the velocity of the cylinder is 50 m s While 50 m s still seems like a high impact velocity the inertial forces become secondary to the overall stiffness of the structure and the deformed shape shown in Figure 13 5 1ndicates a much better quasi static response 13 3 LOADING RATES 200 GPa 0 3 250 MPa Young s Modulus Poisson s Ratio Yield Stress Fixed BC 20 MPa 7800 Kg m 3 Shell Thickness Hardening Modulus Density 3mm Fixed BC Circular Beam Length 1m Rigid Cylinder Figure 13 3 Rigid cylinder impacting beam Figure 13 4 Impact velocity of 400 m s Figure 13 5 Impact velocity of 50 m s 13 4 LOADING RATES While the overall structural response appears to be w
494. o steps should be 1000 N and 3000 N not 1000 N and 2000 N Modifying loads from step to step Applying a load in Abaqus requires more than just providing its magnitude and direction You must also specify how these new loads interact with the existing loads and boundary conditions of the same type that were defined in previous general steps All the loading and boundary condition options such as BOUNDARY CLOAD and DLOAD use the OP parameter to indicate how the loads they define interact with the existing loads of that type The parameter can be set to OP MOD or OP NEW Abaqus assumes OP MOD if no value is provided for the OP parameter 11 2 GENERAL ANALYSIS PROCEDURES Using OP MOD causes the loads defined in the current general step to modify the same types of loads already applied to the model in previous general steps Any load that is not specifically modified in the current step continues to follow its associated amplitude definition provided the amplitude curve 1s defined in terms of total time otherwise the load is maintained at the magnitude it had at the end of the last general step For example consider a cantilever beam modeled with two B22 elements see Figure 11 2 with concentrated loads of 1000 N applied to nodes 3 and 5 in the first general step 1000N 1000N CLOAD 3y 2 LOUL 5y Ap L000 l 2 3 4 5 Vy Figure 11 2 Loads applied to a beam in the first general step Step 1 In the next general
495. ociated with the concentrated force should be set to RAMP1 Modify the history output request for the punch reference node to request output at 200 evenly spaced intervals using the built in anti aliasing filter After these changes the first step definition will appear in the input file as follows k k k Step 1 k k k STEP Apply holder force DYNAMIC EXPLICIT 0 0001 CONTACT PAIR INTERACTION FRIC BLANK B DIE BLANK T HOLDER CONTACT PAIR INTERACTION NOFRIC BLANK T PUNCH BOUNDARY CENTER XSYMM REFDIE 1 6 REFPUNCH 1 6 REFHOLD 1 1 REFHOLD 6 6 CLOAD AMPLITUDE RAMP1 REFHOLD 2 4 4E5 OUTPUT FIELD VARIABLE PRESELECT OUTPUT HISTORY VARIABLE PRESELECT FILTER ANTIALIASING NODE OUTPUT NSET REFPUNCH 13 12 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit RF2 U2 END STEP For the second explicit dynamics step set the time period to 0 007 s Delete the CONTACT CONTROLS option it is relevant only for Abaqus Standard and modify the boundary condition to use the amplitude curve RAMP2 The second step appears as follows k k k Step 2 kk STEP Apply punch stroke DYNAMIC EXPLICIT 0 007 BOUNDARY AMPLITUDE RAMP2 REFPUNCH 2 2 0 030 END STEP To help determine how closely the analysis approximates the quasi static assumption the various energy histories will be useful Especially useful is comparing the kinetic energy to the internal strain energy The energy his
496. ode set For this exercise you will be creating multiple output requests for the bottom most chip node 403 that differ only by the output sample rate which 1s not a component of the history output name To easily distinguish between the similar output requests create two new sets for node 403 Name one of the new sets BotChip all1 and the other BotChip largeInc NSET NSET BotChip all 403 NSET NSET BotChip largeInc 403 Next add a new history output request for the vertical displacement velocity and acceleration of the chips In addition request element logarithmic strain components LE11 LE22 and LE12 and logarithmic principal strain LEP at the top face section point 5 of element set BOTPART of the circuit board to which the bottom most chip is attached For these output requests record the data at every 0 07 ms and apply the built in anti aliasing filter OUTPUT HISTORY TIME INTERVAL 0 07E 3 FILTER ANTIALIASING NODE OUTPUT NSET CHIPS U3 V3 A3 ELEMENT OUTPUT ELSET BOTPART 5 LE11 LE22 LE12 LEP Request history output at every increment for the vertical displacement velocity and acceleration of the bottom most chip Use node set BotChip al1 for this output request OUTPUT HISTORY FREQUENCY 1 NODE OUTPUT NSET BotChip all U3 V3 A3 Add one more output request for the vertical displacement velocity and acceleration of the bottom most chip This time request the output every 0 7 ms and apply the
497. ode and element numbers 10 7 4 Preprocessing creating the model The steps that follow assume that you have access to the full input file for this example This input file mount inp is provided in Blast loading on a stiffened plate Section A 9 in the online HTML version of this manual Instructions on how to fetch and run the script are given in Appendix A Example Files If you use Abaqus CAE or another preprocessor to create the mesh for this model try to create a node set MIDDLE containing all the nodes on the symmetry plane and apply a pressure load of 0 50 MPa to the bottom of the plate Figure 10 45 Check that this pressure results in a total applied load of 5 5 kN 5 5 kN 0 50 MPa x r ri If you can t create the mesh the Abaqus input options used to create the model can be found in Axisymmetric mount Section A 10 10 59 5 EXAMPLE AXISYMMETRIC MOUNT A Node numbers increase by 100 Ot 202 903 904 905 ba Wee lon ex toes toes bes _ _ _ _ _ ee tee el tae le Node a kas kae bis ee numbers bos das kos koe laos lane lee aa faa ka increase by 1 LOL 102 103 04 10 11 12 13 14 as Figure 10 43 Node numbers A Element numbers increase by 100 Element numbers increase by 1
498. odel shapes LJ Use the Allow Multiple Plot States tool to display the deformed model shape with the undeformed model shape superimposed Set the render style for both images to wireframe and toggle off the translucency of the superimposed plot from the Superimpose Plot Options dialog box Rotate the view to obtain a plot similar to that shown in Figure 8 13 By default the deformed shape is plotted for the last increment For clarity the edges of the undeformed shape are plotted using a dashed style Figure 8 13 Deformed and undeformed model shapes of the skew plate Using results from other frames You can evaluate the results from other increments saved to the output database file by selecting the appropriate frame To select a new frame 1 From the main menu bar select Result Step Frame The Step Frame dialog box appears 2 Select Increment 4 from the Frame menu 3 Click OK to apply your changes and to close the Step Frame dialog box Any plots now requested will use results from increment 4 Repeat this procedure substituting the increment number of interest to move through the output database file 8 24 EXAMPLE NONLINEAR SKEW PLATE Note Alternatively you may use the Frame Selector dialog box to select a results frame X Y plotting You saved the displacements of the midspan nodes node set MIDSPAN in the history portion of the output database file skew _n1l odb for each increment of the simulat
499. odulus of 210 0 GPa v 0 3 Its stress strain behavior is shown in Figure 12 19 The material undergoes considerable work hardening as it deforms plastically It is likely that plastic strains will be large in this analysis therefore hardening data are provided up to 50 plastic strain 600 500 400 300 Stress MPa 200 100 0 1 0 2 0 3 0 4 0 5 Plastic strain Figure 12 19 Yield stress vs plastic strain The blank is going to undergo significant rotation as it deforms Reporting the values of stress and strain in a coordinate system that rotates with the blank s motion will make it much easier to interpret the results Therefore an ORIENTATION option should be used to create a coordinate system that is aligned initially with the global coordinate system but moves with the elements as they deform The following input options are needed to define the blank s element and material properties ORIENTATION NAME LOCAL 1 0 0 0 1 0 1 0 SOLID SECTION MATERIAL STEEL ORIENTATION LOCAL ELSET BLANK CONTROL EC 1 SECTION CONTROLS NAME EC 1 HOURGLASS ENHANCED MATERIAL NAME STEEL ELASTIC 2 1E11 0 3 PLASTIC 400 E6 0 0E 2 12 21 5 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL 420 E6 2 0E 2 500 E6 20 0E 2 600 E6 50 0E 2 12 5 5 Contact definitions The contact definitions for each part of the model are discussed here Rigid surfaces The blank holder the punch and the die
500. of Simulation Excellence Fremont CA Tel 1 510 794 5891 simulia west support 3ds com West Lafayette IN Tel 1 765 497 1373 simulia central support 3ds com Northville MI Tel 1 248 349 4669 simulia greatlakes info 3ds com Woodbury MN Tel 1 612 424 9044 simulia central support 3ds com Mayfield Heights OH Tel 1 216 378 1070 simulia erie info 3ds com Mason OH Tel 1 513 275 1430 simulia central support 3ds com Warwick RI Tel 1 401 739 3637 simulia east support 3ds com Lewisville TX Tel 1 972 221 6500 simulia south info 3ds com Richmond VIC Tel 61 3 9421 2900 simulia au support 3ds com Vienna Tel 43 1 22 707 200 simulia at info 3ds com Maarssen The Netherlands Tel 31 346 585 710 simulia benelux support 3ds com Toronto ON Tel 1 416 402 2219 simulia greatlakes info 3ds com Beijing P R China Tel 8610 6536 2288 simulia cn support 3ds com Shanghai P R China Tel 8621 3856 8000 simulia cn support 3ds com Espoo Tel 358 40 902 2973 simulia nordic info 3ds com Velizy Villacoublay Cedex Tel 33 1 61 62 72 72 simulia fr support 3ds com Aachen Tel 49 241 474 01 0 simulia de info 3ds com Munich Tel 49 89 543 48 77 0 simulia de info 3ds com Chennai Tamil Nadu Tel 91 44 43443000 simulia in info 3ds com Lainate MI Tel 39 02 3343061 simulia ity info 3ds com Tokyo Tel 81 3 5442 6302 simulia jp support 3ds com Osaka Tel 81 6 7730 2703 simulia jp support 3ds com Ma
501. of the Abaqus Benchmarks Manual 7 11 Suggested reading e Clough R W and J Penzien Dynamics of Structures McGraw Hill 1975 e NAFEMS Ltd A Finite Element Dynamics Primer 1993 e Spence P W and C J Kenchington The Role of Damping in Finite Element Analysis Report R0021 NAFEMS Ltd 1993 7 12 Summary e Dynamic analyses include the effect of the structure s inertia e The FREQUENCY procedure extracts the natural frequencies and mode shapes of the structure e The mode shapes can then be used to determine the dynamic response of linear systems by modal superposition This technique is efficient but 1t cannot be used for nonlinear problems 7 28 SUMMARY Linear dynamic procedures are available in Abaqus Standard to calculate the transient response to transient loading the steady state response to harmonic loading the peak response to base motion and the response to random loading You should extract enough modes to obtain an accurate representation of the dynamic behavior of the structure The total modal effective mass in the direction in which motion will occur should be at least 90 of the mass that can move to produce accurate results You can define direct modal damping Rayleigh damping and composite modal damping in Abaqus Standard However since the natural frequencies and mode shapes are based on the undamped structure the structure being analyzed should be only lightly damped Modal techniques are
502. ol in the toolbox The Common Plot Options dialog box appears 2 Click the Labels tab 3 Toggle on Show node labels 4 Click Apply Abaqus Viewer applies the change and keeps the dialog box open The customized undeformed plot is shown in Figure 2 9 2 30 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST 04 LOS 103 Figure 2 9 Node number plot To display element numbers 1 In the Labels tabbed page of the Common Plot Options dialog box toggle on Show element labels 2 Click OK Abaqus Viewer applies the change and closes the dialog box The resulting plot is shown in Figure 2 10 Figure 2 10 Node and element number plot Remove the node and element labels before proceeding To disable the display of node and element numbers repeat the above procedure and under Labels toggle off Show node labels and Show element labels 2 31 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST Displaying and customizing a deformed shape plot You will now display the deformed model shape and use the plot options to change the deformation scale factor You will also superimpose the undeformed model shape on the deformed model shape From the main menu bar select Plot Deformed Shape or use the i tool in the toolbox Abaqus Viewer displays the deformed model shape as shown in Figure 2 11 Figure 2 11 Deformed model shape For small displacement analyses the default formulation in Abaqus Standard the
503. ol plot of displacement You can plot principal values of tensor variables such as stress using symbol plots A symbol plot of the principal values of stress yields three vectors at every integration point each corresponding to a principal value oriented along the corresponding principal direction Compressive values are indicated by arrows pointing toward the integration point and tensile values are indicated by arrows pointing away from the integration point You can also plot individual principal values To generate a symbol plot of the principal stresses 1 From the list of variable types on the left side of the Field Output toolbar select Symbol 2 From the list of output variables in the center of the toolbar select S 3 From the list of tensor quantities and components select All principal components as the tensor quantity Abaqus Viewer displays a symbol plot of principal stresses B 4 From the main menu bar select Options Symbol or use the Symbol Options 5 tool in the toolbox to change the arrow length The Symbol Plot Options dialog box appears 5 In the Color amp Style page click the Tensor tab 6 Drag the Size slider to select 2 as the arrow length 5 23 5 EXAMPLE SKEW PLATE 7 Click OK to apply the settings and to close the dialog box The symbol plot shown in Figure 5 15 appears Figure 5 15 Symbol plot of principal stresses on the bottom surface of the plate 8 The principal stresses ar
504. om surface of the shell body In this case it may be easier to define the reference surface to be coincident with the CAD surface and therefore offset from the shell s midsurface Shell offsets can also be used to define a more precise surface geometry for contact problems where shell thickness is important Another situation where the offset from the midsurface may be important is when a shell with continuously varying thickness 1s modeled In this case defining the nodes at the shell midplane can be difficult If one surface is smooth while the other is rough as in some aircraft structures it is easiest to use shell offsets to define the nodes at the smooth surface Offsets can be introduced by specifying an offset value which is defined as the distance measured as a fraction of the shell s thickness from the shell s midsurface to the reference surface containing the element s nodes Positive values of the offset are in the positive normal direction When the offset is set equal to 0 5 or SPOS the top surface of the shell is the reference surface When the offset is set equal to 0 5 or SNEG the bottom surface is the reference surface The default offset is 0 which indicates that the middle surface of the shell is the reference surface These three reference surface offset settings are shown in Figure 5 4 for a mesh where the nodal positions are adjusted to keep the position of the midsurface constant 5 5 5 SHELL FORMUL
505. omb friction can be defined with u or Terit The solid line in Figure 12 2 summarizes the behavior of the Coulomb friction model there is zero relative motion slip of the surfaces when they are sticking the shear stresses are below up Optionally a friction stress limit can be specified if both contacting surfaces are element based surfaces In Abaqus Standard the discontinuity between the two states sticking or slipping can result in convergence problems during the simulation You should include friction in your Abaqus Standard simulations only when it has a significant influence on the response of the model If your contact simulation with friction encounters convergence problems one of the first modifications you should try in diagnosing the difficulty is to rerun the analysis without friction In general friction presents no additional computational difficulties for Abaqus Explicit Simulating ideal friction behavior can be very difficult therefore by default in most cases Abaqus uses a penalty friction formulation with an allowable elastic slip shown by the dotted line in Figure 12 2 The elastic slip is the small amount of relative motion between the surfaces that occurs when the surfaces should be sticking Abaqus automatically chooses the penalty stiffness the slope of the dotted line so that this allowable elastic slip is a very small fraction of the characteristic element length The penalty friction formulati
506. omically without artificially increasing the loading rate Mass scaling is the only option for reducing the solution time in simulations involving a rate dependent material or rate dependent damping such as dashpots In such simulations increasing the loading rate 1s not an option because material strain rates increase by the same factor as the loading rate When the properties of the model change with the strain rate artificially increasing the loading rate artificially changes the process The following equations show how the stable time increment is related to the material density As discussed in Definition of the stability limit Section 9 3 2 the stability limit for the model is the minimum stable time increment of all elements It can be expressed as LE At Cd where L is the characteristic element length and cq is the dilatational wave speed of the material The dilatational wave speed for a linear elastic material with Poisson s ratio equal to zero is given by E Cd 3 pP where p is the material density According to the above equations artificially increasing the material density p by a factor of f decreases the wave speed by a factor of f and increases the stable time increment by a factor of f Remember that when the global stability limit 1s increased fewer increments are required to perform the same analysis which is the goal of mass scaling Scaling the mass however has exactly the same influence
507. on inertial effects as artificially increasing the loading rate Therefore excessive mass scaling just like excessive loading rates can lead to erroneous solutions The suggested approach to determining 13 6 ENERGY BALANCE an acceptable mass scaling factor then is similar to the approach to determining an acceptable loading rate scaling factor The only difference to the approach is that the speedup associated with mass scaling is the square root of the mass scaling factor whereas the speedup associated with loading rate scaling is proportional to the loading rate scaling factor For example a mass scaling factor of 100 corresponds exactly to a loading rate scaling factor of 10 There are several ways to implement mass scaling in your model using the FIXED MASS SCALING or VARIABLE MASS SCALING option in the history definition of the input file Since the option is part of the history definition it can be changed from step to step allowing great flexibility Refer to Mass scaling Section 11 6 1 of the Abaqus Analysis User s Manual for details 13 4 Energy balance The most general means of evaluating whether or not a simulation is producing an appropriate quasi static response involves studying the various model energies The following is the energy balance equation in Abaqus Explicit Byt hy Erp Exe Erne Ew Epw Ecw Emw Eur Ftotat constant where Epy is the internal energy Hy is the viscous energy d
508. on of deformation gradient in a an incompatible mode enhanced deformation gradient element and b a first order element using a standard formulation hole initial geometry i gt lt deformed ey geometry Figure 4 10 Potential kinematic incompatibility between incompatible mode elements that use enhanced displacement fields rather than enhanced deformation gradients Abaqus uses the latter formulation for its incompatible mode elements Incompatible mode elements can produce results in bending problems that are comparable to quadratic elements but at significantly lower computational cost However they are sensitive to element distortions Figure 4 11 shows the cantilever beam modeled with deliberately distorted incompatible mode elements in one case with parallel distortion and in the other with trapezoidal distortion l l l 15 15 L i i 30 30 Z Zz VA Z 7 Z Z 45 45 Parallel distortion Trapezoidal distortion Figure 4 11 Distorted meshes of incompatible mode elements ELEMENT FORMULATION AND INTEGRATION Figure 4 12 shows the tip displacements for the cantilever beam models The tip displacements are normalized with respect to the analytical solution and plotted against the level of element distortion 1 20 1 20 1 00 1 00 0 80 0 80 0 60 0 60 cPS8R o __e CPS4I
509. on works well for most problems including most metal forming applications 12 3 5 INTERACTION BETWEEN SURFACES slipping Va t Shear stress Terit Oe sticking y slip Figure 12 2 Frictional behavior In those problems where the ideal stick slip frictional behavior must be included the Lagrange friction formulation can be used in Abaqus Standard and the kinematic friction formulation can be used in Abaqus Explicit The Lagrange friction formulation 1s more expensive in terms of the computer resources used because Abaqus Standard uses additional variables for each surface node with frictional contact In addition the solution converges more slowly so that additional iterations are usually required This friction formulation is not discussed in this guide Often the friction coefficient at the initiation of slipping from a sticking condition is different from the friction coefficient during established sliding The former is typically referred to as the static friction coefficient and the latter is referred to as the kinetic friction coefficient In Abaqus an exponential decay law is available to model the transition between static and kinetic friction see Figure 12 3 This friction formulation is not discussed in this guide In Abaqus Standard the inclusion of friction in a model adds unsymmetric terms to the system of equations being solved If u is less than about 0 2 the magnitude and influence of t
510. onds to a constant punch velocity of 4 3 m s You will examine the kinetic and internal energy results carefully to check that the solution does not include significant dynamic effects Before starting save a copy of channel inp as channel xpl inp Make all subsequent changes to the channel xpl inp file channel xpl inp is also available in Forming a channel with Abaqus Standard Section A 13 In this section you will modify the input file in order to perform the forming analysis of the blank using Abaqus Explicit This analysis also requires a density setting for the material model Steel so repeat the density specification step in Example forming a channel in Abaqus Explicit Section 13 5 A concentrated force will be applied to the blank holder To compute the dynamic response of the holder a point mass must be assigned to its rigid body reference point The actual mass of the holder is not important what is important is that the mass should be of the same order of magnitude as the mass of the blank 0 78 kg to minimize noise in the contact calculations Choose a point mass value of 0 1 kg To assign the mass append the following statements to the option block for the rigid blank holder ELEMENT TYPE MASS ELSET HOLDER MASS 8000 8000 MASS ELSET HOLDER MASS 0l For the first attempt of this metal forming analysis you will use tabular amplitude curves with the default smoothing parameter for both the application of the hold
511. only conventional shell elements are discussed Henceforth we will refer to them simply as shell elements For more information on continuum shell elements see Shell elements overview Section 29 6 1 of the Abaqus Analysis User s Manual 5 1 1 Shell thickness and section points The shell thickness is required to describe the shell cross section and must be specified In addition to specifying the shell thickness you can choose to have the stiffness of the cross section calculated during ELEMENT GEOMETRY the analysis or once at the beginning of the analysis You define the shell thickness using either the SHELL SECTION or SHELL GENERAL SECTION option If you use the SHELL SECTION option Abaqus uses numerical integration to calculate the stresses and strains independently at each section point integration point through the thickness of the shell thus allowing nonlinear material behavior For example an elastic plastic shell may yield at the outer section points while remaining elastic at the inner section points The location of the single integration point in an S4R 4 node reduced integration element and the configuration of the section points through the shell thickness are shown in Figure 5 1 Top surface of shell Integration point in an S4R element Section through shell Section points through the thickness of the shell at the location of the integration point Figure 5 1 Configuration of section poi
512. ons on how to fetch and run the script are given in Appendix A Example Files If you wish to create the entire model using Abaqus CAE please refer to Abaqus Standard 3 D example shearing of a lap joint Section 12 8 of Getting Started with Abaqus Interactive Edition 12 7 3 Reviewing the input file the model data We first review the model definition including the node and element definitions and section and material properties Model description The input file starts with a relevant description of the simulation and model in the HEADING option 12 37 Abaqus Standard 3 D EXAMPLE SHEARING OF A LAP JOINT HEADING Shearing of a lap joint SI units N kg mm s Nodal coordinates and element connectivity Check that the preprocessor used the correct element type for the plates and rivet Provide meaningful element set names such as PLATE and RIVET for the elements The ELEMENT options in this model follow ELEMENT TYPE C3D81I ELSET PLATE ELEMENT TYPE C3D8R ELSET RIVET ELEMENT TYPE C3D6 ELSET RIVET The model definition also specifies the creation of node sets so that parts of the model can be constrained and moved easily These sets are located at the following locations at the bottom left corner of the bottom plate set CORNER the left face of the bottom plate set FIX the right face of the top plate set PULL and the symmetry plane set SYMM NSET NSET CORNER NSET NSET FIX NSET
513. onse differs suggesting that there are significant modes in the range of 5 30 relating to the early response When five modes are used the total modal effective mass in the 2 direction is only 57 of the moveable mass 2 modes 5 modes 30 modes x10 12 00 8 00 4 00 0 00 4 00 t 8 00 12 00 16 00 20 00 24 00 28 00 DISPLACEMENT U2 0 00 0 10 0 20 0 30 0 40 0 50 STEP TIME Figure 7 10 Effect of different numbers of modes on the results 7 7 Effect of damping In this simulation we used 5 of critical damping in all modes This value was chosen from experience based on the fact that the bolted connections between the trusses and the cross bracing might absorb 1 22 7 8 COMPARISON WITH DIRECT TIME INTEGRATION significant energy as a result of local frictional effects In cases such as this where accurate data are not available it is important to investigate the effect of the choices that you make Figure 7 11 compares the history of the reaction force at one of the top connections point C when 1 5 and 10 of critical damping are used As expected the oscillations at lower damping levels do not diminish as quickly as those at higher damping levels and the peak force is higher in the models with lower damping With damping ratios even as low as 1 the peak pull out force is 85 kN which is still less than the strength of the connection 100 kN Therefore the cargo crane should retain its
514. onstraints The cross bracing unlike the internal truss bracing is bolted to the truss members You can assume that these bolted connections are unable to transmit rotations or torsion The duplicate nodes that were defined at these locations are needed to define this constraint In Abaqus such constraints between nodes can be defined using multi point constraints MPCs or constraint equations Multi point constraints allow constraints to be imposed between different degrees of freedom of the model A large library of MPCs 1s available in Abaqus See Linear constraint equations Section 34 2 1 of the Abaqus Analysis User s Manual for a complete list and a description of each one The format of the MPC option 1s MPC lt type of MPC gt lt node I or node set 1 gt lt node 2 or node set 2 gt seses You can define multiple constraints of the same type with just a single data line by using node sets The MPC type needed to model the bolted connection is PIN The pinned joint created by this MPC constrains the displacements at two nodes to be equal but the rotations if they exist at the nodes remain independent There are many bolted joints in the crane model The following is the complete MPC option block for the model from Cargo crane Section A 4 MPC PIN 101 301 PIN 102 302 PIN 103 303 PIN 105 305 PIN 106 306 PIN 201 401 PIN 202 402 PIN 203 403 PIN 205 405 PIN 206 406 Add a similar option block to
515. ontact The accuracy of the incompatible mode elements available in Abaqus Standard is strongly influenced by the amount of element distortion The numerical accuracy of the results depends on the mesh that has been used Ideally a mesh refinement study should be carried out to ensure that the mesh provides a unique solution to the problem However remember that using a converged mesh does not ensure that the results from the finite element simulation will match the actual behavior of the physical problem that also depends on other approximations and idealizations in the model In general refine the mesh mainly in regions where you want accurate results a finer mesh is required to predict accurate stresses than is needed to calculate accurate displacements Advanced features such as submodeling are available in Abaqus to help you to obtain useful results for complex simulations 4 54 5 1 ELEMENT GEOMETRY Using Shell Elements Use shell elements to model structures in which one dimension the thickness is significantly smaller than the other dimensions and in which the stresses in the thickness direction are negligible A structure such as a pressure vessel whose thickness is less than 1 10 of a typical global structural dimension generally can be modeled with shell elements The following are examples of typical global dimensions e the distance between supports e the distance between stiffeners or large changes in section thick
516. ontinuum elements Abaqus defines the element output variables such as stress and strain with respect to the global Cartesian coordinate system You can change to a local coordinate system by using the ORIENTATION option For three dimensional shell elements Abaqus defines the element output variables with respect to a coordinate system based on the surface of the shell You can change the coordinate system by using the ORIENTATION option For computational efficiency any part of a model can be defined as a rigid body which has degrees of freedom only at its reference node As a method of constraint in an Abaqus Explicit analysis rigid bodies are computationally more efficient than multi point constraints 3 19 4 1 ELEMENT FORMULATION AND INTEGRATION Using Continuum Elements The continuum solid family of stress displacement elements is the most comprehensive of the element libraries in Abaqus There are some differences in the solid element libraries available in Abaqus Standard and Abaqus Explicit Abaqus Standard solid element library The Abaqus Standard solid element library includes first order linear interpolation elements and second order quadratic interpolation elements in two or three dimensions using either full or reduced integration Triangles and quadrilaterals are available in two dimensions and tetrahedra triangular wedges and hexahedra bricks are provided in three dimensions Modified second order
517. ophic failure caused by the collapse of the structure We have already mentioned that the steel would probably exhibit some hardening after it has yielded You suspect that including hardening behavior would allow the lug to withstand this 60 kN load because of the additional stiffness 1t would provide Therefore you decide to add some hardening to the steel s material property definition Assume that the yield stress increases to 580 MPa at a plastic strain of 0 35 which represents typical hardening for this class of steel The stress strain curve for the modified material model is shown in Figure 10 11 580 E6 380 E6 True stress go 0 3529 True strain Figure 10 11 Modified stress strain behavior of the steel Modify your PLASTIC option block as follows so that it includes the hardening data PLASTIC 380 H6 0 00 580 EH6 0 35 10 19 5 EXAMPLE CONNECTING LUG WITH PLASTICITY 10 4 6 Running the analysis with plastic hardening Save the model with plastic hardening to a new input file named lug plas hard inp and run the analysis using the command abaqus job lug plas hard Status file The summary of the analysis in the status file which is shown below shows that Abaqus found a converged solution when the full 60 kN load was applied The hardening data added enough stiffness to the lug to prevent it from collapsing under the 60 kN load SUMMARY OF JOB INFORMATION STEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC
518. option The complete material definition is MATERIAL NAME STEEL ELASTIC 200 E9 0 3 PLASTIC 380 E6 0 0 All other option blocks in the model definition portion of the input file remain unchanged 10 4 2 Modifications to the input file the history data This analysis requires a general nonlinear simulation because of the nonlinear material behavior in the model Therefore the PERTURBATION parameter must be removed from the STEP option The total step time in the STATIC procedure option block has been set to 1 0 and the initial increment size 1s 20 of the total step time This simulation is a static analysis of the lug under the extreme loads you do not know in advance how many increments this simulation may require The default maximum of 100 increments however is reasonably large and should be sufficient for this analysis Also we assume that the effects of geometric nonlinearity will not be important in this simulation so the NUGEOM parameter is omitted from the STEP option This portion of the input file appears as follows STEP STATIC 0 2 1 0 Loading The load applied in this simulation is twice what was applied in the linear elastic simulation of the lug 60 kN vs 30 KN Therefore this model doubles the magnitude of the pressures applied to the lug The modified DLOAD option block looks like DLOAD PRESS P6 1 E 08 10 12 EXAMPLE CONNECTING LUG WITH PLASTICITY Output requests You will use
519. option block which appeared as follows for the static analysis STEP Apply uniform pressure to the hole STATIC Replace this option block with the following one 4 41 5 EXAMPLE CONNECTING LUG xSTEP Dynamic lug loading DYNAMIC EXPLICIT 0 005 Request field output at evenly spaced intervals and default history output Write field output at 125 equally spaced intervals and also write the default history output You can specify output at evenly spaced intervals by appending the NUMBER INTERVAL parameter to the OQUTPUT option block Replace the existing output requests with the following OUTPUT FIELD NUMBER INTERVAL 125 NODE OUTPUT RF U ELEMENT OUTPUT DIRECTIONS YES S OUTPUT HISTORY VARIABLE PRESELECT Save the changes to the input file called lug _xpl inp Then run the simulation using the command abaqus job lug xpl 4 3 10 Postprocessing the dynamic analysis results In the static analysis performed with Abaqus Standard you examined the deformed shape of the lug as well as stress and displacement output For the Abaqus Explicit analysis you can similarly examine the deformed shape stresses and displacements in the lug Because transient dynamic effects may result from a sudden loading you should also examine the time histories for internal and kinetic energy displacement and Mises stress Open the output database odb file created by this job Plotting the deformed shape From the main m
520. order polynomial strain energy function to model the rubber material Indicate these choices by using the N 1 and POLYNOMIAL parameters on the HYPERELASTIC option Use the TEST DATA INPUT parameter to indicate that Abaqus should find the material constants from the test data you will provide The test data are given on options that immediately follow the HYPERELASTIC option The data should be entered as nominal stress and the corresponding nominal strain with negative values indicating compression You may be able to enter the data directly using your preprocessor for instance if you are using Abaqus CAE otherwise you will have to add it to your input file with an editor The material definition for the rubber will look like 10 62 EXAMPLE AXISYMMETRIC MOUNT MATERIAL NAME RUBBER HYPERELASTIC N 1 UNIAXTIAL TEST DATA 0 054E6 0 0380 0 152E6 0 1338 0 254E6 0 2210 0 362E6 0 3450 0 459E6 0 4600 0 583E6 0 6242 0 656H6 0 8510 0 730H6 1 4268 BIAXIAL TEST DATA 0 089E6 0 0200 0 255E6 0 1400 0 503E6 0 4200 0 958EH6 1 4900 1 703E6 2 7500 2 413E6 3 4500 PLANAR TEST DATA 0 055E6 0 0690 0 324E6 0 2828 0 758E6 1 3862 1 269H6 3 0345 1 779H6 4 0621 POLYNOMIAL TEST DATA INPUT The input file for the single element simulation of the three experimental tests 1s shown in Test fit of hyperelastic material data Section A 11 The computational and experimental results for the various types of tests are
521. orithm Abaqus Explicit will decide which type of weighting to use for a given contact pair based on the nature of the two surfaces involved and the constraint enforcement method used The general contact algorithm uses balanced master slave weighting whenever possible pure master slave weighting is used for general contact interactions involving node based surfaces 12 48 MODELING CONSIDERATIONS IN Abaqus Explicit which can act only as pure slave surfaces Use the CONTACT FORMULATION TYPE PURE MASTER SLAVE to specify pure master slave weighting for other general contact interactions For the contact pair algorithm Abaqus Explicit will decide which type of weighting to use for a given contact pair based on the nature of the two surfaces involved and the constraint enforcement method used The weight of the average can be specified by the user for balanced master slave contact with the contact pair algorithm using the WEIGHT parameter on the CONTACT PAIR option For most element types the default weight is 0 5 so that the same weight is used for each of the acceleration corrections Setting WEIGHT to 1 0 specifies a pure master slave relationship with the first surface as the master surface Conversely a weight of zero means that the second surface is the master surface Sliding formulation When defining a contact pair you must decide whether the magnitude of the relative sliding will be small or finite The default and only option for ge
522. ottom of the hole in the lug has displaced about 0 3 mm Field Output Report Source 1 ODB lug odb Step Step 1 Frame Increment 1 Step Time 2 2200E 16 Loc 1 Nodal values from source 1 Output sorted by column Node Label Field Output reported at nodes for part PART 1 1 Node U U2 Label Loc 1 SO 1 313 425E 06 10001 313 494E 06 20001 313 425E 06 Minimum 313 494E 06 At Node 10001 Maximum 313 425E 06 At Node 20001 4 3 9 Rerunning the analysis using Abaqus Explicit You will now evaluate the dynamic response of the lug when the same load 1s applied suddenly Of special interest is the transient response of the lug You will have to modify the model for the Abaqus Explicit analysis Before proceeding copy the existing input file to a input file named lug_ xpl inp Make all subsequent changes to the lug_xpl inp input file Before running the explicit analysis you will need to change the element type add a density to the material model and change the step type In addition you should make modifications to the field output requests Change element type Second order hexahedral elements are not available in the Abaqus Explicit element library Thus you will need to change the element type specified on the ELEMENT option from C3D20R to C3D8R This change also requires that you edit the element nodal connectivity so that only eight nodes are specified for each element For example the following ELEMENT option block w
523. ount of compressibility is introduced into the rubber material model in order to alleviate volumetric locking Provided the amount of compressibility 1s small the results obtained with a nearly incompressible material will be very similar to those obtained with an incompressible material Compressibility is introduced by setting the material constant D to a nonzero value The value is chosen so that the initial Poisson s ratio vo is close to 0 5 The equations given in Hyperelastic behavior of rubberlike materials Section 22 5 1 of the Abaqus Analysis User s Manual can be used to relate D and vo in terms of po and Ko the initial shear and bulk moduli respectively for the polynomial form of the strain energy potential For example the hyperelastic material coefficients obtained earlier from the test data see The hyperelastic material parameters in Example axisymmetric mount Section 10 7 were given as Cio 176051 and Co 4332 63 thus setting D 5 E 7 yields vo 0 46 A model incorporating compressibility with additional mesh refinement to reduce mesh distortion is shown in Figure 10 59 this mesh can be generated easily by changing the edge seeds in Abaqus CAE or another preprocessor 10 79 5 RELATED Abaqus EXAMPLES SE Figu
524. out the release of Abaqus used to run the analysis The header page also contains the phone number address and contact information of your local office or representative who can offer technical support and advice Input file echo After the header page the data file includes an echo of the input file The input data echo is generated by adding the option PREPRINT ECHO YES to the input file By default the parameter ECHO is set to NO ABAQUS INPUT ECHO HEADING Two dimensional overhead hoist frame SI units kg m s N 1l axis horizontal 2 axis vertical LINE 5 PREPRINT ECHO YES MODEL YES HISTORY YES k k 2 20 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST Model definition k NODE NSET NALL LINE 10 101 0 0 0 102 1 0 0 103 2 0 0 104 0 5 0 866 0 105 1 5 0 866 0 LINE 15 ELEMENT TYPE T2D2 ELSET FRAME 11 101 102 12 102 103 13 101 104 14 102 104 LINE 20 15 102 105 16 103 105 17 104 105 SOLID SECTION ELSET FRAME MATERIAL STEEL diameter 5mm gt area 1 963E 5 m 2 LINE 25 1 963E 5 MATERIAL NAME STEEL ELASTIC 200 E9 0 3 Kk LINE 30 History data k STEP PERTURBATION 10kN central load STATIC LINE 35 BOUNDARY 101 ENCASTRE 103 2 CLOAD 102 2 10 E3 LINE 40 NODE PRINT U RF EL PRINT S LINE 45 END STEP Options processed by Abaqus Following the input data echo is a list of the options processed by Abaqus
525. output database odb file so that they can be plotted using Abaqus Viewer The nodal displacements for each mode shape are normalized so that the maximum displacement is unity Therefore these results and the corresponding stresses and strains are not physically meaningful they should be used only for relative comparisons The step terminates with END STEP Step 2 Transient dynamics The MODAL DYNAMIC procedure is used for transient modal dynamic analysis The fixed time increment and the total step time are given on the data line for this option The total time of the simulation is 0 5 seconds with a constant increment of 0 005 seconds The format of this data line is basically the same as that for STATIC However in this case we must be careful to ensure that we give real values of time in dynamic analysis time is a real physical quantity The form of the STEP and MODAL DYNAMIC option blocks for this simulation should be STEP PERTURBATION Crane Response to Dropped Load MODAL DYNAMIC 0 005 0 5 Damping 5 of critical damping should be used in all 30 modes extracted in the first step This input is specified in the following MODAL DAMPING option block MODAL DAMPING MODAL DIRECT 1 30 0 05 7 12 EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING Selecting the eigenmodes The eigenmodes used in a mode based dynamic procedure must be selected with the SELECT EIGENMODES option if MODAL DAMPING is used For this e
526. overhead hoist 2 2 1 Keyword lines Keywords or options always begin with a star or asterisk For example NODE is the keyword for specifying the nodal coordinates and ELEMENT is the keyword for specifying the element connectivity Keywords are often followed by parameters some of which may be required The parameter TYPE is required with the ELEMENT option because the element type must always be given when defining elements For example the following statement indicates that we are defining the connectivity of T2D2 elements two dimensional truss elements with two nodes ELEMENT TYPE T2D2 Many parameters are optional and are defined only in certain circumstances For example the following statement indicates that all the nodes defined in this option block will be put into a set called PART1 NODE NSET PART1 It is not essential to put nodes into sets although it is convenient in many instances 2 5 5 FORMAT OF THE INPUT FILE HEADING Two dimensional overhead hoist frame SI Units l axis horizontal 2 axis vertical PREPRINT ECHO YES MODEL YES HISTORY YES kk Model definition lt a Comment k NODE 101 0 0 0 102 Ley Ons 0 103 ij 0 0 104 0 5 0 866 0 M r r odel data 105 1 5 0 866 0 ELEMENT TYPE T2D2 ELSET FRAME Keyword line 11 101 102 12 102 103 13 101 104 Option 14 102 104 Data lines block 15 102 105 16 103 105 17 104 105 SOLID SECTION ELSET FRA
527. oximately 13 increments to complete The contents of the status file are shown below SUMMARY OF JOB INFORMATION STEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC OF DOF IF DISCON ITERS ITERS TIME TIME LPF TIME LPF MONITOR RIKS ITERS FREQ 1 1 1 11 2 13 0 0500 0 0500 0 05000 1 2 1 3 2 5 0 100 0 100 0 05000 1 3 1 4 2 6 0 175 0 175 0 07500 1 4 1 3 2 5 0 288 0 288 0 1125 1 5 1 4 5 9 0 456 0 456 0 1688 1 6 1U 6 0 6 0 456 0 456 0 1688 1 6 2 3 3 6 0 498 0 498 0 04219 1 7 1 2 6 8 0 541 0 541 0 04219 1 8 1 1 4 5 0 583 0 583 0 04219 1 9 1 0 4 4 0 625 0 625 0 04219 1 10 1 1 2 3 0 688 0 688 0 06328 1 11 1 1 3 4 0 783 0 783 0 09492 1 12 1 2 2 4 0 926 0 926 0 1424 1 13 1 1 2 3 1 00 1 00 0 07441 12 7 7 Postprocessing In Abaqus Viewer examine the deformation of the assembly Deformed model shape and contour plots The basic results of this simulation are the deformation of the joint and the stresses caused by the shearing process Plot the deformed model shape and the Mises stress as shown in Figure 12 31 and Figure 12 32 respectively Contact pressures You will now plot the contact pressures in the lap joint Since it is difficult to see contact pressures when the entire model is displayed use the Display Groups toolbar to display only the top plate in the viewport Create a path plot to examine the variation of the contact pressure around the bolt hole of the top plate To create a path plot 1 In the Results Tree do
528. p to reflect that this 1s now a nonlinear analysis Defining the step time This analysis requires a data line to the STATIC option that specifies the size of the initial time increment ATinitial for the analysis and the total step time for the simulation A total step time of 1 0 is used and AT q1 18 Specified such that Abaqus applies 10 of the load in the first increment The completed STATIC option block will therefore be STATIC 0 1 1 0 8 14 EXAMPLE NONLINEAR SKEW PLATE Output control In a linear analysis Abaqus solves the equilibrium equations once and calculates the results for this one solution A nonlinear analysis can produce much more output because results can be requested at the end of each converged increment If you do not select the output requests carefully the output files become very large potentially filling the disk space on your computer As noted earlier output is available in four different files e the output database odb file which contains data in a neutral binary format necessary to postprocess the results with Abaqus Viewer e the data dat file which contains printed tables of selected results e the restart res file which is used to continue the analysis and e the results 11 file which is used with third party postprocessors Only the options for the output database odb and printed output dat files are discussed here If selected carefully data can be saved
529. pansion In cases where the material is highly confined such as an O ring used as a seal the compressibility must be modeled correctly to obtain accurate results Abaqus Standard has a special family of hybrid elements that must be used to model the fully incompressible behavior seen in hyperelastic materials These hybrid elements are identified by the letter H in their name for example the hybrid form of the 8 node brick C3D8 is called C3D8H Except for plane stress and uniaxial cases it is not possible to assume that the material is fully incompressible in Abaqus Explicit because the program has no mechanism for imposing such a constraint at each material calculation point An incompressible material also has an infinite wave speed resulting in a time increment of zero Therefore we must provide some compressibility The difficulty is that in many cases the actual material behavior provides too little compressibility for the algorithms to work efficiently Thus except for plane stress and uniaxial cases the user must provide enough compressibility for the code to work knowing that this makes the bulk behavior of the model softer than that of the actual material Some judgment is therefore required to decide whether or not the solution is sufficiently accurate or whether the problem can be modeled at all with Abaqus Explicit because of this numerical limitation We can assess the relative compressibility of a material by t
530. perties time has no physical meaning in a static analysis procedure Therefore use a step time of 1 0 in the general analysis steps Step 1 Apply a 4 MN tensile force The options necessary to define the first analysis step including the procedure definition boundary conditions loading and output requests are reviewed Step and analysis procedure definition The first step is a general static step that includes the effect of geometric nonlinearity Specify an initial increment size that is 1 10 the total step time causing Abaqus to apply 10 of the load in the first increment The following option blocks define the analysis procedure and they include a meaningful description of the step to make reviewing the load history much easier STEP NLGEOM YES Apply axial tensile load of 4 0 MN STATIC 0 1 1 0 Boundary conditions The pipe section is clamped at its left end node 1 in the model shown in Figure 11 9 It is also clamped at the other end however the axial force must be applied at this end so only degrees of freedom 2 to 6 are constrained BOUNDARY LEFT 1 6 RIGHT 2 6 Tensile loading Apply a 4 MN tensile force to the right end of the pipe section such that it deforms in the positive axial global 1 direction Forces are applied by default in the global coordinate system Therefore the CLOAD option block looks like CLOAD RIGHT 1 4 0E6 11 12 EXAMPLE VIBRATION OF A PIPING SYSTEM
531. ple CONTACT CONTACT INCLUSIONS ALL EXTERIOR CONTACT PROPERTY ASSIGNMENT FRIC SURFACE INTERACTION NAME FRIC FRICTION 0 1 specifies that all exterior faces in a given model might interact with each other The interaction between all surfaces includes friction with a friction coefficient of 0 1 12 3 3 Slave and master surfaces By default contact pairs in Abaqus Standard use a pure master slave contact algorithm nodes on one surface the slave cannot penetrate the segments that make up the other surface the master as shown in Figure 12 8 The algorithm places no restrictions on the master surface it can penetrate the slave surface between slave nodes as shown in Figure 12 8 The order of the two surfaces given on the CONTACT PAIR option determines which surface is the master surface and which 1s the slave surface the first surface is the slave surface and the second is the master surface 12 10 DEFINING CONTACT IN Abaqus Standard Master surface Segments Slave surface nodes _ _ 0 eel Penetration of master surface N Figure 12 8 The master surface can penetrate the slave surface Due to the strict master slave formulation you must be careful to select the slave and master surfaces correctly in order to achieve the best possible contact simulation Some simple rules to follow are e the slave surface should be the more finely meshed surface and e if the mesh densities a
532. ple if your component is loaded in compression make sure that your test data include compressive rather than tensile loading 10 54 HYPERELASTICITY TENSION COMPRESSION UNIAXIAL TEST BIAXIAL TEST y 2 PLANAR TEST 1 rap VOLUMETRIC TEST eee e 1 Vt a Figure 10 38 Deformation modes and Abaqus input options for the various experimental tests for defining hyperelastic material behavior e Both tension and compression data are allowed with compressive stresses and strains entered as negative values If possible use compression or tension data depending on the application since the fit of a single material model to both tensile and compressive data will normally be less accurate than for each individual test e Try to include test data from the planar test This test measures shear behavior which can be very important 10 55 5 EXAMPLE AXISYMMETRIC MOUNT e Provide more data at the strain magnitudes that you expect the material will be subjected to during the simulation For example if the material will only have small tensile strains say under 50 do not provide much if any test data at high strain values over 100 e Perform one element simulations of the experimental tests and compare the results Abaqus calculates to the experimental data If the computational results are poor for a particular deformation mode that 1s important to you try to obtain more experimental data for that deformation
533. ple you will create and plot the curve using history data To create an X Y plot of the vertical displacement for a node 1 In the Results Tree expand the History Output container underneath the output database named frame xpl odb 2 From the list of available history output double click Spatial displacement U2 at Node 102 in NSET CENTER Abaqus Viewer plots the vertical displacement at the center node along the bottom of the truss as shown in Figure 2 15 Note The chart legend has been suppressed and the axis labels modified in this figure Many X Y plot options are directly accessible by double clicking the appropriate regions of the viewport To enable direct object actions however you must first click in the prompt area to cancel the current procedure if necessary To suppress the legend double click it in the viewport to open the Chart Legend Options dialog box In the Contents tabbed page of this dialog box toggle off Show legend To modify the axis labels double click either axis to open the Axis Options dialog box and edit the axis titles as indicated in Figure 2 15 Exiting Abaqus Viewer Save your model database file then select File Exit from the main menu bar to exit Abaqus Viewer 2 4 Comparison of implicit and explicit procedures Abaqus Standard and Abaqus Explicit are capable of solving a wide variety of problems The characteristics of implicit and explicit procedures determine which method is approp
534. plete description of the elements material models procedures input specifications etc It is the basic manual for Abaqus Standard Abaqus Explicit and Abaqus CFD and it provides both input file usage and Abaqus CAE usage information This guide regularly 5 Abaqus DOCUMENTATION refers to the Abaqus Analysis User s Manual so you should have it available as you work through the examples Abaqus CAE User s Manual This manual includes detailed descriptions of how to use Abaqus CAE for model generation analysis and results evaluation and visualization Abaqus Viewer users should refer to the information on the Visualization module in this manual Using Abaqus Online Documentation This manual contains instructions for navigating viewing and searching the Abaqus HTML and PDF documentation In addition this manual explains how to use the PDF documentation to produce a high quality printed copy and how to use the icon in all PDF books except the Abaqus Scripting Reference Manual and the Abaqus GUI Toolkit Reference Manual to print a selected section of a book Other Abaqus documentation Abaqus Example Problems Manual This manual contains detailed examples designed to illustrate the approaches and decisions needed to perform meaningful linear and nonlinear analysis Many of the examples are worked with several different element types mesh densities and other variations Typical cases are large motion of an elastic plastic p
535. plicit adjusts the nodal coordinates without strain to remove any initial overclosures prior to the first step If the adjustments are large with respect to the element dimensions elements can become severely distorted e In subsequent steps any nodal adjustments to remove initial overclosures in Abaqus Explicit induce strains that can potentially cause severe mesh distortions e When you are interested in results that are likely to contain high frequency oscillations such as accelerations in an impact problem request Abaqus Explicit history output with a relatively high output rate and if the output rate is less than every increment apply an anti aliasing filter then use a postprocessing filter if stronger filtering is desired e The Abaqus Analysis User s Manual contains more detailed discussions of contact modeling in Abaqus Contact interaction analysis overview Section 35 1 1 of the Abaqus Analysis User s Manual is a good place to begin further reading on the subject 12 94 ANALOGY FOR EXPLICIT DYNAMICS 13 Quasi Static Analysis with Abaqus Explicit The explicit solution method is a true dynamic procedure originally developed to model high speed impact events in which inertia plays a dominant role in the solution Out of balance forces are propagated as stress waves between neighboring elements while solving for a state of dynamic equilibrium Since the minimum stable time increment is usually quite small most proble
536. po Gu Seoul Tel 82 2 785 6707 8 simulia kr info 3ds com Puerto Madero Buenos Aires Tel 54 11 4312 8700 Horacio Burbridge 3ds com Stockholm Sweden Tel 46 8 68430450 simulia nordic info 3ds com Warrington Tel 44 1925 830900 simulia uk info 3ds com Authorized Support Centers SMARTtech Sudamerica SRL Buenos Aires Tel 54 11 4717 2717 KB Engineering Buenos Aires Tel 54 11 4326 7542 Solaer Ingenieria Buenos Aires Tel 54 221 489 1738 SMARTtech Mec nica Sao Paulo SP Tel 55 11 3168 3388 Synerma s r 0 Psary Prague West Tel 420 603 145 769 abaqus synerma cz 3 Dimensional Data Systems Crete Tel 30 2821040012 support 3dds gr ADCOM Givataim Tel 972 3 7325311 shmulik keidar adcomsim co il WorleyParsons Services Sdn Bhd Kuala Lumpur Tel 603 2039 9000 abaqus my worleyparsons com Kimeca NET SA de CV Mexico Tel 52 55 2459 2635 Matrix Applied Computing Ltd Auckland Tel 64 9 623 1223 abaqus tech matrix co nz BudSoft Sp z 0 0 Poznan Tel 48 61 8508 466 info budsoft com pl TESIS Ltd Moscow Tel 7 495 612 44 22 info tesis com ru WorleyParsons Pte Ltd Singapore Tel 65 6735 8444 abaqus sg worleyparsons com Finite Element Analysis Services Pty Ltd Parklands Tel 27 21 556 6462 feas feas co za Principia Ingenieros Consultores S A Madrid Tel 34 91 209 1482 simulia principia es Taiwan Simutech Solution Corporation Taipei R O C Tel 886 2 2507 9550 camilla simutec
537. problems where the sliding between the surfaces is small What constitutes small sliding is often difficult to define but a general guideline to follow is that problems can use the small sliding approximation if a point contacting a surface does not slide more than a small fraction of a typical element dimension Small sliding is not available for general contact 12 2 3 Friction models When surfaces are in contact they usually transmit shear as well as normal forces across their interface Thus the analysis may need to take frictional forces which resist the relative sliding of the surfaces into account Coulomb friction is a common friction model used to describe the interaction of contacting surfaces The model characterizes the frictional behavior between the surfaces using a coefficient of friction p The default friction coefficient is zero The tangential motion is zero until the surface traction reaches a critical shear stress value which depends on the normal contact pressure according to the following equation Terit LP where u is the coefficient of friction and p is the contact pressure between the two surfaces This equation gives the limiting frictional shear stress for the contacting surfaces The contacting surfaces will not slip slide relative to each other until the shear stress across their interface equals the limiting frictional shear stress up For most surfaces jz is normally less than unity Coul
538. problems involving complex contact interaction between many independent bodies Abaqus Explicit is particularly well suited for analyzing the transient dynamic response of structures that are subject to impact loads and 9 1 5 EXPLICIT DYNAMIC FINITE ELEMENT METHODS subsequently undergo complex contact interaction within the structure An example of such a problem is the circuit board drop test presented in Chapter 12 Contact In this example a circuit board sitting in foam packaging is dropped on the floor from a height of 1 m The problem involves impact between the packaging and the floor as well as rapidly changing contact conditions between the circuit board and the packaging Complex postbuckling problems Unstable postbuckling problems are solved readily in Abaqus Explicit In such problems the stiffness of the structure changes drastically as the loads are applied Postbuckling response often includes the effects of contact interactions Highly nonlinear quasi static problems For a variety of reasons Abaqus Explicit 1s often very efficient in solving certain classes of problems that are essentially static Quasi static process simulation problems involving complex contact such as forging rolling and sheet forming generally fall within these classes Sheet forming problems usually include very large membrane deformations wrinkling and complex frictional contact conditions Bulk forming problems are characterized by large d
539. qus simulation are adequate Coarse meshes can yield inaccurate results in analyses using implicit or explicit methods The numerical solution provided by your model will tend toward a unique value as you increase the mesh density The computer resources required to run your simulation also increase as the mesh is refined The mesh is said to be converged when further mesh refinement produces a negligible change in the solution As you gain experience you will learn to judge what level of refinement produces a suitable mesh to give acceptable results for most simulations However it is always good practice to perform a mesh convergence study where you simulate the same problem with a finer mesh and compare the results You can have confidence that your model is producing a mathematically accurate solution 1f the two meshes give essentially the same result Mesh convergence is an important consideration in both Abaqus Standard and Abaqus Explicit The connecting lug will be used as an example of a mesh refinement study by further analyzing the connecting lug in Abaqus Standard using four different mesh densities Figure 4 43 The number of elements used in each mesh is indicated in the figure Coarse mesh 14 elements Normal mesh 112 elements gt _ a a E Fine mesh 448 elements Very fine mesh 1792 elements F
540. qus Standard While it is possible to perform springback analyses within Abaqus Explicit Abaqus Standard is much more efficient at solving springback analyses Since springback analyses are simply static simulations without external loading or contact Abaqus Standard can obtain a springback solution in just a few increments Conversely Abaqus Explicit must obtain a dynamic solution over a time period that is long enough for the solution to reach a steady state For efficiency Abaqus has the capability to transfer results back and forth between Abaqus Explicit and Abaqus Standard allowing you to perform forming analyses in Abaqus Explicit and springback analyses in Abaqus Standard The steps that follow assumes that you have access to the full input file for this example This input file channel springback inp is provided in Forming a channel with Abaqus Standard Section A 13 in the online HTML version of this manual Instructions on how to fetch and run the script are given in Appendix A Example Files The first option following HEADING 1s the IMPORT option which reads the element definitions and the state from the corresponding Abaqus Explicit analysis This import input file begins with the following HEADING Analysis of the forming of a channel springback Abaqus Standard springback following channel xpl 5 inp SI units kg m s N 13 26 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit IMPORT STEP 2 STATE YES
541. r 300 x user defined data points o regular data points 100 J P Figure 10 5 Example of user data that can be regularized exactly In this example Abaqus Explicit generates the six regular data points shown and the user s data are reproduced exactly Figure 10 6 shows a case where the user has defined data that are difficult to regularize exactly In this example it is assumed that Abaqus Explicit has regularized the data by dividing the range into 10 intervals that do not reproduce the user s data points exactly 10 8 PLASTICITY IN DUCTILE METALS O 200 i x user defined data points i o regular data points 100 maximum difference 26 gP Figure 10 6 Example of user data that are difficult to regularize Abaqus Explicit attempts to use enough intervals such that the maximum error between the regularized data and the user defined data is less than 3 however you can change this error tolerance If more than 200 intervals are required to obtain an acceptable regularized curve the analysis stops during the data checking with an error message In general the regularization 1s more difficult if the smallest interval defined by the user is small compared to the range of the independent variable In Figure 10 6 the data point for a strain of 1 0 makes the range of strain values large compared to the small intervals defined at low strain levels Removing this last data point enables the data to be regularized much more ea
542. r Specify the view and select the viewpoint method for rotating the view Enter the X Y and Z coordinates of the viewpoint vector as 1 0 5 1 and the coordinates of the up vector as 0 1 0 Verifying shell section assignment You can also visualize the section assignment and the shell thickness while postprocessing the results For example regions with common section assignments can be color coded to verify that the properties were assigned correctly select Sections from the Color Code toolbar to color the mesh according to section assignment To render the shell thickness select View ODB Display Options from the main menu bar In the ODB Display Options dialog box toggle on Render shell thickness and click Apply If the model looks correct as shown in Figure 10 26 toggle off this option and click OK before proceeding with the rest of the postprocessing instructions Otherwise correct the section assignment and rerun the job Animation of results As noted in earlier examples animating your results will provide a general understanding of the dynamic response of the plate under the blast loading First plot the deformed model shape Then create a time history animation of the deformed shape Use the Animation Options dialog box to change the mode to Play once You will see from the animation that as the blast loading is applied the plate begins to deflect Over the duration of the load the plate begins to vibrate and continues to
543. r analytically in the element formulation STRI3 or numerically through the use of a penalty constraint The thick only shell elements are second order quadrilaterals that may produce more accurate results than the general purpose shell elements in small strain applications where the loading is such that the solution is smoothly varying over the span of the shell To decide if a given application 1s a thin or thick shell problem we can offer a few guidelines For thick shells transverse shear flexibility 1s important while for thin shells it is negligible The significance of transverse shear in a shell can be estimated by its thickness to span ratio A shell made of a single isotropic material with a ratio greater than 1 15 is considered thick 1f the ratio is less than 1 15 the shell is considered thin These estimates are approximate you should always check the transverse shear effects in your model to verify the assumed shell behavior Since transverse shear flexibility can be significant in laminated composite shell structures this ratio should be much smaller for thin shell theory to apply Composite shells with very compliant interior layers so called sandwich composites have very low transverse shear stiffness and should almost always be modeled with thick shells if the assumption of plane sections remaining plane is violated continuum elements should be used See Shell section behavior Section 29 6 4 of t
544. r Abaqus Explicit The simulation which normally is run as a background process is the stage in which Abaqus Standard or Abaqus Explicit solves the numerical problem defined in the model Examples of output from a stress analysis include displacements and stresses that are stored in binary files ready for postprocessing Depending on the complexity of the problem being analyzed and the power of the computer being used it may take anywhere from seconds to days to complete an analysis run 5 COMPONENTS OF AN Abaqus ANALYSIS MODEL Postprocessing Abaqus Viewer You can evaluate the results once the simulation has been completed and the displacements stresses or other fundamental variables have been calculated The evaluation is generally done interactively using Abaqus Viewer or another postprocessor Abaqus Viewer which reads the neutral binary output database file has a variety of options for displaying the results including color contour plots animations deformed shape plots and X Y plots 2 1 Components of an Abaqus analysis model An Abaqus model is composed of several different components that together describe the physical problem to be analyzed and the results to be obtained At a minimum the analysis model consists of the following information discretized geometry element section properties material data loads and boundary conditions analysis type and output requests The discussion in this chapter focuses on structural
545. r Step 2 shows that the time increment size 1s constant throughout the step and that each increment requires only one iteration Since modal dynamic analysis involves the linear superposition of the mode shapes no iterating is required For the same reason the message file contains no information about equilibrium or residuals Data file The primary results for Step 1 are the extracted eigenvalues participation factors and effective mass as shown below EIGENVALUE OUTPUT MODE NO EIGENVALUE FREQUENCY GENERALIZED MASS RAD TIME CYCLES TIME 1 1773 4 42 112 6 7023 151 92 0 0000 2 7016 8 83 766 13 332 30 206 0 0000 3 7644 1 87 430 13 915 90 401 0 0000 4 22999 151 65 24 136 250 63 0 0000 5 24714 157 21 25 020 275 90 0 0000 6 34811 186 58 29 695 493 16 0 0000 7 42748 206 76 32 906 1107 1 0 0000 25 2 26885E 05 476 32 75 809 207 47 0 0000 26 2 42800E 05 492 75 78 423 127 02 0 0000 27 2 84057E 05 532 97 84 825 1240 8 0 0000 28 2 92452E 05 540 79 86 069 330 69 0 0000 29 3 13943E 05 560 31 89 175 272 41 0 0000 30 3 64774E 05 603 96 96 124 64 980 0 0000 The highest frequency extracted is 96 Hz with that mode COMPOSITE MODAL DAMPING The period associated with this frequency is 0 0104 seconds which is comparable to the fixed time increment of 0 005 seconds There is no point in extracting modes whose period is substantially smaller than the time increment used Conversely the time increment must be capable of resolving the highe
546. r in a number of general ways to model linear or nonlinear behavior Since Abaqus models the beam s cross section behavior directly in terms of section engineering quantities area moments of inertia etc with this option there is no need for Abaqus to integrate any quantities over the element cross section Therefore BEAM GENERAL SECTION is less expensive computationally than BEAM SECTION The response is calculated in terms of the force and moment resultants the stresses and strains are calculated only when they are requested for output In Abaqus Standard you can also define beams with linearly tapered cross sections General beam sections with linear response and standard library sections are supported Formulation and integration The linear beams B21 and B31 and the quadratic beams B22 and B32 are shear deformable and account for finite axial strains therefore they are suitable for modeling both slender and stout beams The cubic beam elements in Abaqus Standard B23 and B33 do not account for shear flexibility and assume small axial strain although large displacements and rotations of the beams are valid They are therefore suitable for modeling slender beams Abaqus Standard provides variants of linear and quadratic beam elements that are suitable for modeling thin walled open section beams B31OS and B3205 These elements model the effects of torsion and warping in open cross sections such as I beams or U section chann
547. r region are now much more distorted in the initial undeformed configuration However as the analysis progresses and the elements deform their shape actually improves The deformed shape plot shown in Figure 10 57 illustrates that the amount of element distortion in this region is reduced however the level of mesh distortion in the bottom right hand corner of the rubber model is still significant ii Figure 10 57 Deformed shape of the modified mesh The contours of maximum principal stress Figure 10 58 show that the very localized stress in that corner has been reduced only slightly 10 78 TECHNIQUES FOR REDUCING VOLUMETRIC LOCKING S Max Pri inci Ear 4 917e 05 i _ za Figure 10 58 Contours of maximum principal stress in the modified mesh Mesh design for large distortion problems is more difficult than it is for small displacement problems A mesh must be produced where the shape of the elements is reasonable throughout the analysis not just at the start You must estimate how the model will deform using experience hand calculations or the results from a coarse finite element model 10 9 Techniques for reducing volumetric locking A small am
548. r sticking Abaqus Standard applies a constraint for each closed node and removes constraints from any node where the contact state changes from closed to open Abaqus Standard then carries out an iteration and updates the configuration of the model using the calculated corrections In the updated configuration Abaqus Standard checks for changes in the contact conditions at the slave nodes Any node where the clearance after the iteration becomes negative or zero has changed status from open to closed Any node where the contact pressure becomes negative has changed status from closed to open If any contact changes are detected in the current iteration Abaqus Standard labels it a severe discontinuity iteration Abaqus Standard continues to iterate until the severe discontinuities are sufficiently small or no severe discontinuities occur and the equilibrium flux tolerances are satisfied Alternatively you can choose a different approach in which Abaqus Standard will continue to iterate until no severe discontinuities occur before checking for equilibrium The summary for each completed increment in the message and status files shows how many iterations were severe discontinuity iterations and how many were equilibrium iterations an equilibrium iteration 1s one in which no severe discontinuities occur The total number of iterations for an increment is the sum of these two For some increments you may find that all iterations are labeled severe dis
549. r the main members of the two trusses in the crane 2 Local beam section axes a a 0 1 LE Figure 6 16 Cross section geometry and dimensions in m of the main members The beam section axes for the main members should be oriented such that the beam 1 axis is orthogonal to the plane of the truss structures shown in the elevation view Figure 6 12 and the beam 2 axis is orthogonal to the elements in that plane Specify this orientation by giving the approximate direction of the beam 1 axis the n vector on the second data line of the BEAM GENERAL SECTION option To get the correct normal ng in this case you need to provide a very accurate n It is somewhat easier to provide an approximate direction which would be the negative 3 direction However given the logic that Abaqus uses to determine n s given t and nj the normal n is rotated slightly from its proper orientation if we use this approximate n You can specify the same nj direction for all elements in each of the two truss structures The third data line contains the elastic and shear moduli assuming a mild strength steel with amp 200 0 GPa v 0 25 and G 80 0 GPa These modeling data are included in the input file in the following option blocks BEAM GENERAL SECTION SECTION BOX ELSET OUTA 0 10 0 05 0 005 0 005 0 005 0 005 0 1118 0 0 0 9936 200 E9 80 E9 6 17 EXAMPLE CARGO CRANE BEAM GENERAL SECTION SECTION BOX ELSET OUTB 0 10 0 05 0
550. raditional contact pairs for Abaqus Standard see Understanding contact and constraint detection Section 15 6 of the Abaqus CAE User s Manual 12 7 Abaqus Standard 3 D example shearing of a lap joint This simulation of the shearing of a lap joint illustrates the use of general contact in Abaqus Standard The model consists of two overlapping aluminum plates that are connected with a titanium rivet The left end of the bottom plate is fixed and the force is applied to the right end of the top plate to shear the joint Figure 12 27 shows the basic arrangement of the components Because of symmetry only half of the joint is modeled to reduce computational cost Frictional contact is assumed 12 7 1 Mesh design Select the element type before designing the mesh The mesh used for the plates should consist of C3D8I elements the rivet should be meshed with C3D8R and C3D6 elements a representative mesh 1s shown in Figure 12 28 12 35 a Abaqus Standard 3 D EXAMPLE SHEARING OF A LAP JOINT Top plate Bottom plate Rivet Figure 12 27 Lap joint analysis Figure 12 28 Mesh 12 36 Abaqus Standard 3 D EXAMPLE SHEARING OF A LAP JOINT 12 7 2 Preprocessing creating the model The steps that follow assume that you have access to the full input file for this example This input file lap joint inp is provided in Shearing of a lap joint Section A 14 in the online HTML version of this manual Instructi
551. rain node 103 in the 2 direction degree of freedom 2 only any of the following data line formats can be used 103 2 2 0 0 Or 103 2 2 Or 103 2 Boundary conditions on a node are cumulative Thus the following input constrains node 101 in both directions and 2 101 1 101 2 Rather than specifying each constrained degree of freedom some of the more common constraints can be given directly using the following named constraints Degree of freedom Description ENCASTRE Constraint on all displacements and rotations at a node PINNED Constraint on all translational degrees of freedom XSYMM Symmetry constraint about a plane of constant x1 YSYMM Symmetry constraint about a plane of constant x9 ZSYMM Symmetry constraint about a plane of constant x3 XASYMM Antisymmetry constraint about a plane of constant 71 YASYMM Antisymmetry constraint about a plane of constant ro ZASYMM Antisymmetry constraint about a plane of constant z3 Thus another way to constrain all the active degrees of freedom at node 101 in the hoist model is 101 ENCASTRE The complete BOUNDARY option block for our hoist problem is BOUNDARY 101 ENCASTRE 103 2 In this example all of the constraints are in the global 1 or 2 directions In many cases constraints are required in directions that are not aligned with the global directions The 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST x TRANSFORM option can be used in such cases to define a loc
552. raint and causing large jumps in acceleration at that node Consequently it is good modeling practice to extend surfaces somewhat beyond the regions that will actually contact In general we recommend covering each contacting body entirely with surfaces the additional computational expense 1s minimal 12 50 MODELING CONSIDERATIONS IN Abaqus Explicit valid simply connected surface invalid surface invalid surface Figure 12 38 Valid and invalid three dimensional surfaces for the contact pair algorithm both sides belong to the same surface valid double sided surface Figure 12 39 Valid double sided surface Figure 12 40 shows two simple box like bodies constructed of brick elements The upper box has a contact surface defined only on the top face of the box While it is a permissible surface definition in Abaqus Explicit the lack of extensions beyond the raw edge could be problematic In the lower box the surface wraps some distance around the side walls thereby extending beyond the flat upper surface If contact is to occur only at the top face of the box this extended surface definition minimizes contact problems by keeping any contacting nodes from going behind the contact surface 12 51 a MODELING CONSIDERATIONS IN Abaqus Explicit Perimeter of contact surface Only top of box defined as surface Perimeter of contact surface Side of box included in surface definition Figure 12 40 S
553. rces to the rigid elements The default thickness is zero Alternatively the NODAL THICKNESS parameter defines an average facet thickness based on the thickness at the nodes These data are required when applying body forces or when the thickness is needed for the contact definition Formulation and integration Since the rigid elements are not deformable they do not use numerical integration points and there are no optional formulations Element output variables There are no element output variables The only output from rigid elements is the motion of the nodes In addition reaction forces and reaction moments are available at the rigid body reference node Summary Abaqus has an extensive library of elements that can be used for a wide range of structural applications Your choice of element type has important consequences regarding the accuracy and efficiency of your simulation The elements available in Abaqus Explicit are in general a subset of those available in Abaqus Standard e The degrees of freedom active at a node depend on the element types attached to the node 3 18 SUMMARY The element name completely identifies the element s family formulation number of nodes and type of integration All elements must refer to a section property definition The section property provides any additional data required to define the geometry of the element and also identifies the associated material property definition For c
554. re 10 59 Modified mesh with refinement at both corners The deformed shape associated with this model is shown in Figure 10 60 T UZ H P as 2 B8 1 Figure 10 60 Deformed shape of the modified mesh It is clear from this figure that the mesh distortion has been reduced significantly in the critical regions of the rubber model Examining contour plots of the pressure without averaging across elements reveals a smooth variation in pressure stress between elements Thus volumetric locking has been eliminated 10 10 Related Abaqus examples e Pressurized rubber disc Section 1 1 7 of the Abaqus Benchmarks Manual e Necking of a round tensile bar Section 1 1 9 of the Abaqus Benchmarks Manual e Fitting of rubber test data Section 3 1 4 of the Abaqus Benchmarks Manual 10 80 SUMMARY e Uniformly loaded elastic plastic plate Section 3 2 1 of the Abaqus Benchmarks Manual 10 11 Suggested reading The follo
555. re probably will be a small fillet between the lug and the parent structure and the parent structure will be deformable not rigid If the exact stress in this location is required the fillet between the components must be modeled accurately see Figure 4 46 and the stiffness of the parent structure must also be considered 4 50 MESH CONVERGENCE Sharp corner gives a stress singularity Fillet YV Actual geometry of Finite element model component idealization Figure 4 46 Idealizing a fillet as a sharp corner Itis common to omit small details like fillet radii from a finite element model to simplify the analysis and to keep the model size reasonable However the introduction of any sharp corner into a model will lead to a stress singularity at that location This normally has a negligible effect on the overall response of the model but the predicted stresses close to the singularity will be inaccurate For complex three dimensional simulations the available computer resources often dictate a practical limit on the mesh density that you can use In this case you must use the results from the analysis carefully Coarse meshes are often adequate to predict trends and to compare how different concepts behave relative to each other However you should use the actual magnitudes of displacement and stress calculated with a coarse mesh with caution It is rarely necessary to use a uniformly fine mesh throughout the struct
556. re similar the slave surface should be the surface with the softer underlying material The general contact algorithm in Abaqus Standard enforces contact in an average sense between interacting surfaces Abaqus Standard automatically assigns master and slave roles 12 3 4 Contact discretization Abaqus Standard offers two contact discretization methods a traditional node to surface method and a surface to surface method The node to surface discretization method defines contact conditions between each slave node and the master surface The surface to surface discretization method considers the shape of both the master and slave surfaces when defining the contact constraints The contact pair algorithm can use either discretization method general contact uses only the surface to surface approach 12 3 5 Small and finite sliding When using the small sliding formulation Abaqus Standard establishes the relationship between the slave nodes and the master surface at the beginning of the simulation Abaqus Standard determines which segment on the master surface will interact with each node on the slave surface It maintains these relationships throughout the analysis never changing which master surface segments interact with which slave nodes If geometric nonlinearity is included in the model by setting the NUGEOM parameter equal to YES on the STEP option the small sliding algorithm accounts for any rotation and deformation of the master surface an
557. reedom are part of the rigid body and are constrained by the motion of the rigid body reference node The nodes defining the rigid body cannot have any boundary conditions multi point constraints or constraint equations applied to them Boundary conditions multi point constraints constraint equations and loads can be applied however to the rigid body reference node 3 2 3 Rigid elements The rigid body capability in Abaqus allows most elements not just rigid elements to be part of a rigid body For example shell elements or rigid elements can be used to model the same effect 1f the RIGID BODY option refers to the element set that contains the elements forming the rigid body The rules governing rigid bodies such as how loads and boundary conditions are applied pertain to all element types that form the rigid body including rigid elements The names of all rigid elements begin with the letter R The next characters indicate the dimensionality of the element For example 2D indicates that the element is planar and AX that the element is axisymmetric The final character represents the number of nodes in the element Rigid element library The three dimensional quadrilateral R3D4 and triangular R3D3 rigid elements are used to model the two dimensional surfaces of a three dimensional rigid body Another element a two node rigid beam element RB3D2 1is provided in Abaqus Standard mainly to model components
558. resolving support issues efficiently You must register with the system to check on a support issue If you contact us by means outside the system to discuss an existing support problem and you know the incident or support request number please mention it so that we can consult the database to see what the latest action has been 1 5 2 Systems support Abaqus systems support engineers can help you resolve issues related to the installation and running of Abaqus including licensing difficulties that are not covered by technical support You should install Abaqus by carefully following the instructions in the Abaqus Installation and Licensing Guide If you encounter problems with the installation or licensing first review the instructions in the Abaqus Installation and Licensing Guide to ensure that they have been followed correctly If this method does not resolve the problems search for known installation problems in the Dassault Systemes Knowledge Base at www 3ds com support knowledge base or the SIMULIA Online Support System which is accessible through the My Support page at www simulia com If this method does not address your situation please contact your local support office a list of local support offices is available from the Locations page at www simulia com Send whatever information is available to define the problem error messages from an aborted analysis or a detailed explanation of the problems encountered Whenever possible please s
559. results of the first simulation attempt indicate it is desirable to use a different amplitude curve that allows the blank to accelerate more smoothly When considering what type of loading amplitude to use remember that smoothness 1s important in all aspects of a quasi static analysis The preferred approach is to move the punch as smoothly as possible the desired distance in the desired amount of time We will now analyze the forming stage using a smoothly applied holder force and a smoothly applied punch displacement we will compare the results to those obtained earlier Refer to Smooth amplitude curves Section 13 2 1 for an explanation of the smooth step amplitude curve Revise the existing amplitude curve definitions RAMP1 and RAMP2 so that they define smooth step amplitude curves You can make this change by appending DEFINITION SMOOTH STEP to each AMPLITUDE option The amplitude curves will now be smooth in both their first and second 13 15 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit derivatives Therefore using a smooth step amplitude curve for the displacement control also assures us that the velocity and acceleration are smooth Save the channel xpl inp input file and submit it for analysis Monitor the solution progress correct any modeling errors that are detected and investigate the cause of any warning messages Evaluating the results for attempt 2 The kinetic energy history is shown in Figure 13 11 Kinetic Ener
560. rface 1s poor compared to the dimensions of the features on the master surface If the deformable surface were more refined the penetrations of the rigid surface would be much less severe rigid master surface deformable slave surface Figure 12 46 Example of inadequate slave surface discretization Tie constraints Using the TIE option prevents surfaces initially in contact from penetrating separating or sliding relative to one another Tie constraints are therefore an easy means of mesh refinement Since any gaps that exist between the two contact surfaces however small will result in nodes that are not 12 57 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST tied to the opposite contact boundary you must use the ADJUST YES parameter to ensure that the two surfaces are exactly in contact at the start of the analysis The tie constraint formulation constrains translational and optionally rotational degrees of freedom When using tied contact with structural elements you must ensure that any unconstrained rotations will not cause problems 12 9 4 Initial contact overclosure Abaqus Explicit will automatically adjust the undeformed coordinates of nodes on contact surfaces to remove any initial overclosures When using the balanced master slave approach both surfaces are adjusted when using the pure master slave approach only the slave surface is adjusted Displacements associated with adjusting the surface to remove ov
561. rhead hoist model 1s NODE 101 0 0 0 102 1 0 0 103 2 0 0 104 0 5 0 866 0 105 1 5 0 866 0 The first piece of data in each data line is an integer that defines the node number The second third and fourth entries are floating point numbers that specify the x1 2 3 coordinates of the node The data can consist of a mixture of integer floating point or alphanumeric values Floating point values can be entered in a variety of ways for example Abaqus interprets all of the following as the number four 4 0 4 4 4 0E 0 AE 40 E 1 Data items are separated by commas as in Figure 2 2 which allows fairly arbitrary spacing of the input values on the data line If there is only one item on a data line it must be followed by a comma 2 7 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST 2 3 2 3 Example creating a model of an overhead hoist The simulation of the pin jointed overhead hoist in Figure 2 1 is used to illustrate the creation of an Abaqus input file using an editor As you read through this section you should type the data into a file using one of the editors available on your computer The Abaqus input file must have an inp file extension For convenience name the input file frame inp The file identifier which can be chosen to identify the analysis is called the jobname In this case use the jobname frame to associate it easily with the input file called frame inp
562. riate for a given problem For those problems that can be solved with either method the efficiency with which the problem can be solved can determine which product to use Understanding the characteristics of implicit and explicit procedures will help you answer this question Table 2 2 lists the key differences between the analysis products which are discussed in detail in the relevant chapters in this guide 2 40 COMPARISON OF IMPLICIT AND EXPLICIT PROCEDURES x1 E 3 0 0 Displacement mm A oO f l 1 l 1 l f l f l 0 000 0 002 0 004 0 006 0 008 0 010 Time Figure 2 15 Vertical displacement at the midspan of the truss Table 2 2 Key differences between Abaqus Standard and Abaqus Explicit Quantity Abaqus Standard Abaqus Explicit Element library Offers an extensive element library Offers an extensive library of elements well suited for explicit analyses The elements available are a Subset of those available in Abaqus Standard Analysis procedures General and linear perturbation General procedures are available procedures are available Material models Offers a wide range of material models Similar to those available in Abaqus Standard a notable difference is that failure material models are allowed Contact formulation Has a robust capability for solving Has a robust contact functionality contact problems that readily solves even the most complex contact simulations 2 41 5 CO
563. rnal forces I and the external forces P must balance each other 5 THE SOLUTION OF NONLINEAR PROBLEMS Load u Displacement Figure 8 7 Nonlinear load displacement curve a External loads in a simulation b Internal forces acting at a node Figure 8 8 Internal and external loads on a body Abaqus Standard uses the Newton Raphson method to obtain solutions for nonlinear problems In a nonlinear analysis the solution usually cannot be calculated by solving a single system of equations as would be done in a linear problem Instead the solution is found by applying the specified loads gradually and incrementally working toward the final solution Therefore Abaqus Standard breaks the simulation into a number of load increments and finds the approximate equilibrium configuration at the end of each load increment It often takes Abaqus Standard several iterations to determine an acceptable solution to a given load increment The sum of all of the incremental responses is the approximate solution for the nonlinear analysis Thus Abaqus Standard combines incremental and iterative procedures for solving nonlinear problems THE SOLUTION OF NONLINEAR PROBLEMS Abaqus Explicit determines a solution to the dynamic equilibrium equation P J Mu without iterating by explicitly advancing the kinematic state from the end of the previous increment Solving a problem explicitly does not require the formation of tangent stiffness matrices
564. roach Divide the analysis into several steps if necessary and apply the loading slowly making sure that the contact conditions are well established e In general it is best to use a separate step for each part of the analysis in Abaqus Standard even if it is just to change boundary conditions to loads You will almost certainly end up with more steps than anticipated but the model should converge much more easily Contact analyses are much more difficult to complete if you try to apply all the loads in one step e In Abaqus Standard achieve stable contact conditions between all components before applying the working loads to the structure If necessary apply temporary boundary conditions which may be removed ata later stage The final results should be unaffected provided that the constraints produce no permanent deformation e Do not apply boundary conditions to nodes on contact surfaces that constrain the node in the direction of contact in Abaqus Standard If there is friction do not constrain these nodes in any degree of freedom zero pivot messages may result e Always try to use first order elements for contact simulations in Abaqus Standard e Both Abaqus Standard and Abaqus Explicit provide two distinct algorithms for modeling contact general contact defined with the CONTACT option and contact pairs defined with the CONTACT PAIR option e General contact interactions allow you to define contact between many or all regions o
565. rs 2 Select ODB field output from this dialog box and click Continue to proceed The XY Data from ODB Field Output dialog box appears 3 Inthe Variables tabbed page of this dialog box accept the default selection of Integration Point for the variable position and select 11 from the list of available stress components 11 22 EXAMPLE RESTARTING THE PIPE VIBRATION ANALYSIS At the bottom of the dialog box toggle Select for the section point and click Settings to choose a section point In the Field Report Section Point Settings dialog box that appears select the category beam and choose any of the available section points for the pipe cross section Click OK to exit this dialog box In the Elements Nodes tabbed page of the XY Data from ODB Field Output dialog box select Element labels as the selection Method There are 30 elements in the model and they are numbered consecutively from 1 to 30 Enter any element number for example 25 in the Element labels text field that appears on the right side of the dialog box Click Active Steps Frames and select Step 3 as the only step from which to extract data At the bottom ofthe XY Data from ODB Field Output dialog box click Plot to see the history of axial stress in the element The plot traces the axial stress history at each integration point of the element in the restart analysis Since the restart is a continuation of an earlier job it 1s often useful to view
566. rs AE BE and their internal bracing and truss B consists of members CE DE and their internal bracing The ratio of the typical cross section dimension to global axial length in the main members of the crane is much less than 1 15 The ratio is approximately 1 15 in the shortest member used for internal bracing Therefore it is valid to use beam elements to model the crane 6 4 1 Coordinate system You should use the default global rectangular Cartesian coordinate system shown in Figure 6 11 and Figure 6 12 Locate the origin of the coordinate system midway between points A and D If you build your model with a different origin or orientation of the coordinate system ensure that the input data in your model reflect your coordinate system and not the one shown here 6 12 EXAMPLE CARGO CRANE 8 0 N oO gt Ke Plan 0 5 a L ene 0 667 1 333 2 0 20 20 gt Elevation Figure 6 12 Dimensions in m of the cargo crane 6 4 2 Mesh design The cargo crane will be modeled with three dimensional slender cubic beam elements B33 The cubic interpolation in these elements allows us to use a single element for each member and still obtain accurate results under the applied bending load The mesh that you use in the simulation is shown in Figure 6 13 The welded joints in the crane provide complete continuity of the translations and rotations from one element to the next You therefore n
567. s e The choice between using implicit or explicit methods depends largely on the nature of the problem 2 44 FINITE ELEMENTS 3 Finite Elements and Rigid Bodies Finite elements and rigid bodies are the fundamental components of an Abaqus model Finite elements are deformable whereas rigid bodies move through space without changing shape While users of finite element analysis programs tend to have some understanding of what finite elements are the general concept of rigid bodies within a finite element program may be somewhat new For computational efficiency Abaqus has a general rigid body capability Any body or part of a body can be defined as a rigid body most element types can be used in a rigid body definition the exceptions are listed in Rigid body definition Section 2 4 1 of the Abaqus Analysis User s Manual The advantage of rigid bodies over deformable bodies is that the motion of a rigid body is described completely by no more than six degrees of freedom at a reference node In contrast deformable elements have many degrees of freedom and require expensive element calculations to determine the deformations When such deformations are negligible or not of interest modeling a component as a rigid body produces significant computational savings without affecting the overall results 3 1 Finite elements A wide range of elements is available in Abaqus This extensive element library provides you with a powerful set of
568. s C3D4 and C3D6 are poor elements fine meshes are needed to obtain accurate results as a result these elements should generally be used only when necessary to complete a mesh and even then they should be far from any areas where accurate results are needed e Some preprocessors contain free meshing algorithms that mesh arbitrary geometries with tetrahedral elements The quadratic tetrahedral elements in Abaqus Standard C3D10 or C3D10I are suitable for general usage but when used with contact they should be used only with the surface to surface contact discretization An alternative to these elements is the modified quadratic tetrahedral element C3D10M available in both analysis products This element is robust for large deformation problems and contact problems using either the traditional node to surface or the surface to surface contact discretization and exhibits minimal shear and volumetric locking With either type of element however the analysis will take longer to run than an equivalent mesh of hexahedral elements You should not use a mesh containing only linear tetrahedral elements C3D4 the results will be inaccurate unless you use an extremely large number of elements Abaqus Standard users should also consider the following recommendations e Use quadratic reduced integration elements CAX8R CPE8R CPS8R C3D20R etc for general analysis work unless you need to model very large strains or hav
569. s The simplest is to specify an extra node on the data line defining the element in the ELEMENT option The vector v from the first node in the beam element to this additional node see Figure 6 4 is used initially as an approximate nj direction Abaqus then defines the beam s N direction as t x v Having determined ny Abaqus defines the actual n direction as ny x t This procedure ensures that the local tangent and local beam section axes form an orthogonal system 6 4 BEAM CROSS SECTION GEOMETRY Additional node given on the data line defining the element Figure 6 4 Orientation of the beam element tangent t and beam section axes n and ng Alternatively you can give an approximate nj direction on the element section option either BEAM SECTION or BEAM GENERAL SECTION Abaqus then uses the procedure described above to calculate the actual beam section axes If you specify both an extra node and an approximate n direction the additional node method takes precedence Abaqus uses the vector from the origin to the point 0 0 0 0 1 0 as the default n direction if you provide no approximate nj direction There are two methods that can be used to override the ny direction defined by Abaqus One is to give the components of n as the 4th 5th and 6th data values following the nodal coordinates on the data lines of the NODE option The alternative is to use the NORMAL option If both methods are used the
570. s The vector should be nearly parallel to the global 2 direction Since the angle between the normals from one element to the next is always greater than 20 the normals are not averaged at the nodes 6 18 EXAMPLE CARGO CRANE Depending on the exact orientation of the members in the cross bracing it 1s possible that we would have to define the normals individually for each of the cross bracing elements Such an exercise would be very similar to what you have already done by defining the normals for the two truss structures Since the square cross bracing members are subjected to primarily axial loading their deformation is not sensitive to cross section orientation Therefore we accept the default normals that Abaqus calculates to be correct The approximate n vector for the cross bracing is aligned with the y axis The following option block specifies the cross bracing BEAM GENERAL SECTION SECTION BOX ELSET CROSSEL 0 03 0 03 0 003 0 003 0 003 0 003 0 0 1 0 0 0 200 E9 80 E9 Beam section orientation In this model you will have a modeling error if you provide data that only define the orientation of the approximate n vector The averaging of beam normals at the nodes see Beam element curvature Section 6 1 3 causes Abaqus to use incorrect geometry for the cargo crane model To see this you can use Abaqus Viewer to display the beam section axes and beam tangent vectors see Postprocessing Section 6 4 7 However
571. s A B C and D see Figure 7 5 can only withstand a maximum pull out force of 100 kN You have to decide whether or not any of these connections will break Figure 7 5 Cargo crane EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING The short duration of the loading means that inertia effects are likely to be important making dynamic analysis essential You are not given any information regarding the damping of the structure Since there are bolted connections between the trusses and the cross bracing the energy absorption caused by frictional effects is likely to be significant Based on experience you therefore choose 5 of critical damping in each mode The magnitude of the applied load versus time is shown in Figure 7 6 x10 12 00 APPLIED LOAD N 0 00 0 05 0 10 0 15 0 20 0 25 TIME s Figure 7 6 Load time characteristic The steps that follow assumes that you have access to the full input file for this example This input file dynamics inp is provided in Cargo crane dynamic loading Section A 5 in the online HTML version of this manual Instructions on how to fetch and run the script are given in Appendix A Example Files If you prefer to create this example interactively using Abaqus CAE refer to Example cargo crane under dynamic loading Section 7 5 of Getting Started with Abaqus Interactive Edition 7 5 1 Modifications to the input file the model data The model data are the same
572. s and frequencies but the savings obtained in the calculation of the response greatly outweigh the cost If nonlinearities are present in the simulation the natural frequencies may change significantly during the analysis and modal superposition cannot be employed In this case direct integration of the dynamic equation of equilibrium is required which is much more expensive than modal analysis A problem should have the following characteristics for it to be suitable for linear transient dynamic analysis e The system should be linear linear material behavior no contact conditions and no nonlinear geometric effects e The response should be dominated by relatively few frequencies As the frequency content of the response increases such as is the case in shock and impact problems the modal superposition technique becomes less effective e The dominant loading frequencies should be in the range of the extracted frequencies to ensure that the loads can be described accurately e The initial accelerations generated by any suddenly applied loads should be described accurately by the eigenmodes e The system should not be heavily damped DAMPING 7 2 Damping If an undamped structure is allowed to vibrate freely the magnitude of the oscillation is constant In reality however energy is dissipated by the structure s motion and the magnitude of the oscillation decreases until the oscillation stops This energy dissipation is known
573. s assume that shear deformations are negligible Generally if the cross section dimensions are less than 1 15 of the typical axial dimensions of the structure this assumption is valid 6 2 2 FORMULATION AND INTEGRATION Torsional response warping Structural members are often subjected to torsional moments which occur in almost any three dimensional frame structure Loads that cause bending in one member may cause twisting in another as shown in Figure 6 8 Torsion and ao bending Bending Figure 6 8 Torsion induced in a frame structure The response of a beam to torsion depends on the shape of its cross section Generally torsion in a beam produces warping or nonuniform out of plane displacements in the cross section Abaqus considers the effects of torsion and warping only in the three dimensional elements The warping calculation assumes that the warping displacements are small The following cross sections behave differently under torsion solid cross sections closed thin walled cross sections and open thin walled cross sections Solid cross sections A solid non circular cross section does not remain plane under torsion instead the section warps Abaqus uses St Venant warping theory to calculate a single component of shear strain caused by the warping at each section point in the cross section The warping in such solid cross sections is considered unconstrained and creates negligible axial stresses Warpin
574. s in Abaqus Explicit Section 38 2 2 of the Abaqus Analysis User s Manual The normal contact constraint for contact pairs can optionally be enforced with the penalty contact method which can model some types of contact that the kinematic method cannot For example the penalty method allows modeling of contact between two rigid surfaces except when both surfaces are analytical rigid surfaces When the penalty contact formulation is used equal and opposite contact forces with magnitudes equal to the penalty stiffness times the penetration distance are applied to the master and slave nodes at the penetration points The penalty stiffness 1s chosen automatically by Abaqus Explicit and is similar to that used by the general contact algorithm A penalty scale factor can also be specified To select the penalty method for a contact pair analysis set the MECHANICAL CONSTRAINT parameter to PENALTY on the CONTACT PAIR option Contact surface weighting In the pure master slave approach one of the surfaces is the master surface and the other is the slave surface As the two bodies come into contact the penetrations are detected and the contact constraints are applied according to the constraint enforcement method kinematic or penalty Pure master slave weighting regardless of the constraint enforcement method will resist only penetrations of slave nodes into master facets Penetrations of master nodes into the slave surface can go undetected as
575. s input file blast base inp is provided in Example blast loading on a stiffened plate Section 10 5 in the online HTML version of this manual Instructions on how to fetch and run the script are given in Appendix A Example Files If you wish to create the entire model using Abaqus CAE please refer to Example blast loading on a stiffened plate Section 10 5 of Getting Started with Abaqus Interactive Edition Figure 10 20 shows all the sets necessary to apply the element properties loads and boundary conditions This model includes all the nodes on the perimeter of the plate in a node set called EDGE These nodes will have a completely fixed boundary condition For output purposes a node set called NOUT has been created containing the node at the center of the plate Plate elements are included in an element set called PLATE and the stiffener elements in an element set called STIFF In addition the four center elements on the central stiffener are included in an element set called STIFFMAX this element set is for output purposes These center elements will be subject to the maximum bending stress in the stiffeners 10 30 EXAMPLE BLAST LOADING ON A STIFFENED PLATE element set STIFF node set EDGE y KN NX N ISN NNN NIN INNING i node set EDGE node set NOUT center node of plate BNN NN SN NSN NINN SN NAN NS Y lt S N NN NG element set STIFFMAX center elements on th
576. s only a small amount from one increment to the next If the acceleration is smooth it follows that the changes in velocity and displacement are also smooth Abaqus has a simple built in type of amplitude called SMOOTH STEP that automatically creates a smooth loading amplitude When you define time amplitude data pairs using AMPLITUDE DEFINITION SMOOTH STEP Abaqus Explicit automatically connects each of your data pairs with curves whose first and second derivatives are smooth and whose slopes are zero at each of your data points Since both of these derivatives are smooth you can apply a displacement loading with SMOOTH STEP using only the initial and final data points and the intervening motion will be smooth 13 2 LOADING RATES Using this type of loading amplitude allows you to perform a quasi static analysis without generating waves due to discontinuity in the rate of applied loading For example for the following amplitude definition Abaqus Explicit creates the amplitude curve shown in Figure 13 2 AMPLITUDE DEFINITION SMOOTH STEP 0 0 0 0 1 0E 5 1 0 1 0 amplitude O 1 0E 5 2 0E 5 time Figure 13 2 Amplitude definition using AMPLITUDE DEFINITION SMOOTH STEP 13 2 2 Structural problems In a static analysis the lowest mode of the structure usually dominates the response Knowing the frequency and correspondingly the period of the lowest mode you can estimate the time required to obtain the proper static response T
577. s refer to a local coordinate system Check that the small strain assumption was valid for this simulation The axial strain corresponding to the peak stress is 11 0 008 Because the strain is typically considered small if it is less than 4 or 5 a Strain of 0 8 is well within the appropriate range to be modeled with S8R5 elements Look at the reaction forces and moments in the following table THE FOLLOWING TABLE IS PRINTED FOR ALL NODES NODE FOOT RF1 RF2 RF3 RM1 RM2 RM3 NOTE 1 0 000 0 000 109 9 1 775 0 3283 0 000 2 0 000 0 000 6 448 7 597 36 46 0 000 3 0 000 0 000 239 9 6 568 35 46 0 000 4 0 000 0 000 455 4 6 806 88 26 0 000 5 0 000 0 000 260 5 6 948 51 13 0 000 6 0 000 0 000 750 8 8 305 126 5 0 000 7 0 000 0 000 73 90 8 749 62 23 0 000 8 0 000 0 000 2286 31 06 205 8 0 000 9 0 000 0 000 37 19 1 610 76 45 0 000 1201 0 000 0 000 37 19 1 610 76 45 0 000 1202 0 000 0 000 2286 31 06 205 8 0 000 1203 0 000 0 000 73 90 8 749 62 23 0 000 1204 0 000 0 000 750 8 8 305 126 5 0 000 1205 0 000 0 000 260 5 6 948 51 13 0 000 1206 0 000 0 000 455 4 6 806 88 26 0 000 1207 0 000 0 000 239 9 6 568 35 46 0 000 1208 0 000 0 000 6 448 7 597 36 46 0 000 1209 0 000 0 000 109 9 1 775 0 3283 0 000 TOTAL 0 000 0 000 8000 3 7096E 11 1 8769E 09 0 000 The reaction forces were written in the global coordinate system because ofhow we requested the reaction force output GLOBAL YES on the NODE PRINT option Otherwise the reactions for t
578. s shown in Figure 6 1 In this case you provide the required cross section dimensions the same way as you would with BEAM SECTION The vector on the second data line again defines the approximate normal n On the third line you enter the elastic material constants because BEAM GENERAL SECTION does not refer to any material option block If you define the section s properties geometrically with this option the material behavior must be linear elastic The alternative is to set the SECTION parameter to GENERAL or NONLINEAR GENERAL in which case you provide the section engineering properties area moments of inertia and torsional constants instead of the cross section dimensions These parameters allow you to combine the beam s geometry and material behavior to define its response to loads This response may be linear or nonlinear See Using a general beam section to define the section behavior Section 29 3 7 of the Abaqus Analysis User s Manual for further details 6 2 BEAM CROSS SECTION GEOMETRY In Abaqus Standard you can also define beams with linearly tapered cross sections General beam sections with linear response and standard library sections are supported Meshed beam cross sections allow a description of the beam cross section that includes multiple materials and complex geometry This type of beam profile is discussed further in Meshed beam cross sections Section 10 6 1 of the Abaqus Analysis User s Manual
579. s subjected to dynamic motion of its fixed points The motion of the fixed points is known as base motion an example is a seismic event causing ground motion Typically the method is used when an estimate of the peak response is required for design purposes Random response The RANDOM RESPONSE option predicts the response of a system subjected to random continuous excitation The excitation is expressed in a statistical sense using a power spectral density function Examples of random response analysis include the following e The response of an airplane to turbulence e The response of a structure to noise such as that emitted by a jet engine 7 9 2 Nonlinear dynamics As mentioned earlier the MODAL DYNAMIC procedure is suitable only for linear problems When nonlinear dynamic response is of interest the equations of motion must be integrated directly The direct integration of the equations of motion is performed in Abaqus Standard using an implicit dynamics procedure DYNAMIC When this procedure is used the mass damping and stiffness matrices are assembled and the equation of dynamic equilibrium is solved at each point in time Since these operations are computationally intensive direct integration dynamics is more expensive than the modal methods 1 27 SUMMARY Since the nonlinear dynamic procedure in Abaqus Standard uses implicit time integration it 1s suitable for nonlinear structural dynamics problems for exampl
580. s the plate thin or thick Are the strains small or large The plate is quite thin with a thickness to minimum span ratio of 0 02 The thickness is 0 8 cm and the minimum span is 40 cm While we cannot readily predict the magnitude of the strains in the structure we think that the strains will be small Based on this information 5 12 EXAMPLE SKEW PLATE End built in Origin zero rotation Plan Elevation Figure 5 10 Sketch of the skew plate you choose quadratic shell elements S8R5 because they give accurate results for thin shells in small strain simulations For further details on shell element selection consult Choosing a shell element Section 29 6 2 of the Abaqus Analysis User s Manual 5 5 3 Preprocessing creating the model The input file for the skew plate example is skew inp which is available in Skew plate Section A 3 This example uses the mesh shown in Figure 5 11 by creating the node sets shown in Figure 5 12 and stores all of the the elements in an element set called PLATE The following steps in this example describe how the material and history information is defined in this input file This exercise will give you a better understanding of how the various option blocks combine to define an Abaqus model If you wish to create the entire model using Abaqus CAE refer to Example skew plate Section 5 5 of Getting Started with Abaqus Interactive Edition 5 13 5 EXAMPLE SKEW
581. s the state at the end of the previous general step that is at the end of the forming process Step 3 The response in the previous perturbation step Step 4 is ignored The two perturbation steps are therefore separate independent simulations of the sink s response to loads applied to the base state of the model If another general step is included in the analysis the condition of the structure at the start of the step is that at the end of the previous general step Step 3 Step 6 could therefore be a general step with loads modeling the sink being filled with water The response in this step may be linear or nonlinear Following this general step Step 7 could be a simulation repeating the analysis performed in Step 4 However in this case the base state the state of the structure at the end of the previous general step 1s the state of the model at the end of Step 6 Therefore the response will be that of a full sink rather than an empty one Performing another steady state dynamics simulation would produce inaccurate results because the mass of the water which would change the response considerably would not be considered in the analysis 11 7 5 LINEAR PERTURBATION ANALYSIS Punch Blank f f f holder _ LZ Die f Step 1 Apply blank holder pressure Step 2 Form sink 4 4 Step 3 Remove tooling i 7 Step 4 Stand on sink E J gt Step 5 Run waste Step 6 Fill sink disposal unit l
582. s the value of the INC parameter In this analysis it required four more increments Abaqus gives a summary at the end of the message file of how the analysis progressed and how many error and warning messages it issued The summary for this analysis is shown below An important item to check is how many iterations Abaqus uses In this analysis it performed 15 iterations over the six increments the model s system of equations was solved 15 times 1 e 15 matrix decompositions illustrating the increased computational expense of nonlinear analyses compared with linear simulations THE ANALYSIS HAS BEEN COMPLETED ANALYSIS SUMMARY TOTAL OF 6 INCREMENTS 0 CUTBACKS IN AUTOMATIC INCREMENTATION 15 ITERATIONS INCLUDING CONTACT ITERATIONS IF PRESENT 15 PASSES THROUGH THE EQUATION SOLVER OF WHICH 15 INVOLVE MATRIX DECOMPOSITION INCLUDING DECOMPOSITION S OF THE MASS MATRIX REORDERING OF EQUATIONS TO MINIMIZE WAVEFRONT ADDITIONAL RESIDUAL EVALUATIONS FOR LINE SEARCHES ADDITIONAL OPERATOR EVALUATIONS FOR LINE SEARCHES WARNING MESSAGES DURING USER INPUT PROCESSING WARNING MESSAGES DURING ANALYSIS ANALYSIS WARNINGS ARE NUMERICAL PROBLEM MESSAGES ANALYSIS WARNINGS ARE NEGATIVE EIGENVALUE MESSAGES ERROR MESSAGES OOOOrFRCOFrFO JOB TIME SUMMARY USER TIME SEC 0 50000 SYSTEM TIME SEC 0 0000 TOTAL CPU TIME SEC 0 50000 WALLCLOCK TIME SEC 2 8 21 5 EXAMPLE NONLINEAR SKEW PLATE You should always check this summary at the en
583. sed later 0 000 0 005 from A3 N 403 NSET CHIPS 0 010 0 015 0 020 0 025 Vertical Displacement m 0 030 0 035 0 5 10 15 20 x1 E 3 Time s Figure 12 60 Displacement of the bottom chip in the Z direction Why are the velocity and displacement curves calculated by integrating the acceleration data different from the velocity and displacement recorded during the analysis In this example the acceleration data has been corrupted by a phenomenon called aliasing Aliasing is a form of data corruption that occurs when a signal such as the results of an Abaqus analysis is sampled at a series of discrete points in time but not enough data points are saved in order to correctly describe the signal The aliasing phenomenon can be addressed using digital signal 12 77 5 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST processing DSP methods a fundamental principle of which is the Nyquist Sampling Theorem also known as the Shannon Sampling Theorem The Sampling Theorem requires that a signal be sampled at a rate that is greater than twice the signal s highest frequency Therefore the maximum frequency content that can be described by a given sampling rate is half that rate the Nyquist frequency Sampling storing a signal with large amplitude oscillations at frequencies greater than the Nyquist frequency of the sample rate may produce significantly distorted results due to aliasing In this example
584. sed to visualize the results graphically using Abaqus Viewer 2 3 9 Postprocessing Graphical postprocessing is important because of the great volume of data created during a simulation For any realistic model it is impractical for you to try to interpret results in the tabular form of the data file Abaqus Viewer allows you to view the results graphically using a variety of methods including deformed shape plots contour plots vector plots animations and X Y plots All of these methods are discussed in this guide For more information on any of the postprocessing features discussed in this guide consult the sections on the Visualization module in the Abaqus CAE User s Manual For this example you will use Abaqus Viewer to do some basic model checks and to display the deformed shape of the frame Start Abaqus Viewer by typing the following command at the operating system prompt abaqus viewer The Abaqus Viewer window appears To begin this exercise open the output database file that Abaqus Standard generated during the analysis of the problem 2 28 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST To open the output database file 1 From the main menu bar select File Open or use the i tool in the File toolbar The Open Database dialog box appears 2 From the list of available output database files select frame odb 3 Click OK Tip You can also open the output database frame odb by typing the following command at
585. sign parameters that affect the stability limit are also addressed These model parameters include the model mass material and mesh 1 Conditional stability of the explicit method With the explicit method the state of the model is advanced through an increment of time At based on the state of the model at the start of the increment at time t The amount of time that the state can be advanced and still remain an accurate representation of the problem is typically quite short If the time increment is larger than this maximum amount of time the increment is said to have exceeded the stability limit A possible effect of exceeding the stability limit is a numerical instability which may lead to an unbounded solution It generally is not possible to determine the stability limit exactly so conservative estimates are used instead The stability limit has a great effect on reliability and accuracy so it must be determined consistently and conservatively For computational efficiency Abaqus Explicit chooses the time increments to be as close as possible to the stability limit without exceeding it 2 Definition of the stability limit The stability limit is defined in terms of the highest frequency in the system wmax Without damping the stability limit is defined by the expression 2 Atstabie Wmax and with damping it is defined by the expression Aftstable v ha Gs Wmax where is the fraction of critical damping
586. sily Interpolation between data points Abaqus interpolates linearly between the data points provided or in Abaqus Explicit regularized data to obtain the material s response and assumes that the response is constant outside the range defined by the input data as shown in Figure 10 7 Thus the stress in this material will never exceed 480 MPa when the stress in the material reaches 480 MPa the material will deform continuously until the stress 1s reduced below this value Material calibration in Abaqus CAE Abaqus CAE allows you to calibrate a material model from test data With this capability you can import material test data into Abaqus CAE process the data and derive elastic and plastic isotropic material behaviors from the data This feature is discussed further in Creating material calibrations Section 12 17 of the Abaqus CAE User s Manual 10 9 5 SELECTING ELEMENTS FOR ELASTIC PLASTIC PROBLEMS 500 450 400 350 300 True stress MPa 0 00 0 05 0 10 015 0 20 0 25 Plastic strain Figure 10 7 Material curve used by Abaqus 10 3 Selecting elements for elastic plastic problems The incompressible nature of plastic deformation in metals places limitations on the types of elements that can be used for an elastic plastic simulation The limitations arise because modeling incompressible material behavior adds kinematic constraints to an element in this case the limitations constrain the volu
587. sing filter was applied it had no effect because there was no high frequency response to remove Next compare the acceleration A3 history output recorded every increment with the two acceleration A3 history curves recorded every 0 07 ms Plot the data recorded at every increment first so that 1t does not obscure the other results To plot the acceleration histories 1 In the Results Tree filter the History Output container according to A3 Node 403 and double click the acceleration A3 history output for the node set BotChip all 2 Select the two acceleration A3 history output objects for Node 403 in the set CHIPS one filtered with the built in anti aliasing filter and the other with no filtering using Ctrl Click click mouse button 3 and select Add to Plot from the menu that appears The X Y plot appears in the viewport Zoom in to view only the first third of the results and customize the plot appearance to obtain a plot similar to Figure 12 62 First consider the acceleration history recorded every increment This curve contains a lot of data including high frequency solution noise which becomes so large in magnitude that it obscures the structurally significant lower frequency components of the acceleration When output is requested every increment the output time increment is the same as the stable time increment which in order to ensure stability is based on a conservative estimate of the highest possible frequency response o
588. sional problem The material is steel with the properties shown in Figure 9 1 The free end of the bar is subjected to a blast load with a magnitude of 1 0 x 10 Pa and a duration of 3 88 x 10 s The normalized load versus time is shown in Figure 9 2 1 50 1 00 Amplitude 0 50 0 00 0 00 0 05 0 10 0 15 0 20 x10 Time Figure 9 2 Blast amplitude versus time Using the material properties neglecting Poisson s ratio we can calculate the wave speed of the material using the equations introduced in the previous section 9 10 OS SR ry Lt IA MASAN NNN NN ONES ey yy 5 15 x 10 m s 0 2 m EXAMPLE STRESS WAVE PROPAGATION IN A BAR 207 x 109 Pa 7800 kg m the stress propagation along the length of the bar through time we need an adequately refined mesh to capture the stress wave accurately We will assume that the blast load will take place over the span of 10 elements To determine the length of these 10 elements multiply the blast duration by the wave speed At this speed the wave passes to the fixed end of the bar in 1 94 x 10 s Since we are interested in 3 88 x 107 s ca Lioel along the length To keep the mesh uniform we will also have 10 elements in each of the transverse The length of 10 elements is 0 2 m Since the total length of the bar is 1 0 m we would have 50 elements directions making the mesh 50 x 10 x 10 This mesh is shown in Figure 9 3 Figure 9 3 50 x 10 x
589. st frequencies of interest The column for generalized mass lists the mass of a single degree of freedom system associated The table of participation factors indicates the predominant degrees of freedom in which the modes act as shown below PARTICIPATION FACTORS Y ROTATION MODE NO X COMPONENT Y COMPONENT Z COMPONENT X ROTATION 1 6 11690E 04 6 14531E 03 1 4284 1 4276 2 0 18470 0 25678 8 31883E 04 2 09977E 03 3 0 17440 1 5515 4 88139E 03 5 59953E 03 4 8 69482E 05 9 61288E 03 8 23644E 02 0 25721 7 15 6 0252 6 05062E 03 3 24483E 02 1 2335 Z ROTATION 3 34721E 02 1 7751 9 3618 2 97485E 02 5 EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING 5 3 80669E 03 1 13896E 03 3 04330E 02 0 60741 1 7592 2 01080E 02 6 3 71619E 02 0 35674 6 05207E 03 1 37690E 02 6 71471E 03 0 98290 7 2 48375E 03 1 58340E 03 6 19483E 02 8 18701E 02 0 29885 5 73966E 04 25 8 25367E 02 0 22220 3 54513E 02 1 61838E 02 2 18156E 02 0 14563 26 1 98899E 02 0 35108 4 61344E 02 1 80975E 03 1 27588E 02 0 17942 27 1 71767E 02 2 51338E 02 2 26535E 02 1 06724E 03 4 31578E 02 1 92991E 02 28 4 73374E 02 2 79248E 02 0 11861 7 32078E 03 0 24177 2 37795E 02 29 9 83570E 03 3 64867E 03 4 65417E 03 8 45350E 04 1 56687E 02 7 74623E 03 30 4 83653E 02 1 85437E 02 0 13423 4 49321E 02 0 35873 4 29368E 02 Mode 1 acts predominately in the 3 direction The table of effective mass indicates the amount of mass active in each degree of free
590. st increment of the first step the check that the largest corrections to nodal variables are less than 1 of the largest incremental values will always fail However if Abaqus judges the solution to be linear a judgement based on the magnitude of the residuals r az lt 10 g it will ignore this criterion Since Abaqus did not find an equilibrium solution in the first iteration it tries a second iteration as shown below CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 2 AVERAGE FORCE 1 00 TIME AVG FORCE 1 00 LARGEST RESIDUAL FORCE 0 173 AT NODE 1051 DOF 1 LARGEST INCREMENT OF DISP 5 582E 03 AT NODE 651 DOF 3 LARGEST CORRECTION TO DISP 7 050E 05 AT NODE 1201 DOF 1 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE AVERAGE MOMENT 1 12 TIME AVG MOMENT 1 12 LARGEST RESIDUAL MOMENT 8 698E 04 AT NODE 208 DOF 5 LARGEST INCREMENT OF ROTATION 1 597E 02 AT NODE 1051 DOF 5 LARGEST CORRECTION TO ROTATION 1 305E 04 AT NODE 409 DOF 4 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED In the second iteration r az has fallen to 0 173 N at node 1051 in degree of freedom 1 However equilibrium is not satisfied in this iteration because 0 005 xq where q 1 00 N is still less than r az The displacement correction criterion also failed again because C aa 7 050 x 10 which occurred at node 1201 in degree of freedom 1 is more than 1 of Au aa 75 582 x 10 the maximum displacement increment Both the moment residual check and the larges
591. std 0 05 forceDisp xpl forceDisp xpl bw1 100 ab O a 2 70 10 O am 5 A 0 15 0 20 0 000 0 005 0 010 0 015 0 020 0 025 0 030 Punch displacement Figure 13 17 Steady punch force comparison for Abaqus Standard and Abaqus Explicit readily However when choosing Abaqus Explicit for quasi static analysis you should be aware that you may need to iterate on an appropriate loading rate In determining the loading rate it is recommended that you begin with faster loading rates and decrease the loading rate as necessary This will help optimize the run time for the analysis 13 5 4 Methods of speeding up the analysis Now that we have obtained an acceptable solution to the forming analysis we can try to obtain similar acceptable results using less computer time Most forming analyses require too much computer time to be run in their physical time scale because the actual time period of forming events is large by explicit dynamics standards running in an acceptable amount of computer time often requires making changes to the analysis to reduce the computer cost There are two ways to reduce the cost of the analysis 1 Artificially increase the punch velocity so that the same forming process occurs in a shorter step time This method is called load rate scaling 2 Artificially increase the mass density of the elements so that the stability limit increases allowing the analysis to take fewer increments This metho
592. step Step 2 loads of 2000 N are specified on nodes 4 and 5 using the OP MOD parameter Thus these loads modify those applied in Step 1 The loading applied to the model at the end of Step 2 is shown in Figure 11 3 2000N 2000N 1000N CLOAD OP MOD Ay 2 2000 Dy 2 2000 Figure 11 3 Loads applied in Step 2 with OP MOD Using OP NEW causes Abaqus to remove all existing loads of that type and only apply the loads specified in this current step to the model If OP NEW is specified on the CLOAD option in Step 2 the loading on our example beam is shown in Figure 11 4 11 3 5 LINEAR PERTURBATION ANALYSIS 2000N 2000N CLOAD OP NEW 4 2 2000 5y 27 2000 yono o o I 2 3 4 5 M Figure 11 4 Loads applied in Step 2 with OP NEW Be very careful when you use the OP NEW parameter on the BOUNDARY option to remove a boundary constraint from your model All boundary constraints are removed from the model not just the one you want removed therefore you must respecify all the boundary conditions that should remain active in the model Remember that the boundary conditions that you specify must provide enough constraints to prevent rigid body motions in all components of your model Failure to do so will cause Abaqus to issue numerical singularity warnings and leads to excessive displacements 11 2 Linear perturbation analysis Linear perturbation analysis steps are available only in Abaqus Standard The starting point
593. stiffness displacement curve click Plot Expression at the bottom of the Operate on XY Data dialog box 7 Click Cancel to close the dialog box 8 Open the Axis Options dialog box and switch to the Title tabbed page 9 Customize the axis titles so they appear as shown in Figure 10 51 STIFF Z I ao 1 40 _ 1 20 V Q lt 1 00 p 0 0 80 0 00 100 200 300 400 5 00 x10 Displacement m Figure 10 51 Stiffness characteristic of the mount 10 Click Dismiss to close the Axis Options dialog box 10 71 5 EXAMPLE AXISYMMETRIC MOUNT The stiffness of the mount increases by almost 100 as the mount deforms This is a result of the nonlinear nature of the rubber and the change in shape of the mount as it deforms Alternatively you could have created the stiffness displacement curve directly by combining all the operators above into one expression To define the stiffness curve directly 1 In the Results Tree double click XYData The Create XY Data dialog box appears 2 Select Operate on XY data and click Continue The Operate on XY Data dialog box appears 3 From the Operators listed click differentiate X differentiate appears in the text field at the top of the dialog box 4 In the XY Data field double click SWAPPED The expression differentiate SWAPPED appears in the text field 5 Place the cursor in the text field directly after the SWAPPED data object and type 5500 to multiply th
594. surface For the sake of efficiency Abaqus does not check for highly warped surfaces every increment Rigid surfaces are checked for high warpage only at the start of the step since rigid surfaces do not change shape during the analysis Deformable surfaces are checked for high warpage every 20 increments by default Some analyses may have surfaces whose warpage increases in severity quite suddenly making the default 20 increment frequency check inadequate The user can change 12 55 5 MODELING CONSIDERATIONS IN Abaqus Explicit the frequency of the warping checks by setting the WARP CHECK PERIOD parameter on the CONTACT CONTROLS option to the desired number of increments Some analyses in which the surface warping is less than 20 may also require the more accurate contact search approach associated with highly warped surfaces Use the WARP CUT OFF parameter on the CONTACT CONTROLS option to redefine the angle that defines high warpage Rigid element discretization Complex rigid surface geometries can be modeled using rigid elements Rigid elements in Abaqus Explicit are not smoothed they remain faceted exactly as defined by the user The advantage of unsmoothed surfaces is that the surface defined by the user is exactly the same as the surface used by Abaqus the disadvantage is that faceted surfaces require much higher mesh refinement to define smooth bodies accurately In general using a large number of rigid elements to define a rigid
595. surface does not increase the CPU costs significantly However a large number of rigid elements does increase the memory overhead significantly The user must ensure that the discretization of any curved geometry on rigid bodies is adequate If the rigid body discretization is too coarse contacting nodes on the deformable body may snag leading to erroneous results as illustrated in Figure 12 45 blank motion snagging sheet metal rigid tool blank Figure 12 45 Potential effect of coarse rigid body discretization A node that is snagged on a sharp corner may be trapped from further sliding along the rigid surface for some time Once enough energy is released to slide beyond the sharp corner the node will snap dynamically before contacting the adjacent facet Such motions cause noisy solutions The more refined the rigid surface the smoother the motion of the contacting slave nodes The general contact algorithm includes some numerical rounding of features that prevents snagging of nodes from becoming a concern for discrete rigid surfaces In addition penalty enforcement of the contact constraints reduces the tendency for snagging to occur Analytical rigid surfaces should normally be used with the contact pair algorithm for rigid bodies whose shape is an extruded profile or a surface of revolution 12 56 MODELING CONSIDERATIONS IN Abaqus Explicit 12 9 2 Overconstraining the model Just as multiple conflicting
596. t 1 In the Visualization toolbox click MV to open the Curve Options dialog box 2 In the Curves field select S33 T2 3 Choose the dotted line style for the S33 T2 curve The 33 T2 curve becomes dotted 4 Repeat Steps 2 and 3 to make the 33 T3 curve dashed 5 Dismiss the Curve Options dialog box The customized plot appears in Figure 9 8 For clarity the default grid and legend positions have been changed We can see that the length of the bar affected by the stress wave is approximately 0 2 m in each of the three curves This distance should correspond to the distance that the blast wave travels during its time of application which can be checked by a simple calculation If the length of the wave front 1s 0 2 m and the wave speed is 5 15 x 10 m s the time it takes for the wave to travel 0 2 m is 3 88 x 10 s 9 19 5 EXAMPLE STRESS WAVE PROPAGATION IN A BAR x10 20 00 0 00 f 20 00 40 00 60 00 Stress S33 Pa 80 00 100 00 0 00 0 20 040 0 60 080 1 00 Distance along bar m Figure 9 8 Stress S33 along the bar at three different time instances As expected this is the duration of the blast load that we applied The stress wave is not exactly square as it passes along the bar In particular there is ringing or oscillation of the stress behind the sudden changes in stress Linear bulk viscosity discussed later in this chapter damps the ringing so that it does not affect
597. t dat provided that you used the PREPRINT MODEL YES option in the model data section of the input file The material test data are also written in the file so that you can ensure that Abaqus used the correct data as shown below MATERIAL DESCRIPTION MATERIAL NAME RUBBER HYPERELASTIC MATERIAL PROPERTIES UNIAXIAL TEST DATA NOMINAL STRAIN NOMINAL STRESS TEST NOMINAL STRESS ABAQUS 3 8000E 02 5 4000E 04 3 9605E 04 0 1338 1 5200E 05 1 2803E 05 0 2210 2 5400E 05 1 9764E 05 0 3450 3 6200E 05 2 8404E 05 0 4600 4 5900E 05 3 5477E 05 0 6242 5 8300E 05 4 4505E 05 0 8510 6 5600E 05 5 5627E 05 1 427 7 3000E 05 8 0275E 05 HYPERELASTIC MATERIAL PROPERTIES BIAXIAL TEST DATA NOMINAL STRAIN NOMINAL STRESS TEST NOMINAL STRESS ABAQUS 2 0000E 02 8 9000E 04 4 1264E 04 0 1400 2 5500E 05 2 2551E 05 0 4200 5 0300E 05 4 6078E 05 1 490 9 5800E 05 1 0063E 06 2 750 1 7030E 06 1 7767E 06 3 450 2 4130E 06 2 3301E 06 HYPERELASTIC MATERIAL PROPERTIES PLANAR TEST DATA 10 68 EXAMPLE AXISYMMETRIC MOUNT NOMINAL STRAIN NOMINAL STRESS TEST NOMINAL STRESS ABAQUS 6 9000E 02 5 5000E 04 9 0339E 04 0 2828 3 2400E 05 2 9189E 05 1 386 7 5800E 05 8 3431E 05 3 034 1 2690E 06 1 4500E 06 4 062 1 7790E 06 1 8235E 06 HYPERELASTICITY MOONEY RIVLIN STRAIN ENERGY D1 C10 col 0 00000000 176050 524 4332 63031 If there were any problems with the stability of the hyperelastic material model warning messages would be given before th
598. t View ODB Display Options 2 In the ODB Display Options dialog box click the Mirror Pattern tab 3 Select rectangular from the Mirror CSYS list 4 5 Click Apply Select XZ as the mirror plane The mirrored image appears 10 73 5 EXAMPLE AXISYMMETRIC MOUNT 6 Click the Sweep Extrude tab 7 Toggle on Sweep elements and set the sweep range from 0 to 270 degrees Set the number of segments to 45 8 Click OK The swept image appears To more clearly distinguish between the rubber and the steel color code the model based on section assignment You will now plot the deformed model shape of the mount This will allow you to evaluate the quality of the deformed mesh and to assess the need for mesh refinement To plot the deformed model shape From the main menu bar select Plot Deformed Shape or use the R tool to plot the deformed model shape of the mount see Figure 10 53 HH an rH an a T i I Figure 10 53 Deformed model shape of the rubber under an applied load of 5500 N mirrored swept image The plate has been pushed up causing the rubber to bulge at the sides Zoom in on the bottom left corner of the mesh using the tool from the View Manipulation toolbar Click mouse button 1 and hold it down to define the first corner of the new view move the mouse to create a box enclosing the viewing area that you want Figure 10 54 and release the mouse button Alternatively you can zoom and
599. t correction to rotation check were satisfied in this second iteration however Abaqus must perform two more iterations because the solutions did not pass the force residual check or the largest correction to displacement criterion The message file summaries for the additional iterations necessary to obtain a solution in the first increment are shown below 8 19 5 EXAMPLE NONLINEAR SKEW PLATE CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 3 AVERAGE FORCE 0 997 TIME AVG FORCE 0 997 LARGEST RESIDUAL FORCE 5 838E 03 AT NODE 459 DOF 2 LARGEST INCREMENT OF DISP 5 582E 03 AT NODE 651 DOF 3 LARGEST CORRECTION TO DISP 9 150E 06 AT NODE 559 DOF 3 FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE AVERAGE MOMENT 1 12 TIME AVG MOMENT 1 12 LARGEST RESIDUAL MOMENT 1 338E 06 AT NODE 908 DOF 5 LARGEST INCREMENT OF ROTATION 1 597E 02 AT NODE 1051 DOF 5 LARGEST CORRECTION TO ROTATION 3 233E 05 AT NODE 809 DOF 5 THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION 4 AVERAGE FORCE 0 997 TIME AVG FORCE 0 997 LARGEST RESIDUAL FORCE 1 581E 07 AT NODE 1002 DOF 1 LARGEST INCREMENT OF DISP 5 582E 03 AT NODE 651 DOF 3 LARGEST CORRECTION TO DISP 1 945E 09 AT NODE 559 DOF 3 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED AVERAGE MOMENT 1 12 TIME AVG MOMENT 1 12 LARGEST RESIDUAL MOMENT 3 691E 10 AT NODE 259 DOF 5 LARGEST INCREMENT OF ROTATION 1 597E 02 AT NODE 1051 DOF 5 LARGEST CORRECTION TO ROTATION 6 461E 09 AT
600. t file using the approximate sizes given near the bottom of the data file during a datacheck analysis In this example request output of the deformed shape to the output database file at the end of every fifth increment There will be 100 increments in the step 0 5 0 005 therefore there will be 20 frames of output OUTPUT FIELD FREQUENCY 5 VARIABLE PRESELECT The displacements of the independent tip node which is assigned to a node set named TIP and the reaction forces at the fixed nodes which are grouped into a node set named ATTACH are written as history data to the output database file every increment so that a higher resolution of these 7 13 5 EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING data will be available In dynamic analyses we are also concerned about the energy distribution in the model and what form the energy takes Kinetic energy is present in the model as a result of the motion of the mass strain energy is present as a result of the displacement of the structure energy is also dissipated through damping We can output the kinetic energy ALLKE strain energy ALLSE energy dissipated through damping ALLVD external work on the entire model ALLWK and the total energy balance in the model ETOTAL The history portion of the output request is written as follows NSET NSET TIP 104 OUTPUT HISTORY FREQUENCY 1 NODE OUTPUT NSET TIP U NODE OUTPUT NSET ATTACH RF ENERGY OUTPUT ALLKE ALLSE A
601. t in the middle of the bar This is the element affected next by the stress wave 5 Specify 33 0 5 as the curve legend text and change the curve style to dotted 6 In the Curves field select the temporary X Y data label that corresponds to the element closest to the fixed end of the bar This is the element affected last by the stress wave Specify 33 0 75 as the curve legend text and change the curve style to dashed 8 Click Dismiss to close the dialog box The customized plot appears in Figure 9 9 For clarity the default grid and legend positions have been changed In the history plot we can see that stress at a given point increases as the stress wave travels through the point Once the stress wave has passed completely through the point the stress at the point oscillates about zero 9 4 6 How the mesh affects the stable time increment and CPU time In Automatic time incrementation and stability Section 9 3 we discussed how mesh refinement affects the stability limit and the CPU time Here we will illustrate this effect with the wave propagation problem We began with a reasonably refined mesh of square elements with 50 elements along the length and 10 elements in each of the two transverse directions For illustrative purposes we will now use a coarse mesh of 25 x 5 x 5 elements and observe how refining the mesh in the various directions changes the CPU time The four meshes are shown in Figure 9 10
602. ta dialog box should appear as butterworthFilter xyData U2 xpl cutof fFrequency 1100 Click Save As to save the calculated displacement curve as U2 xpl1 bw1100 Combine the filtered Abaqus Explicit force and displacement histories The expression at the top of the Operate on XY Data dialog box should appear as combine U2 xpl bw1100 RF2 xpl bw1100 Click Save As to save the calculated displacement curve as forceDisp xpl bw1100 Add forceDisp xp1 bw1100 to the plot of forceDisp std and forceDisp xpl Customize the plot appearance to obtain a plot similar to Figure 13 17 As seen in Figure 13 17 the steady punch force predicted by Abaqus Explicit is approximately 12 higher than that predicted by Abaqus Standard The differences between the Abaqus Standard and Abaqus Explicit results are primarily due to two factors First Abaqus Explicit regularizes the material data Second friction effects are handled slightly differently in the two analysis products Abaqus Standard uses penalty friction whereas Abaqus Explicit uses kinematic friction From these comparisons it 1s clear that both Abaqus Standard and Abaqus Explicit are capable of handling difficult contact analyses such as this one However there are some advantages to running this type of analysis in Abaqus Explicit Abaqus Explicit is able to handle complex contact conditions more 13 21 5 EXAMPLE FORMING A CHANNEL IN Abaqus Explicit x1 E6 0 00 forceDisp
603. tandard A 13 Shearing of a lap joint A 14 Circuit board drop test A 15 Forming a channel with Abaqus Explicit A 16 1 1 1 THE Abagus PRODUCTS Introduction Abaqus is a suite of powerful engineering simulation programs based on the finite element method that can solve problems ranging from relatively simple linear analyses to the most challenging nonlinear simulations Abaqus contains an extensive library of elements that can model virtually any geometry It has an equally extensive list of material models that can simulate the behavior of most typical engineering materials including metals rubber polymers composites reinforced concrete crushable and resilient foams and geotechnical materials such as soils and rock Designed as a general purpose simulation tool Abaqus can be used to study more than just structural stress displacement problems It can simulate problems in such diverse areas as heat transfer mass diffusion thermal management of electrical components coupled thermal electrical analyses acoustics soil mechanics coupled pore fluid stress analyses piezoelectric analysis electromagnetic analysis and fluid dynamics Abaqus offers a wide range of capabilities for simulation of linear and nonlinear applications Problems with multiple components are modeled by associating the geometry defining each component with the appropriate material models and specifying component interactions In a nonlinear analysis Abaqus auto
604. teractive Edition 11 3 4 Reviewing the input file the model data The steps that follow assumes that you have access to the full input file for this example This input file pipe 2 inp is provided in Vibration of a piping system Section A 12 in the online HTML version of this manual Instructions on how to fetch and run the script are given in Appendix A Example Files The model definition including the model description node and element definitions section properties and material properties is discussed next Model description The HEADING option should include a suitable title in the data lines In the sample input file this option looks like the following 11 10 EXAMPLE VIBRATION OF A PIPING SYSTEM HEADING Analysis of a 5 meter long pipe under tensile load Pipe has OD of 180 mm and ID of 140 mm S I Units Nodal coordinates and element connectivity Check that the correct element type PIPE32 has been used and that the element set names are suitably descriptive ELEMENT TYPE PIPE32 ELSET PIPE Create node sets containing the nodes at either end of the pipe section The following option blocks create the node sets for the model shown in Figure 11 9 NSET NSET LEFT 1 NSET NSET RIGHT 61 Beam properties The BEAM SECTION SECTION PIPE option will be used with the PIPE32 elements The outer radius 90 mm and the wall thickness 20 mm are needed to define this beam section type geo
605. tered acceleration A3 ANTIALIASING history output objects for Node 403 click mouse button 3 and select Add to Plot from the menu that appears The X Y plot appears in the viewport Zoom out and customize the plot appearance to obtain a plot similar to Figure 12 63 Figure 12 63 clearly illustrates some of the problems that can arise when the built in anti aliasing filter is used with too large an output time increment First notice that many of the oscillations in the acceleration output are filtered out when the acceleration is recorded with large time increments In this dynamic impact problem it is likely that a significant portion of the removed frequency content is physically meaningful Previously we estimated that the frequency of the structural response may be as large as 2 3 kHz however when the sample interval is 0 7 ms filtering 1s performed with a low cutoff frequency of 0 24 kHz sample interval of 0 7 ms corresponds to a sample frequency of 1 43 kHz one sixth of which is the 0 24 kHz cutoff frequency Even though the results recorded every 0 7 ms may not capture all physically meaningful frequency content it does capture the low frequency content of the acceleration data without distortions due to aliasing Keep in mind that filtering decreases the peak value estimations which is desirable if only solution noise is filtered but can be misleading when physically meaningful solution variations have been removed 12 83 5
606. terials container underneath the output database file named Mount odb 6 Click mouse button 3 on RUBBER and select Replace from the menu that appears to replace the current display with the selected elements 7 The viewport display changes and displays only the rubber mount elements as shown in Figure 10 55 S Max Principal Avg 75 1 363e 05 5 822e 04 1 984e 04 9 789e 04 EE ees Maximum principal stress around 88 2 kPa 3 321e 05 4 101e 05 4 882e 05 2a eS Ye Anna S eS Se eee a ho om emo MEN 2 Largest principal stress 100 kPa is in i the distorted element Figure 10 55 Contours of maximum principal stress in the rubber mount The maximum principal stress in the model reported in the contour legend is 136 kPa Although the mesh in this model is fairly refined and thus the extrapolation error should be minimal you may want to use the query tool 0O to determine the more accurate integration point values of the maximum principal stress When you look at the integration point values you will discover that the peak value of maximum principal stress occurs in one of the distorted elements in the bottom right hand part of the model This value is likely to be unreliable because of the levels of element distortion and 10 76 MESH DESIGN FOR LARGE DISTORTIONS volumetric locking If this value is ignored there is an area near the plane of symmetry where the maximum princip
607. terminal ends or a closed loop Figure 12 37 shows examples of valid and invalid two dimensional surfaces 12 49 5 MODELING CONSIDERATIONS IN Abaqus Explicit Valid Closed Simply Connected 2 D Surface mara a Valid Open Simply Connected 2 D Surface e eee a ae Invalid 2 D Surface Figure 12 37 Valid and invalid two dimensional surfaces for the contact pair algorithm e In three dimensions an edge of an element face belonging to a valid surface may be either on the perimeter of the surface or shared by one other face Two element faces forming a contact surface cannot be joined just at a shared node they must be joined across a common element edge An element edge cannot be shared by more than two surface facets Figure 12 38 illustrates valid and invalid three dimensional surfaces e In addition it is possible to define three dimensional double sided surfaces In this case both sides of a shell membrane or rigid element are included in the same surface definition as shown in Figure 12 39 Extending surfaces Abaqus Explicit does not extend surfaces automatically beyond the perimeter of the surface defined by the user If a node from one surface is in contact with another surface and it slides along the surface until it reaches an edge it may fall off the edge Such behavior can be particularly troublesome because the node may later reenter from the back side of the surface thereby violating the kinematic const
608. th steps are shown and the time associated with the linear perturbation step Step 2 is very small the FREQUENCY procedure or any linear perturbation procedure does not contribute to the general loading history of the model 11 3 8 Postprocessing Run Abaqus Viewer using the command abaqus viewer odb pipe 11 14 EXAMPLE VIBRATION OF A PIPING SYSTEM Deformed shapes from the linear perturbation steps When Abaqus Viewer starts it automatically uses the last available frame on the output database file The results from the second step of this simulation are the natural mode shapes of the pipe and the corresponding natural frequencies Plot the first mode shape To plot the first mode shape 1 From the main menu bar select Result Step Frame The Step Frame dialog box appears 2 Select step Step 2 and frame Mode 1 3 Click OK 4 From the main menu bar select Plot Deformed Shape o 5 Click the i tool in the toolbox to allow multiple plot states in the viewport then click the tool or select Plot Undeformed Shape to add the undeformed shape plot to the existing deformed plot in the viewport 6 Include node symbols on both plots the superimpose options control the appearance of the undeformed shape when multiple plot states are displayed Change the color of the node symbols to green and the symbol shape to a solid circle 7 Click the auto fit tool so that the entire plot is rescaled to fit in the viewport
609. th the following option ORIENTATION SYSTEM RECTANGULAR NAME LOCALR er gt aol gt p lt a gt lt ai gt er gt r lt gt 5 9 5 SHELL MATERIAL DIRECTIONS 4 j circumferential 1 global o Cylindrical Rectangular b z meridional y circumferential 3 x radial 1 global Spherical Figure 5 8 Definition of local coordinate systems The parameter NAME specifies a label for this orientation and the coordinates of point a x3 x and point b xt x x are given in the global Cartesian system The local coordinate system is then referred to by the ORIENTATION parameter on the SHELL SECTION or SHELL GENERAL SECTION option You must still specify another piece of information Abaqus must also be told which of the local axes corresponds to which material direction On the second data line following ORIENTATION specify the local axis 1 2 or 3 that 1s closest to being normal to the shell s surface Abaqus follows a cyclic permutation 1 2 3 of the axes and projects the axis following your selection onto the shell region to form the material 1 direction For example if you choose the x axis Abaqus projects the y axis onto the shell to form the material 1 direction The material 2 direction is defined by the cross product of the shell normal and the material 1 direction Normally the final material 2 direction and the projection of the other local axis in this case the z axis will not
610. that this is the curve we know to be corrupted by aliasing The curve jumps from point to point by directly including whatever the raw acceleration value happens to be after each 0 07 ms interval The variable nature of the high frequency noise makes this aliased result very sensitive to otherwise imperceptible variations in the solution due to differences between computer platforms for example hence the results you recorded every 0 07 increments may be significantly different from those shown in Figure 12 62 Similarly the velocity and displacement curves we produced by integrating the aliased acceleration Figure 12 59 and Figure 12 60 data are extremely sensitive to small differences in the solution noise When the built in anti aliasing filter is applied to the output requested every 0 07 ms frequency content that is too high to be captured by the 14 3 kHz sample rate 1s filtered out before the result 1s written to the output database To do this Abaqus internally defines a low pass 12 82 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST second order Butterworth filter Low pass filters attenuate the frequency content of a signal that is above a specified cutoff frequency An ideal low pass filter would completely eliminate all frequencies above the cutoff frequency while having no effect on the frequency content below the cutoff frequency In reality there is a transition band of frequencies surrounding the cutoff frequency that
611. the ALL EXTERIOR parameter on the CONTACT INCLUSIONS option to specify self contact for the unnamed all inclusive surface defined automatically by Abaqus Explicit The CONTACT PROPERTY ASSIGNMENT option is used to assign the contact property named FRIC to the general contact interaction CONTACT CONTACT INCLUSIONS ALL EXTERIOR CONTACT PROPERTY ASSIGNMENT FRIC 12 10 6 Reviewing the input file the history data The DYNAMIC EXPLICIT option is used to select a dynamic stress displacement analysis using explicit integration The time period of the step is defined as 20 ms STEP DYNAMIC EXPLICIT 0 02 Output requests The preselected field data are written to the output database file by including the following line in the input file OUTPUT FIELD VARIABLE PRESELECT Values of vertical nodal displacement U3 velocity V3 and acceleration A3 will be written for each of the attached chips as history data to the output database file An output interval of 0 07 ms has been selected OUTPUT HISTORY TIME INTERVAL 0 07E 3 NODE OUTPUT NSET CHIPS U3 V3 A3 Energy values will be written summed over the entire model Specifically write values for kinetic energy ALLKE internal energy ALLIE elastic strain energy ALLSE artificial energy ALLAE and the energy dissipated by plastic deformation ALLPD 12 69 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST ENERGY OUTPUT ALLIE ALLKE ALLPD ALLAE
612. the chip acceleration was sampled every 0 07 ms which is a sampling rate of 14 3 kHz the sample rate is the inverse of the sample size The recorded data was aliased because the chip acceleration response has frequency content above 7 2 kHz half the sample rate Aliasing of a sine wave To better understand how aliasing distorts data consider a 1 kHz sine wave sampled using various sampling rates as shown in Figure 12 61 Original signal sine wave frequency 1 kHz 3 kHz sampling rate Nyquist frequency 1 5 kHz E E 1 1 kHz sampling rate Nyquist frequency 0 55 kHz s NIN NAY B o 2 0 4 0 6 0 Time ms Amplitude 10 0 Figure 12 61 1 kHz sine wave sampled at 1 1 kHz and 3 kHz According to the Sampling Theorem this signal must be sampled at a rate greater than 2 kHz to avoid alias distortions We will evaluate what happens when the sample rate is greater than or less than this value Consider the data recorded with a sample rate of 1 1 kHz this rate is less than the required 2 kHz rate The resulting curve exhibits alias distortions because it is an extremely misleading representation of the original kHz sine wave Now consider the data recorded with a sample rate of 3 kHz this rate 1s greater than the required 2 kHz rate The frequency content of the original signal is captured without aliasing However this sample rate is not high enough to guarantee that the peak values of the sampled signal are cap
613. the deformation history of the drop test take note of when the foam is in contact with the floor You should observe that the initial impact occurs over the first 4 ms of the analysis A second impact occurs from about 8 ms to 15 ms The deformed state of the foam and board at approximately 4 ms after impact is shown in Figure 12 56 Plotting model energy histories Plot graphs of various energy variables versus time Energy output can help you evaluate whether an Abaqus Explicit simulation 1s predicting an appropriate response To plot energy histories 1 N Oo O89 FP OW KN In the Results Tree click mouse button 3 on History Output for the output database named circuit odb From the menu that appears select Filter In the filter field enter ALL to restrict the history output to just the energy output variables Select the ALLAE output variable and save the data as Artificial Energy Select the ALLIE output variable and save the dataas Internal Energy Select the ALLKE output variable and save the dataas Kinetic Energy Select the ALLPD output variable and save the dataas Plastic Dissipation Select the ALLSE output variable and save the data as Strain Energy 12 72 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST SNS SESSO CPOE IIA SSD A CA Oe Wists senth 628 ee Figure 12 56 Deformed mesh at 4 ms 8 In the Results Tree expand the XYData container 10 11 12 13
614. the end of the increment is based solely on the displacements velocities and accelerations at the beginning of the increment This method integrates constant accelerations exactly For the method to produce accurate results the time increments must be quite small so that the accelerations are nearly constant during an increment Since the time increments must be small analyses typically require many thousands of increments Fortunately each increment is inexpensive because there are no simultaneous equations to solve Most of the computational expense lies in the element calculations to determine the internal forces of the elements acting on the nodes The element calculations include determining element strains and applying material constitutive relationships the element stiffness to determine element stresses and consequently internal forces Here is a summary of the explicit dynamics algorithm 1 Nodal calculations a Dynamic equilibrium 9 3 5 EXPLICIT DYNAMIC FINITE ELEMENT METHODS a M Pq Ie b Integrate explicitly through time Atw az Ati Ueta Beaty 2 n Uttar Ua Atatay ac 2 Element calculations a Compute element strain increments Ae from the strain rate b Compute stresses o from constitutive equations O t At flow Ae c Assemble nodal internal forces I 4 a 3 Set t At to t and return to Step 1 9 2 2 Comparison of implicit and explicit time
615. the normals in the crane model appear to be correct in Abaqus Viewer yet they are in fact slightly incorrect You can also find such modeling mistakes by examining the averaged nodal normals that are printed in the data dat file Some of the normals in the incorrect model of the cargo crane are shown in the following output NODE DEFINITIONS NODE COORDINATES NORMAL SINGLE POINT CONSTRAINTS NUMBER TYPE PLUS DOF 100 0 00000E 00 0 00000E 00 1 0000 0 18202 0 98308 2 04813E 02 ENCASTRE 101 2 0000 0 37500 0 77500 0 18202 0 98308 2 04813E 02 102 4 0000 0 75000 0 55000 0 25486 0 96655 2 86770E 02 103 6 0000 1 1250 0 32500 0 18202 0 98308 2 04813E 02 The problem is the normal vector for node 102 which does not match those at the other nodes defining the lower main member in truss A see Figure 6 14 Four elements 101 102 112 and 113 contain node 102 When the averaging of beam normals at nodes produces multiple independent normals the additional normals at the node are also printed in the data file see Beam element curvature Section 6 1 3 for details The correct geometry for the crane model requires three independent beam normals at node 102 one each for the bracing elements 112 and 113 and a single normal for elements 101 and 102 The normal shown above for node 102 is not the normal needed for elements 101 and 102 If it were it would match the normals shown for nodes 100 101 or 103 Nor is it the correct normal for e
616. the operating system prompt abaqus viewer odb frame Abaqus Viewer opens the output database created by the job and displays the undeformed model shape as shown in Figure 2 8 2 o Figure 2 8 Undeformed model shape You can choose to display the title block and state block at the bottom of the viewport these blocks are not shown in Figure 2 8 The title block at the bottom of the viewport indicates the following e The description of the model from the job description e The name of the output database from the name of the analysis job e The product name Abaqus Standard or Abaqus Explicit and release used to generate the output database e The date the output database was last modified The state block at the bottom of the viewport indicates the following e Which step is being displayed e The increment within the step e The step time 2 29 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST The view orientation triad indicates the orientation of the model in the global coordinate system The 3D compass located in the upper right corner of the viewport allows you to manipulate the view directly You can suppress the display of and customize the title block state block view orientation triad and 3D compass by selecting Viewport Viewport Annotation Options from the main menu bar for example many of the figures in this manual do not include the title block or the compass The Results Tree You will
617. the results from the entire original and restarted analysis To generate a history plot of the axial stress in the pipe for the entire analysis 1 From the main menu bar select File Open or use the Save the current plot by clicking Save at the bottom of the XY Data from ODB Field Output dialog box Two curves are saved one for each integration point and default names are given to the curves Rename either curve RESTART and delete the other curve S tool in the File toolbar to open the file pipe odb Following the procedure outlined above save the plot of the axial stress history for the same element and integration section point used above Name this plot ORIGINAL In the Results Tree expand the XYData container The ORIGINAL and RESTART curves are listed underneath Select both plots with Ctrl Click Click mouse button 3 and select Plot from the menu that appears to create a plot of axial stress history in the pipe for the entire simulation 7 To change the style of the line open the Curve Options dialog box For the RESTART curve select a dotted line style 9 Click Dismiss to close the dialog box 10 11 To change the axis titles open the Axis Options dialog box In this dialog box switch to the Title tabbed page Change the X axis title to TOTAL TIME and change the Y axis title to STRESS S11 11 23 RELATED Abaqus EXAMPLES 12 Click Dismiss to close the dialog box
618. the results adversely Creating a history plot Another way to study the results is to view the time history of stress at three different points within the bar To plot the stress history 1 In the Results Tree click mouse button 3 on History Output and deselect Group Children from the menu that appears 2 Select the data for the three elements Use Ctrl Click to select multiple X Y data sets 3 Click mouse button 3 and select Plot from the menu that appears Abaqus Viewer displays an X Y plot of the longitudinal stress in each element versus time 4 Click A in the prompt area to cancel the current procedure As before you can customize the appearance of the plot 9 20 EXAMPLE STRESS WAVE PROPAGATION IN A BAR To customize the X Y plot 1 Double click the X axis The Axis Options dialog box appears 2 Switch to the Title tabbed page 3 Specify Total time s as the X axis title 4 Click Dismiss to close the dialog box To customize the appearance of the curves in the X Y plot In the Visualization toolbox click MV to open the Curve Options dialog box Inthe Curves field select the temporary X Y data label that corresponds to the element closest to the free end of the bar Of the elements in this set this one is affected first by the stress wave 3 Enter 33 0 25 as the curve legend text 4 In the Curves field select the temporary X Y data label that corresponds to the elemen
619. the top half of the history data reads 10kN central load which is the first data line given in the STEP option block This line reminds you of the loads applied in this step 10kN central load FIXED TIME INCREMENTS TIME INCREMENT IS 2 220E 16 TIME PERIOD IS 2 220E 16 GLOBAL STABILIZATION CONTROL IS NOT USED THIS IS A LINEAR PERTURBATION STEP ALL LOADS ARE DEFINED AS CHANGE IN LOAD TO THE REFERENCE STATE EXTRAPOLATION WILL NOT BE USED CHARACTERISTIC ELEMENT LENGTH 1 00 DETAILS REGARDING ACTUAL SOLUTION WAVEFRONT REQUESTED DETAILED OUTPUT OF DIAGNOSTICS TO DATABASE REQUESTED PRINT OF INCREMENT NUMBER TIME ETC TO THE MESSAGE FILE EVERY 1 INCREMENTS DATABASE OUTPUT GROUP 1 THE FOLLOWING FIELD OUTPUT WILL BE WRITTEN EVERY 1 INCREMENT S THE FOLLOWING OUTPUT WILL BE WRITTEN FOR ALL ELEMENTS OF TYPE T2D2 OUTPUT IS AT THE INTEGRATION POINTS S E 2 23 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST THE FOLLOWING OUTPUT WILL BE WRITTEN FOR ALL NODES U RF CF END OF DATABASE OUTPUT GROUP 1 DATABASE OUTPUT GROUP 2 THE FOLLOWING HISTORY OUTPUT WILL BE WRITTEN EVERY 1 INCREMENT S THE FOLLOWING ENERGY OUTPUT QUANTITIES WILL BE WRITTEN FOR THE WHOLE MODEL ALLKE ALLSE ALLWK ALLPD ALLCD ALLVD ALLKL ALLAE ALLEE ALLIE ETOTAL ALLFD ALLJD ALLSD ALLDMD END OF DATABASE OUTPUT GROUP 2 History data summary ALLQB The second half of the history data is displayed below This section summarizes the element and nodal output
620. tical displacement of the node on the steel plate for which you wrote data to the output database file Data were written for the node in set OUT in this model 10 69 5 EXAMPLE AXISYMMETRIC MOUNT To create a history curve of vertical displacement and swap the X and Y axes 1 In the Results Tree expand the History Output container underneath the output database named mount odb Locate and select the vertical displacement U2 at the node in set OUT Click mouse button 3 and select Save As from the menu that appears to save the X Y data The Save XY Data As dialog box appears In the Save XY Data As dialog box name the curve SWAPPED and select swap XY as the save operation click OK The plot of time displacement appears in the viewport You now have a curve of time displacement What you need is a curve showing force displacement This is easy to create because in this simulation the force applied to the mount is directly proportional to the total time in the analysis All you have to do to plot a force displacement curve is multiply the curve SWAPPED by the magnitude of the load 5 5 KN To multiply a curve by a constant value 1 In the Results Tree double click XY Data The Create XY Data dialog box appears Select Operate on XY data and click Continue The Operate on XY Data dialog box appears In the XY Data field double click SWAPPED The expression SWAPPED appears in the text fie
621. to establish firm contact contact stabilization as described above will be used Step 1 In this step contact will be established between the blank holder and the blank while the punch and die are held fixed Given the quasi static nature of the problem and the fact that nonlinear response will be considered a static general step is required The effects of geometric nonlinearity must be considered in this simulation so set the NUGEOM parameter equal to YES on the STEP option Set the initial time increment to 0 05 and the total time period to 1 0 12 25 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL Constrain the blank holder in degrees of freedom 1 and 6 where degree of freedom 6 is the rotation in the plane of the model constrain the punch and die completely All of the boundary conditions for the rigid surfaces are applied to their respective rigid body reference nodes Apply symmetric boundary constraints on the nodes of the blank lying on the symmetry plane node set CENTER Recall that in this simulation the required blank holder force is 440 kN Thus apply a concentrated force to set REFHOLD and specify a magnitude of 440 E3 for degree of freedom 2 Finally specify that the preselected field output be written every 20 increments for this step In addition request that the vertical reaction force and displacement RF2 and U2 at the punch reference node node set REFPUNCH be written every increment as history data Use th
622. to indicate the applied boundary conditions as shown in Figure 2 13 2 Figure 2 13 Applied boundary conditions on the overhead hoist Tabular data reports In addition to the graphical capabilities described above Abaqus Viewer allows you to write data to a text file in a tabular format This is a convenient alternative to writing printed data to the data dat file especially for complicated models Output generated this way has many uses for example it can be used in written reports In this problem you will generate a report containing the element stresses nodal displacements and reaction forces To generate field data reports 1 From the main menu bar select Report Field Output 2 34 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST 2 Inthe Variable tabbed page of the Report Field Output dialog box accept the default position labeled Integration Point Click the triangle next to S Stress components to expand the list of available variables From this list toggle on 11 3 In the Setup tabbed page name the report Frame rpt In the Data region at the bottom of the page toggle off Column totals 4 Click Apply The element stresses are written to the report file 5 In the Variable tabbed page of the Report Field Output dialog box change the position to Unique Nodal Toggle off S Stress components and select U1 and U2 from the list of available U Spatial displacement variables 6 Click Apply
623. to the Title tabbed page and customize the X and Y axis labels as shown in Figure 10 16 Click Dismiss to close the Axis Options dialog box It will also be helpful to display a symbol at each data point of the curve Open the Curve Options dialog box From the Curves field select the stress strain curve SVE11 The SVE11 data object is highlighted Toggle on Show symbol Accept the defaults and click Dismiss at the bottom of the dialog box The stress strain plot appears with a symbol at each data point of the curve You should now have a plot similar to the one shown in Figure 10 16 The stress strain curve shows that the material behavior was linear elastic for this integration point during the first two increments of the simulation In this plot it appears that the material remains linear during the third increment of the analysis however it does yield during this increment This illusion is created by the extent of strain shown in the plot If you limit the maximum strain displayed to 0 01 and set the minimum value to 0 0 the nonlinear material behavior in the third increment can be seen more clearly see Figure 10 17 10 26 EXAMPLE CONNECTING LUG WITH PLASTICITY x10 500 00 qq ooo 400 00 300 00 200 00 100 00 STRESS INVARIANT MISES 0 00 0 02 0 04 0 06 0 08 STRAIN E11 Figure 10 16 Mises stress vs direct strain E11 along the lug in the corner element x10 500
624. to the shell normal direction and a zero rotation is specified therefore the projection of the y axis onto the shell s surface is the material 1 direction Thus the material 1 direction is always circumferential and the corresponding material 2 direction is always axial 5 4 Selecting shell elements e The linear finite membrane strain fully integrated quadrilateral shell element S4 can be used when greater solution accuracy is desired for problems prone to membrane or bending mode hourglassing or for problems where in plane bending is expected 5 11 5 EXAMPLE SKEW PLATE e The linear finite membrane strain reduced integration quadrilateral shell element S4R is robust and is suitable for a wide range of applications e The linear finite membrane strain triangular shell elements S3 S3R can be used as general purpose elements A refined mesh may be needed to capture bending deformations or high strain gradients because of the constant strain approximation in the elements e To account for the influence of shear flexibility in laminated composite shell models use the shell elements suitable for modeling thick shells S4 S4R S3 S3R S8R check that the assumption of plane sections remaining plane is satisfied e Quadratic shell elements either quadrilateral or triangular are very effective for general small strain thin shell applications These elements are not susceptible to shear or membrane locking e If you
625. tory is written to the output database file as part of the preselected history output Running the job Save the input file and submit the job for analysis Monitor the solution progress correct any modeling errors that are detected and investigate the cause of any warning messages Strategy for evaluating the results Before looking at the results that are ultimately of interest such as stresses and deformed shapes we need to determine whether or not the solution is quasi static One good approach is to compare the kinetic energy history to the internal energy history In a metal forming analysis most of the internal energy is due to plastic deformation In this model the blank is the primary source of kinetic energy the motion of the holder is negligible and the punch and die have no mass associated with them To determine whether an acceptable quasi static solution has been obtained the kinetic energy of the blank should be no greater than a few percent of its internal energy For greater accuracy especially when springback stresses are of interest the kinetic energy should be lower This approach is very useful because it applies to all types of metal forming processes and does not require any intuitive understanding of the stresses in the model many forming processes may be too complex to permit an intuitive feel for the results While a good primary indication of the caliber of a quasi static analysis the ratio of kinetic energy to i
626. triangular and tetrahedral elements are also provided In addition hybrid and incompatible mode elements are available in Abaqus Standard Abaqus Explicit solid element library The Abaqus Explicit solid element library includes reduced integration first order linear interpolation elements in two or three dimensions Modified second order interpolation triangles and tetrahedra are also available Full integration or regular second order elements are not available in Abaqus Explicit with the exception of the fully integrated first order hexahedral element an incompatible mode version of this element is also available For detailed information on the options available for continuum elements please see Solid continuum elements Section 28 1 1 of the Abaqus Analysis User s Manual When the permutations of all these various element options are made the total number of solid elements available to you is large over 20 just for three dimensional models The accuracy of your simulation will depend strongly on the type of element you use in your model The thought of choosing which of these elements is best for your model may seem daunting especially at first However you will come to view this selection as a 20 piece tool set that provides you with the ability to choose just the right tool or element for a particular job This chapter discusses the effect that different element formulations and levels of integration have on the accurac
627. tric strain rate 9 24 DAMPING OF DYNAMIC OSCILLATIONS Quadratic bulk viscosity Quadratic bulk viscosity is included only in continuum elements except for the plane stress element CPS4R and is applied only if the volumetric strain rate is compressive The bulk viscosity pressure is quadratic in the strain rate according to the following equation po p beL vor min 0 Exot where bz is the damping coefficient whose default value is 1 2 The quadratic bulk viscosity smears a shock front across several elements and is introduced to prevent elements from collapsing under extremely high velocity gradients Consider a simple one element problem in which the nodes on one side of the element are fixed and the nodes on the other side have an initial velocity in the direction of the fixed nodes as shown in Figure 9 11 gt v Figure 9 11 Element with fixed nodes and prescribed velocities The stable time increment size is precisely the transit time of a dilatational wave across the element Therefore if the initial nodal velocity is equal to the dilatational wave speed of the material the element collapses to zero volume in one time increment The quadratic bulk viscosity pressure introduces a resisting pressure that prevents the element from collapsing Fraction of critical damping due to bulk viscosity The bulk viscosity pressures are based on only the dilatational modes of each element The fraction of critical da
628. ts for the various simulations to the beam theory value of 3 09 mm are shown in Table 4 1 The linear elements CPS4 and C3D8 underpredict the deflection so badly that the results are unusable The results are least accurate with coarse meshes but even a fine mesh 8 x 24 still predicts a tip displacement that is only 56 of the theoretical value Notice that for the linear fully integrated elements it makes no difference how many elements there are through the thickness of the beam The underprediction of tip deflection is caused by shear locking which 1s a problem with all fully integrated first order solid elements 5 ELEMENT FORMULATION AND INTEGRATION Table 4 1 Normalized tip displacements with fully integrated elements Mesh Size Depth x Length 0 074 0 242 0 242 0 561 CPS8 0 994 1 000 1 000 1 000 C3D8 0 077 0 248 0 243 0 563 C3D20 0 994 1 000 1 000 1 000 As we have seen shear locking causes the elements to be too stiff in bending It is explained as follows Consider a small piece of material in a structure subject to pure bending The material will distort as shown in Figure 44 CEE ee Fey ot Figure 4 4 Deformation of material subjected to bending moment M Lines initially parallel to the horizontal axis take on constant curvature and lines through the thickness remain straight The angle between the horizontal and vertical lines remains at 90 The edges of a linear element are unable to curve therefore
629. tude of the velocity are specified on the data line as follows lt node or node set gt lt dof gt lt velocity gt For example INITIAL CONDITIONS TYPE VELOCITY NALL 1 10 0 would set the velocity in the 1 direction of all the nodes in node set NALL to 10 m s Time variation of load The magnitude of the load applied to the tip of the crane is time dependent as illustrated in Figure 7 6 The time dependence of a load is defined using the AMPLITUDE option The AMPLITUDE option must appear as part of the model data even though the CLOAD option referring to it is part of the history data 7 10 7 5 2 EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING Four pairs of time and magnitude data are given on each data line for the AMPLITUDE option and a name 1s assigned to the amplitude curve using the NAME parameter For your simulation the option block defining the amplitude curve should look similar to the following AMPLITUDE NAME BOUNCE VALUE RELATIVE SMOOTH 0 25 0 0 0 0 0 01 240 0 2 1 0 0 21 0 0 The name of the curve BOUNCE will be used to refer the loading option CLOAD to this amplitude curve The actual load applied will be the product of the magnitude on the loading option and the amplitude on the BOUNCE curve The parameter VALUE RELATIVE is used to indicate this approach You can choose to define the absolute magnitude of the loading on the AMPLITUDE option by using VALUE ABSOLUTE Modifications to the
630. tured 12 78 Abaqus Explicit EXAMPLE CIRCUIT BOARD DROP TEST very accurately To guarantee 95 accuracy of the recorded local peak values the sampling rate must exceed the signal frequency by a factor of ten or more Avoiding aliasing In the previous two examples of aliasing the aliased chip acceleration and the aliased sine wave it would not have been obvious from the aliased data alone that aliasing had occurred In addition there is no way to uniquely reconstruct the original signal from the aliased data alone Therefore care should be taken to avoid aliasing your analysis results particularly in situations when aliasing is most likely to occur Susceptibility to aliasing depends on a number of factors including output rate output variable and model characteristics Recall that signals with large amplitude oscillations at frequencies greater than half the sampling rate the Nyquist frequency may be significantly distorted due to aliasing The two output variables that are most likely to have large amplitude high frequency content are accelerations and reaction forces Therefore these variables are the most susceptible to aliasing Displacements on the other hand are lower in frequency content by nature so they are much less susceptible to aliasing Other result variables such as stress and strain fall somewhere in between these two extremes Any model characteristic that reduces the high frequency response of the solution will d
631. tures continue to vibrate with constant amplitude Over the 50 ms ofthis simulation the frequency of the oscillation can be seen to be approximately 100 Hz A constant amplitude vibration is not the response that would be expected in practice since the vibrations in this type of structure would tend to die out over time and effectively disappear after 5 10 oscillations The energy loss typically occurs by a variety of mechanisms including frictional effects at the supports and damping by the air Consequently we need to consider the presence of damping in the analysis to model this energy loss The energy dissipated by viscous effects ALLVD is nonzero in the analysis indicating that there is already some damping present By default a bulk viscosity damping discussed in Chapter 9 Nonlinear Explicit Dynamics is always present and is introduced to improve the modeling of high speed events In this shell model only linear damping is present With the default value the oscillations would eventually die away but it would take a long time because the bulk viscosity damping is very small Material damping should be used to introduce a more realistic structural response Modify the material data block to include damping setting the mass proportional damping to 50 0 DAMPING ALPHA 50 0 BETA 0 0 BETA is the parameter that controls stiffness proportional damping and at this stage we will leave it set to zero The duration of the oscillation
632. tween the PLASTIC and DENSITY options as shown in the following input would cause Abaqus to terminate the analysis with an error message 10 1 5 PLASTICITY IN DUCTILE METALS MATERIAL NAME STEEL ELASTIC 2 1E11 0 3 PLASTIC 2 0E8 0 0 3 0E8 0 2 a Because of this option block BOUNDAR Y Abaqus does not know eee i which MATERIAL option q ee 7800 0 this option block belongs to 10 2 Plasticity in ductile metals Many metals have approximately linear elastic behavior at low strain magnitudes see Figure 10 1 and the stiffness of the material known as the Young s or elastic modulus is constant Stress Young s modulus E Strain Figure 10 1 Stress strain behavior for a linear elastic material such as steel at small strains At higher stress and strain magnitudes metals begin to have nonlinear inelastic behavior see Figure 10 2 which is referred to as plasticity 10 2 1 Characteristics of plasticity in ductile metals The plastic behavior of a material is described by its yield point and its post yield hardening The shift from elastic to plastic behavior occurs at a certain point known as the elastic limit or yield point on a material s stress strain curve see Figure 10 2 The stress at the yield point is called the yield stress In most metals the initial yield stress is 0 05 to 0 1 of the material s elastic modulus 10 2 PLASTICITY IN DUCTILE METALS Ulti
633. uble click Paths In the Create Path dialog box select Edge list as the type and click Continue 2 In the Edit Edge List Path dialog box select the instance corresponding to the top plate and click Add After 3 In the prompt area select by shortest distance as the selection method 12 43 Abaqus Standard 3 D EXAMPLE SHEARING OF A LAP JOINT Figure 12 31 Deformed model shape S Mises Avg 75 9 264e 02 8 499e 02 7 734e 02 6 968e 02 6 203e 02 5 438e 02 4 672e 02 3 907e 02 3 142e 02 2 377e 02 1 611e 02 8 459e 01 8 057e 00 Figure 12 32 Mises stress 4 Inthe viewport select the edge at the left end of the bolt hole as the starting edge of the path and the node at the right end of the bolt hole as the end node of the path as shown in Figure 12 33 12 44 5 Abaqus Standard 3 D EXAMPLE SHEARING OF A LAP JOINT Figure 12 33 Path definition 5 Click Done in the prompt area to indicate that you have finished making selections for the path Click OK to save the path definition and to close the Edit Edge List Path dialog box 6 In the Results Tree double click XYData Select Path in the Create XY Data dialog box and click Continue 7 In the Y Values frame of the XY Data from Path dialog box click Step Frame In the Step Frame dialog box select the last frame of the step Click OK to close the Step Frame dialog box 8 Make sure that the field output variable is set to CPRESS and
634. udes a mixture of general and perturbation steps consider the bow and arrow shown in Figure 11 6 0 0254 m a0 R m l 1 0 in 0 1 in 1 27 m 50 0 in String BON SECTION A A LLII Step 1 Pretension Step 2 Pull Back Step 4 Dynamic Release Figure 11 6 Simple bow and arrow Step 1 might be to string the bow to pretension the bowstring Step 2 would then follow this by pulling back the string with an arrow thus storing more strain energy in the system Step 3 might then be a linear perturbation analysis step an eigenvalue frequency analysis to investigate the natural frequencies of the loaded system Such a step might also have been included between Steps 1 and 2 to find the natural frequencies of the bow and string just after the string is pretensioned but before it is pulled back to shoot Step 4 is then a nonlinear dynamic analysis in which the bowstring is released so that the strain energy that was stored in the system by pulling back the bowstring in Step 2 imparts kinetic energy to the arrow and causes it to leave the bow This step thus continues to develop the nonlinear response of the system but now with dynamic effects included In this case it is obvious that each nonlinear general analysis step must use the state at the end of the previous nonlinear general analysis step as its initial condition For example the dynamic part of the history has no loading the dynamic response is caused by the release of some of th
635. uirements grow rapidly so that in practice the maximum size of an implicit analysis that can be solved on a given machine often is dictated by the amount of disk space and memory available on the machine rather than by the required computation time 9 2 3 Advantages of the explicit time integration method The explicit method is especially well suited to solving high speed dynamic events that require many small increments to obtain a high resolution solution If the duration of the event is short the solution can be obtained efficiently Contact conditions and other extremely discontinuous events are readily formulated in the explicit method and can be enforced on a node by node basis without iteration The nodal accelerations can be adjusted to balance the external and internal forces during contact The most striking feature of the explicit method is the absence of a global tangent stiffness matrix which is required with implicit methods Since the state of the model is advanced explicitly iterations and tolerances are not required 9 5 5 AUTOMATIC TIME INCREMENTATION AND STABILITY 9 3 9 3 9 3 Automatic time incrementation and stability The stability limit dictates the maximum time increment used by the Abaqus Explicit solver Itis a critical factor in the performance of Abaqus Explicit The following sections describe the stability limit and discuss how Abaqus Explicit determines this value Issues surrounding the model de
636. ulation Its origin is placed at the level of the bottom of the plate as shown in Figure 10 39 10 58 EXAMPLE AXISYMMETRIC MOUNT 10 7 3 Mesh design The mesh in this example uses a 30 x 15 mesh of first order axisymmetric hybrid solid elements CAX4H for the rubber mount Only the bottom half of the mount is specified in the model as shown in Figure 10 42 Line of symmetry Rubber i 4 T F EARR a i a a100 Piate Figure 10 42 Mesh for the rubber mount ta _ N 4 Hybrid elements are required in this example because the material is fully incompressible The elements are not expected to be subjected to bending so shear locking in these fully integrated elements should not be a concern Model the steel plates with a single layer of incompatible mode elements CAX4I because it is possible that the plates may bend as the rubber underneath them deforms The node and element numbers from the input file given in Axisymmetric mount Section A 10 are shown in Figure 10 43 and Figure 10 44 These will be used in the discussion of this example If you build the model yourself it will probably have different n
637. ull out force at the attachment points create an X Y plot of the reaction force in the 1 direction variable RF1 at the attached nodes This involves plotting multiple curves at the same time To plot multiple curves 1 In the Results Tree click mouse button 3 on History Output for the output database named dynamics odb From the menu that appears select Filter Inthe filter field enter RF1 to restrict the history output to just the reaction force components in the 1 direction 3 From the list of available history output select the four curves using Ctrl Click that have the following form Reaction Force RF1 PI TRUSS 1 Node xxx in NSET ATTACH 7 19 5 EXAMPLE CARGO CRANE UNDER DYNAMIC LOADING 4 Click mouse button 3 and select Plot from the menu that appears Abaqus Viewer displays the selected curves 5 Click a in the prompt area to cancel the current procedure To position the grid 1 Double click the plot to open the Chart Options dialog box 2 In this dialog box switch to the Grid Area tabbed page 3 In the Size region of this page select the Square option 4 Use the slider to set the size to 75 5 In the Position region of this page select the Auto align option 6 From the available alignment options select the last one position the grid in the lower right corner of the viewport 7 Click Dismiss To position the legend 1 Double click the legend to open the Chart Legen
638. ully integrated second order elements in Abaqus Standard use the hybrid versions which are designed to model incompressible behavior however the additional degrees of freedom in these elements will make the analysis more computationally expensive A family of modified second order triangular and tetrahedral elements is available that provides improved performance over the first order triangular and tetrahedral elements and that avoids some of the problems that exist for conventional second order triangular and tetrahedral elements In particular these elements exhibit minimal shear and volumetric locking These elements are available in addition to fully integrated and hybrid elements in Abaqus Standard they are the only second order continuum solid elements available in Abaqus Explicit 10 4 Example connecting lug with plasticity You have been asked to investigate what happens if the steel connecting lug from Chapter 4 Using Continuum Elements is subjected to an extreme load 60 kN caused by an accident The results from the linear analysis indicate that the lug will yield You need to determine the extent of the plastic deformation in the lug and the magnitude of the plastic strains so that you can assess whether or not the lug will fail You do not need to consider inertial effects in this analysis thus you will use Abaqus Standard to examine the static response of the lug The only inelastic material data available for the steel
639. ure 12 12 Modeling small features on the rigid surface With a sufficiently refined mesh on the deformable surface Abaqus Standard will prevent the rigid surface from penetrating the slave surface e The contact algorithm in Abaqus Standard requires the master surface of a contact pair to be smooth Rigid surfaces are always the master surface and so should always be smoothed Abaqus Standard does not smooth discrete rigid surfaces The level of refinement controls the smoothness of a discrete rigid surface Analytical rigid surfaces can be smoothed using the FILLET RADIUS parameter on the SURFACE option to define a fillet radius that is used to smooth any sharp corners in the rigid surface definition see Figure 12 13 e The rigid surface normal must always point toward the deformable surface with which it will interact If it does not Abaqus Standard will detect severe overclosures at all of the nodes on the deformable surface the simulation will probably terminate due to convergence difficulties The normals for an analytical rigid surface are defined as the directions obtained by the 90 counterclockwise rotation of the vectors from the beginning to the end of each line and circular segment forming the surface see Figure 12 14 12 15 5 Abaqus Standard 2 D EXAMPLE FORMING A CHANNEL ral Sharp corners in a rigid surface Define a fillet radius can cause convergence problems to smooth sharp corners in the analytical rigid surface
640. ure being analyzed You should use a fine mesh mainly in the areas of high stress gradients and use a coarser mesh in areas of low stress gradients or where the magnitude of the stresses is not of interest For example Figure 4 47 shows a mesh that is designed to give an accurate prediction of the stress concentration at the bottom of the hole LA fii x 4 SSS SSX Y N RSS lt s Ser SSX a ONY T y N Ky KS Figure 4 47 Mesh refined around the hole 4 51 5 RELATED Abaqus EXAMPLES A fine mesh is used only in the region of high stress gradients and a coarse mesh is used elsewhere The results from an Abaqus Standard simulation with this locally refined mesh are shown in Table 4 4 This table shows that the results are comparable to those from the very fine mesh but the simulation with the locally refined mesh required considerably less CPU time than the analysis with the very fine mesh Table 4 4 Comparison of very fine and locally refined meshes Displacement of Stress at Relative ae of hole BE of hole a time Very fine fine B SE 4 15E 4 345 E6 E6 a 5 Locally refined 3 14E 4 346 E6 You can often predict the locations of the highly stressed regions of a model and hence the regions where a fine mesh is required using your knowledge of similar components or with hand calculations This information can also be gained by using a coarse mesh initial
641. urface the z direction in this 5 15 5 EXAMPLE SKEW PLATE model as well as an additional rotation zero using this method The following ORIENTATION option block creates the proper local coordinate system named SKEW ORIENTATION NAME SKEW SYSTEM RECTANGULAR 10 0E 2 5 77E 2 0 0 5 77E 2 10 0E 2 0 0 3 0 0 Alternatively you can define exactly the same local coordinate system by choosing point a and point b to lie on the global coordinate 1 and 2 axes and specifying an additional rotation of 30 ORIENTATION NAME SKEW SYSTEM RECTANGULAR Lez Oss Osp Oxy Lez 0a 3 30 Section properties Since the structure is made ofa single material with constant thickness the section properties are the same for all elements Therefore you can use the element set PLATE which includes all elements to assign the physical and material properties to the elements Since you assume that the plate is linear elastic the SHELL GENERAL SECTION option is more efficient than using the SHELL SECTION option The following element property option block defines the section properties for this example SHELL GENERAL SECTION ELSET PLATE MATERIAL MATI1 ORIENTATION SKEW 0 8E 2 The ORIENTATION parameter tells Abaqus to use the local coordinate system named SKEW to define the material directions for the shells in element set PLATE All element variables will be defined in the SKEW coordinate system Material properties The plate is made
642. urface perimeters Mesh seams Two nodes with the same coordinate double nodes can generate a seam or crack in a valid surface that appears to be continuous as shown in Figure 12 41 A node sliding along the surface can fall through this crack and slide behind the contact surface A large nonphysical acceleration correction may be caused once penetration is detected Mesh seams can be detected in Abaqus Viewer by drawing the free edges of the model Any seams that are not part of the desired perimeter can be double noded regions Complete surface definition Figure 12 42 illustrates a two dimensional model of a simple connection between two parts 12 52 MODELING CONSIDERATIONS IN Abaqus Explicit Both nodes have the same coordinates They are separated to show the crack in the surface Figure 12 41 Example of a double noded mesh surface 1 surface 2 these nodes on surface 3 are behind surfaces 1 and 2 CONTACT PAIR SURFACE 1 SURFACE 3 SURFACE 2 SURFACE 3 V Analysis will stop after the first increment with message that elements are badly distorted Figure 12 42 Example of an incorrect surface definition The contact definition shown in the figure is not adequate for modeling this connection because the surfaces do not represent a complete description of the geometry of the bodies At the beginning of 12 53 5 MODELING CONSIDERATIONS IN Abaqus Explicit the analysis some ofthe nodes on surface 3 find
643. urfaces does not change during a perturbation step points that were closed in the base state remain closed and points that were open remain open 11 2 1 Time in linear perturbation steps If another general step follows a perturbation step Abaqus Standard uses the state of the model at the end of the last general step as its starting point not the state of the model at the end of the perturbation step Thus the response from a linear perturbation step has no permanent effect on the simulation Therefore Abaqus Standard does not include the step time of linear perturbation steps in the total time for the analysis In fact what Abaqus Standard actually does is to define the step time of a perturbation step to be very small 10 so that it has no effect when it is added to the total accumulated time The exception to this rule is the MODAL DYNAMIC procedure 11 2 2 Specifying loads in linear perturbation steps Loads and prescribed boundary conditions given in linear perturbation steps are always local to that step The load magnitudes including the magnitudes of prescribed boundary conditions given in a linear perturbation step are always the perturbation increment of the load not the total magnitude Likewise the value of any solution variable is output as the perturbation value only the value of the variable in the base state 1s not included 11 5 5 LINEAR PERTURBATION ANALYSIS As an example of a simple load history that incl
644. ut prior notice No part of this documentation may be reproduced or distributed in any form without prior written permission of Dassault Syst mes or its subsidiary The Abaqus Software is a product of Dassault Systemes Simulia Corp Providence RI USA Dassault Syst mes 2012 Abaqus the 3DS logo SIMULIA CATIA and Unified FEA are trademarks or registered trademarks of Dassault Syst mes or its subsidiaries in the United States and or other countries Other company product and service names may be trademarks or service marks of their respective owners For additional information concerning trademarks copyrights and licenses see the Legal Notices in the Abaqus 6 12 Installation and Licensing Guide SIMULIA Worldwide Headquarters SIMULIA European Headquarters United States Australia Austria Benelux Canada China Finland France Germany India Italy Japan Korea Latin America Scandinavia United Kingdom Argentina Brazil Czech amp Slovak Republics Greece Israel Malaysia Mexico New Zealand Poland Russia Belarus amp Ukraine Singapore South Africa Spain amp Portugal Locations Rising Sun Mills 166 Valley Street Providence RI 02909 2499 Tel 1 401 276 4400 Fax 1 401 276 4408 simulia support 3ds com http www simulia com Stationsplein 8 K 6221 BT Maastricht The Netherlands Tel 31 43 7999 084 Fax 31 43 7999 306 simulia europe info 3ds com Dassault Systemes Centers
645. ution Abaqus Standard obtains should be closer to equilibrium sometimes Abaqus Standard may need many iterations to obtain an equilibrium solution When an equilibrium solution has been obtained the increment is complete Results can be requested only at the end of an increment Abaqus Explicit does not need to iterate to obtain the solution in an increment 8 2 2 Equilibrium iterations and convergence in Abaqus Standard The nonlinear response of a structure to a small load increment AP is shown in Figure 8 9 Abaqus Standard uses the structure s initial stiffness Ko which is based on its configuration at uo and AP to calculate a displacement correction Ca for the structure Using ca the structure s configuration is updated to u4 Load AP Displacement Figure 8 9 First iteration in an increment Convergence Abaqus Standard forms a new stiffness Ka for the structure based on its updated configuration Ua Abaqus Standard also calculates in this updated configuration The difference between the total applied load P and Ia can now be calculated as baad dz where Ra 1s the force residual for the iteration If Ra 1s zero at every degree of freedom in the model point a in Figure 8 9 would lie on the load deflection curve and the structure would be in equilibrium In a nonlinear problem it is almost impossible to have Ra equal zero so Abaqus Standard compares it to a tolerance value If Ra 1s less than
646. ver the lost content To demonstrate the differences between filtering in Abaqus Viewer and filtering in Abaqus Explicit we will filter the acceleration of the bottom chip in Abaqus Viewer and compare the results to the filtered data Abaqus Explicit wrote to the output database To filter acceleration history 1 In the Results Tree select the acceleration A3 history output for the node set BotChip all and save the data as A3 all1 2 In the Results Tree double click XYData then select Operate on XY data in the Create XY Data dialog box Click Continue 3 In the Operate on XY Data dialog box filter A3 a11 with filter options that are equivalent to those applied by the Abaqus Explicit built in anti aliasing filter when the output increment is 0 7 ms Recall that the built in anti aliasing filter is a second order Butterworth filter with a cutoff frequency that 1s one sixth of the output sample rate hence the expression at the top of the dialog box should appear as butterworthFilter xyData A3 all cutoffFrequency 1 6 0 0007 4 Click Plot Expression to plot the filtered acceleration curve 5 In the Results Tree click mouse button 3 on the filtered acceleration A3 ANTIALIASING history output for node set BotChip largeInc and select Add to Plot from the menu that appears If you wish also add the filtered acceleration history for node 403 in the set CHIPS The X Y plot appears in the viewport As before customize t
647. vibrate after the blast load has dropped to zero The maximum displacement occurs at approximately 8 ms and a displaced plot of that state is shown in Figure 10 27 The animation images can be saved to a file for playback at a later time To save the animation 1 From the main menu bar select Animate Save As The Save Image Animation dialog box appears 2 In the Settings field enter the file name blast base The format of the animation can be specified as AVI QuickTime VRML or Compressed VRML 10 40 EXAMPLE BLAST LOADING ON A STIFFENED PLATE Figure 10 26 Plate with shell thickness displayed Figure 10 27 Displaced shape at 8 ms 3 Choose the QuickTime format and click OK The animation is saved as blast base mov in your current directory Once saved your animation can be played external to Abaqus Viewer using industry standard animation software History output Since it is not easy to see the deformation of the plate from the deformed plot it is desirable to view the deflection response of the central node in the form of a graph The displacement of the node in the center of the plate is of particular interest since the largest deflection occurs at this node Display the displacement history of the central node as shown in Figure 10 28 with displacements in millimeters 10 41 5 EXAMPLE BLAST LOADING ON A STIFFENED PLATE 50 00 40 00 30 00 Displacement mm 20 00 10 00 0 00
648. w input file HEADING Increase tensile load on the piping system 11 19 5 EXAMPLE RESTARTING THE PIPE VIBRATION ANALYSIS and determine lowest frequency RESTART READ Neither the INCREMENT nor the STEP parameter is included on the RESTART READ option since by default Abaqus will read the data for the last increment written to the restart file Since you are continuing the simulation from the end of the previous analysis no parameters are needed 11 5 2 Reviewing the input file the history data The history data consist of two steps Apply a tensile load 8 MN to the pipe section in Step 3 The following option block must be placed in Step 3 CLOAD RIGHT 1 8 0E6 Set the initial time increment in Step 3 to 1 10 the total step time which should be 1 0 Step 4 is an exact copy of Step 2 from the previous analysis All of the load history option blocks necessary to define this restart analysis are shown below STEP NLGEOM YES Apply 8 MN axial tensile load STATIC 0 1 1 CLOAD RIGHT 1 8 0E6 RESTART WRITE FREQUENCY 10 OUTPUT FIELD FREQUENCY 10 VARIABLE PRESELECT OUTPUT HISTORY ELEMENT OUTPUT ELSET ELEMENT25 S SINV END STEP STEP PERTURBATION Extract modes and frequencies FREQUENCY 8 RESTART WRITE OUTPUT FIELD VARIABLE PRESELECT END STEP The complete input file for this restart analysis is listed in Vibration of a piping system Section A 12 11 20 EX
649. wave propagating through the mesh This example sets the parameter VARIABLE PRESELECT on the OUTPUT FIELD option to write the default field data fora DYNAMIC EXPLICIT procedure to the output database file In addition stress S history output in element set EOUT is requested for every increment OUTPUT FIELD VARIABLE PRESELECT NUMBER INTERVAL 4 OUTPUT HISTORY FREQUENCY 1 ELEMENT OUTPUT ELSET EOUT S END STEP 9 4 4 Running the analysis After storing your input in a file called wave _ 50x10x10 inp run the analysis using the following command abaqus job wave 50x10x10 If your analysis does not complete check the data file wave _ 50x10x10 dat and status file wave 50x10x10 sta for error messages Modify your input file to remove the errors If you still have trouble running your analysis compare your input file to the one given in Stress wave propagation in a bar Section A 7 Status file The status file wave 50x10x10 sta contains information about moments of inertia followed by information concerning the initial stability limit The 10 elements with the lowest stable time limits are listed in rank order Most critical elements Element number Rank Time increment Increment ratio 1 1 1 819458E 06 1 000000E 00 19 2 1 819458E 06 1 000000E 00 201 3 1 819458E 06 1 000000E 00 219 4 1 819458E 06 1 000000E 00 301 5 1 819458E 06 1 000000E 00 319 6 1 819458E 06 1 000000E 00 501 7 1 819458E 06 1 000000E 00 5
650. wever to practice using the above methods to manipulate your views as you deem fit To specify the view 1 From the main menu bar select View Specify or double click the 3D compass The Specify View dialog box appears 4 24 EXAMPLE CONNECTING LUG 3 Incremen t 1 Step Time 2 2200E 16 Deformed Var U Deformation Scale Factor 2 968e 01 Figure 4 24 Deformed model shape of connecting lug shaded 2 From the list of available methods select Viewpoint In the Viewpoint method you enter three values representing the X Y and Z position of an observer You can also specify an up vector Abaqus positions your model so that this vector points upward 3 Enter the X Y and Z coordinates of the viewpoint vector as 1 1 3 and the coordinates of the up vector as 0 1 0O 4 Click OK Abaqus Viewer displays your model in the specified view as shown in Figure 4 25 2 ncremen 1 Step Time 2 2200E 16 Deformed Var U Deformation Scale Factor 2 968e 01 Figure 4 25 Deformed model shape viewed from specified viewpoint 4 25 5 EXAMPLE CONNECTING LUG Visible edges Several options are available for choosing which edges will be visible in the model display The previous plots show all exterior edges of the model Figure 4 26 displays only feature edges 2 ncremen 1 Step Time 2 2200E 16 Deformed Var U Deformation Scale Factor 2 968e 01 Figure 4 26 Deformed shape with only f
651. wing provides the interested user with additional references on material modeling General texts on materials e Ashby M F and D R H Jones Engineering Materials Pergamon Press 1980 e Callister W D Materials Science amp Engineering An Introduction John Wiley 1994 e Pascoe K J An Introduction to the Properties of Engineering Materials Van Nostrand 1978 Plasticity e SIMULIA Metal Inelasticity in Abaqus e Lubliner J Plasticity Theory Macmillan Publishing Co 1990 e Calladine C R Engineering Plasticity Pergamon Press 1969 Rubber elasticity e SIMULIA Modeling Rubber and Viscoelasticity with Abaqus e Gent A Engineering with Rubber How to Design Rubber Components Hanser Publishers 1992 10 12 Summary e Abaqus contains an extensive library to model the behavior of various engineering materials It includes models for metal plasticity and rubber elasticity e The stress strain data for the metal plasticity model must be defined in terms of true stress and true plastic strain e The metal plasticity model in Abaqus assumes incompressible plastic behavior e For efficiency Abaqus Explicit regularizes user defined material curves by fitting them with curves composed of equally spaced points e The hyperelastic material model in Abaqus Standard allows true incompressibility The hyperelastic material model in Abaqus Explicit does not the default Poisson s ratio for hyperelastic materials in Ab
652. wn in Figure 8 6 Undeformed shape Load As the panel snaps through the stiffness becomes negative Positive stiffness is regained once the panel Applied pressure snaps through Initial stiffness ee all Deflection Snapped through shape Figure 8 6 Snap through of a large shallow panel In this example there is a dramatic change in the stiffness of the panel as it deforms As the panel snaps through the stiffness becomes negative Thus although the magnitude of the displacements relative to the panel s dimensions is quite small there is significant geometric nonlinearity in the simulation which must be taken into consideration An important difference between the analysis products should be noted here by default Abaqus Standard assumes small deformations while Abaqus Explicit assumes large deformations 8 2 The solution of nonlinear problems The nonlinear load displacement curve for a structure is shown in Figure 8 7 The objective of the analysis is to determine this response Consider the external forces P and the internal nodal forces I acting on a body see Figure 8 8 a and Figure 8 8 b respectively The internal loads acting on a node are caused by the stresses in the elements that contain that node For the body to be in static equilibrium the net force acting at every node must be zero Therefore the basic statement of static equilibrium is that the inte
653. would complete the analysis as originally defined HEADING Restart of interrupted run RESTART READ STEP lt step gt INC lt increment gt Continuing with additional steps If the previous analysis completed successfully and having viewed the results you want to add additional steps to the load history the specified step and increment should be the last step and last increment of the previous analysis Alternatively they can be omitted and by default Abaqus will read the last available data in the restart file The RESTART option is followed by any new step definitions HEADING Add new step data RESTART READ STEP lt lJast step gt INC lt l ast increment gt STEP new Step definition END STEP Changing an analysis Sometimes having viewed the results of the previous analysis you may want to restart the analysis from an intermediate point and change the remaining load history data in some manner for example to add more output requests to change the loading or to adjust the analysis controls Often this is necessary when a step has exceeded its maximum number of increments If the analysis is restarted as described above Abaqus thinks that the analysis is partway through a step tries to complete the step and promptly exceeds the maximum number of increments again In such situations the END STEP parameter should be included on the RESTART option to indicate that the current step should be terminated at the
654. written to the report file If the difference is large enough to be of concern this is an indication that the mesh may be too coarse The table listing the reaction forces at the constrained nodes is shown below The Total entry at the bottom of the table contains the net reaction force components for this group of nodes The results confirm that the total reaction force in the 2 direction at the constrained nodes is equal and opposite to the applied load of 30 KN in that direction Field Output Report Source 1 ODB lug odb Step Step 1 Frame Increment 1 Step Time 2 2200E 16 Loc 1 Nodal values from source 1 Output sorted by column Node Label Field Output reported at nodes for part PART 1 1 Node RF RF1 RF RF2 RF RF3 Label Loc 1 Loc 1 Loc 1 3241 872 912 765 17 936 541 3243 10 7924E 03 139 598 2 69241E 03 3245 2 5436E 03 29 2367 636 668 3247 3 47143E 03 248 065 879 401 3249 124 431E 03 366 58 94 6864E 03 23249 124 431E 03 366 58 94 6864E 03 23251 3 47251E 03 247 215 879 699 23253 2 54332E 03 29 3956 636 906 23255 10 7918E 03 139 991 2 69226E 03 23257 873 161 765 137 936 363 Minimum 18 4323E 03 470 038 2 69241E 03 At Node 13243 13249 3243 4 39 5 EXAMPLE CONNECTING LUG Maximum 18 431E 03 3 3654E 03 2 69241E 03 At Node 13255 8241 23243 Total 600 502E 06 30 0000E 03 454 747E 12 The table showing the displacements of the nodes along the bottom of the hole listed below indicates that the b
655. xample the form of this option is SELECT EIGENMODES GENERATE 1 30 1 Loading Apply the concentrated force to the tip of the crane at node 104 in the negative global 2 direction The EQUATION constraint between nodes 104 and 204 in degree of freedom 2 means that the load will be carried equally by both nodes and thus by both halves of the crane The concentrated force is defined using the CLOAD option This example uses the parameter AMPLITUDE BOUNCE to indicate that the amplitude curve named BOUNCE previously defined as part of the model data should be used to define the time varying magnitude of the load during the step CLOAD AMPLITUDE BOUNCE 104 2 1 0E4 The actual magnitude of the load applied at any point in time is obtained by multiplying the magnitude given on the CLOAD option 10 000 N and the value of the BOUNCE amplitude curve at that time Boundary conditions The same boundary conditions that were applied in Step 1 are still in effect for this step Since the boundary conditions cannot be changed between a FREQUENCY step and any subsequent modal dynamic steps no boundary conditions should be specified Output Dynamic analyses usually require many more increments than static analyses to complete As a consequence the volume of output from dynamic analyses can be very large and you should control the output requests to keep the output files to a reasonable size You can estimate the size of the restar
656. xpanding to 15 equally spaced points with increments of 0 025 To illustrate the error message that is produced when Abaqus Explicit cannot regularize the material data try setting the regularization tolerance RTOL to 0 001 and include one additional data pair as shown below MATERIAL NAME STEEL RTOL 0 001 ELASTIC 210 0E9 a3 PLASTIC 300 0E6 0 0 349 0E6 0 001 lt additional data pair 350 0EFE6 0 025 375 0E6 0 10 394 0E6 0 20 400 0EFE6 0 35 10 34 EXAMPLE BLAST LOADING ON A STIFFENED PLATE The combination of the low tolerance value RTOL 0 001 and the small interval in the user defined data leads to difficulty in regularizing this material definition The following error message 1s produced in the status sta file ERROR Failed to regularize material data Please check your input data to see if they meet both criteria as explained in the MATERIAL DEFINITION section of the Abaqus Analysis User s Manual In general regularization is more difficult if the smallest interval defined by the user is small compared to the range of the independent variable Before continuing set the regularization tolerance back to the default value 0 03 and remove the additional pair of data points Boundary conditions The edges of the plate are fully constrained using the node set EDGE defined previously BOUNDARY EDGE ENCASTRE Alternatively you could specify the degrees of freedom by number BOUNDAR
657. y A a N 4 y Ki A w 4 y Nee x Figure 5 17 Plot of material orientation directions in the plate Evaluating results based on tabular data As noted previously a convenient alternative to writing printed data to the data dat file is to generate a tabular report using Abaqus Viewer With the aid of display groups create a tabular data report of the whole model element stresses Components 11 S22 and 12 the reaction forces and moments at the supported nodes sets ENDA and ENDB and the displacements of the midspan nodes set MIDSPAN The stress data are shown below Field Output Report ODB skew odb Step Step 1 Frame Increment 1 Step Time 2 2200E 16 1 0 1 0 Loc 1 Integration point values at shell general SNEG fraction Loc 2 Integration point values at shell general SPOS fraction Output sorted by column Element Label Field Output reported at integration points for part PLATE 1 5 26 EXAMPLE SKEW PLATE Element Int S S11 S S11 S S22 S S22 S S12 S S12 Label Pt Loc 1 Loc 2 Loc 1 Loc 2 Loc 1 Loc 2 1 1 42 7593E 06 42 7593E 06 9 30515E 06 9 30515E 06 6 75836E 06 6 75836E 06 1 2 74 7242E 06 74 7242E 06 2 78322E 06 2 78322E 06 10 5987E 06 10 5987E 06 1 3 73 2731E 06 73 2731E 06 28 832E 06 28 832E 06 21 4032E 06 21 4032E 06 1 4 82 8849E 06 82 8849E 06 18 9513E 06 18 9513E 06 14 7861E 06 14 7861E 06 114 1 82 8849E 06 82 8849E 06 18 9513E 06 18 9513E 06 1
658. y a 90 counterclockwise rotation from the direction going from node 1 to node 2 For three dimensional shell elements the positive normal is given by the right hand rule going around the nodes in the order in which they appear in the element definition The top surface ofa shell is the surface in the positive normal direction and is called the SPOS face for contact definition The bottom surface is in the negative direction along the normal and is called the SNEG face for contact definition Normals should be consistent among adjoining shell elements The positive normal direction defines the convention for element based pressure load application and output of quantities that vary through the shell thickness A positive element based pressure load applied to a shell element produces a load that acts in the direction of the positive normal The element based pressure load convention for shell elements is opposite to that for continuum elements the surface based pressure load conventions for shell and continuum elements are identical For more on the difference between element based and surface based distributed loads see Distributed loads Section 33 4 3 of the Abaqus Analysis User s Manual 5 3 ELEMENT GEOMETRY 5 1 3 Initial shell curvature Shells in Abaqus with the exception of element types S3 S3R S3RS S4R S4RS S4RSW and STRI3 are formulated as true curved shell elements true curved shell elements require speci
659. y of a particular analysis Some general guidelines for selecting continuum elements are also given These provide the foundation upon which you can build your knowledge as you gain more experience using Abaqus The example at the end of this section will allow you to put this knowledge to use as you build and analyze a connecting lug Element formulation and integration The influence that the order of the element linear or quadratic the element formulation and the level of integration have on the accuracy of a structural simulation will be demonstrated by considering a static analysis of the cantilever beam shown in Figure 4 1 5 ELEMENT FORMULATION AND INTEGRATION es Figure 4 1 Cantilever beam under a point load P at its free end This is a classic test used to assess the behavior of a given finite element Since the beam is relatively slender we would normally model it with beam elements However it is used here to help assess the effectiveness of various solid elements The beam is 150 mm long 2 5 mm wide and 5 mm deep built in at one end and carrying a tip load of 5 N at the free end The material has a Young s modulus E of 70 GPa and a Poisson s ratio of 0 0 Using beam theory the static deflection of the tip of the beam for a load P is given as Pre tip a7 3h1 where J bd 12 lis the length b is the width and dis the depth of the beam For P 5 N the tip deflection is 3 09 mm 4 1 1 Full integratio
660. y punch stroke STATIC 05 1 0 CONTACT CONTROLS MASTER PUNCH SLAVE BLANK T STABILIZE 0 001 BOUNDARY REFPUNCH 2 2 0 030 END STEP Running the analysis Save the input in the file channel inp see Forming a channel with Abaqus Standard Section A 13 abaqus job channel Check the status and message files while the job is running to see how it is progressing Status file This analysis should take approximately 180 increments to complete The top of the status file is shown below SUMMARY OF JOB INFORMATION STEP NNNNNNPPPPPPEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC OF DOF IF DISCON ITERS ITERS TIME TIME LPF TIME LPF MONITOR RIKS ITERS FREQ 1 1 4 0 4 0 0500 0 0500 0 05000 2 1 2 0 2 0 100 0 100 0 05000 3 1 2 0 2 0 175 0 175 0 07500 4 1 2 0 2 0 288 0 288 0 1125 5 1 3 0 3 0 456 0 456 0 1688 6 1 2 0 2 0 709 0 709 0 2531 7 1 2 0 2 1 00 1 00 0 2906 1 1U 2 1 3 1 00 0 000 0 05000 1 2U 4 0 4 1 00 0 000 0 01250 1 3 29 0 29 1 00 0 00313 0 003125 2 1 5 0 5 1 01 0 00547 0 002344 3 1 6 0 6 1 01 0 00781 0 002344 4 1 9 0 9 1 01 0 0113 0 003516 Abaqus has a difficult time determining the contact state in the first increment of Step 2 It needs three attempts before it finds the proper configuration of the PUNCH and BLANK T surfaces and achieves equilibrium After this difficult start Abaqus quickly increases the increment size to a more reasonable value The end of the status file is shown below
661. your model may be different from those shown here 6 15 5 EXAMPLE CARGO CRANE 6 4 3 Preprocessing creating the model The full input file for this example is crane inp and it is available in Cargo crane Section A 4 The Abaqus input options used to create the nodes and elements shown on the preceding pages can be found in Cargo crane Section A 4 If you wish to create the entire model using Abaqus CAE refer to Example cargo crane Section 6 4 of Getting Started with Abaqus Interactive Edition 6 4 4 Reviewing the input file the model data This section describes how the model data are described in the input file for this example These data include the descriptions for the input file heading its nodes and elements beam sections and orientations constraints and boundary conditions Heading The heading used in this example provides a short description of the model and the units used HEADING 3 D model of light service cargo crane S I Units m kg N sec Nodal coordinates and element connectivity Define the nodal coordinates in a NODE option block If you decide to do this with an editor you may want to use the mesh generation commands found in Cargo crane Section A 4 In this example a node set called ATTACH is created this node set contains the nodes at points A B C and D the points at which the crane is attached to the parent structure NSET NSET ATTACH 100 107 200 207
662. ysis in Abaqus Explicit for comparison This time we are interested in the dynamic response of the hoist to the same load applied suddenly at the midspan Before continuing save a copy of frame inp as frame xpl inp Make all subsequent changes to the frame xpl inp input file You will need to replace the static step with an explicit dynamic step modify the output requests and the material definition and change the element library before you can resubmit the job Modifying the material definition Since Abaqus Explicit performs a dynamic analysis a complete material definition requires that you specify the material density For this problem assume the density is equal to 7800 kg m You can modify the material definition by adding the DENSITY option to the material option block The form of this option is as follows DENSITY lt p gt Thus the complete material definition for the hoist members is MATERIAL NAME STEEL ELASTIC 200 E9 0 3 DENSITY 7800 Replacing the analysis step The step definition must change to reflect a dynamic explicit analysis Locate the existing STEP option block which appears as follows 2 37 5 EXAMPLE CREATING A MODEL OF AN OVERHEAD HOIST STEP PERTURBATION 10kN central load Replace this option block with the following one STEP 10kN central load suddenly applied The analysis procedure the type of simulation must be defined immediately following the STEP option block I

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