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User Manual - LS-OPT Support Site

1. clean bat in Windows in the directory containing the database This clean file must be set to be executable and can contain lines such as rm rf d3hsp scr00 LS TaSC will execute this clean script in every directory where LS DYNA ran successfully You can also use the advanced options capability see section 4 3 9 to read results from the d3part database instead 4 3 Setting up the Problem The GUI consists of a number of panels Complete the panels from top to bottom as described in the following subsections 4 3 1 The Toplevel GUI The toplevel GUI contains the LS TaSC tool as shown in Figure 4 1 The toolbar associated with the LS TaSC tool is also shown The feature tree contains all the items in the currently open LS TaSC database such as parts Feature Tree Tool bar anje tn Beaded Goom wih ze3 c Foz dere Figure 4 1 The toplevel GUI 26 4 3 2 The Cases Panel The cases panel contains all of the load cases to be analyzed using LS DYNA See the following table and Figure 4 2 for more details Cases data Name Execution Command Input File Weight Number of jobs Queue system Each case is identified with a unique name e g TRUCK The same name would be used to create a directory to store all simulation data The complete solver command or script e g complete path of LS DYNA executable is specified The LS DYNA input deck path is provided The weight assoc
2. OptDesign lt iteration_no gt k OptDesign lt iteration_no gt k 1 1 d3plot log lt process_id gt log lt proc_no gt Figure 4 14 Directory structure 4 6 Opening and Saving Projects The standard File pulldown is provides the ability to open and save projects The name of the database can also be specified on the command line when staring the GUI as stasc Ist project lstasc 4 7 Restart The program always attempts to restart from the existing results To prevent a restart you have to delete the previous run directories and the LS TaSC runtime databases use the Clear Results button on the run panel Do not delete any files if a restart is required unless you suspect the file has been corrupted If a larger number of LS TaSC iterations are desired then it can be restarted from the last iteration Simply set the number of iterations higher and run the LS TaSC job The successfully completed iterations will not be rerun If the LS TaSC job has been interrupted then it can be restarted using the same procedure Simply rerun the LS TaSC job in the same directory 41 You can add certain minor edits to the LS DYNA input deck between restarts Say the optimization stops at iteration 12 due to a convergence problem If you modify the input and restart then it should resume LS DYNA analysis at iteration 12 after reading the results for the previous iterations This will work for minor model changes like contact definitions
3. LEFT NODOUT L LEFT Weight 130 MID NODOUT_M MID Weight 4 1204 a 11 I 5 1004 2 2 90 E ae 804 1 704 T 20 40 20 40 Iteration Iteration Multiple histories Multiple histories Figure 5 21 Constraint convergence history for multiple load case example using dynamic weighing is shown on the left Note the improvement with respect to not using dynamic weighing The corresponding weight factors are shown on the right Multiple histories l Mass_Redistribution P101_ElFrac P101_MassFrac O 0 0 4 0 2 20 40 Iteration Figure 5 22 Various histories of the load case weight for multiple load case example using dynamic weighing mass redistribution the fraction of elements kept and the mass fraction The evolution of the topology under multiple loading conditions is shown in Figure 5 23 The final structure evolved in a tabular structure with the two cross members as legs The structure had more material in the center section due to the high importance assigned to the center weight There were many cavities in the structure such that the final structure could be considered equivalent to a truss like structure as one would expect LS DYNA USER INPUT y Contours of MIDA 1Ast_VariableFraction k Fringe Levels min 0 at elem 1001923 1 000e 00 max 0 375 at elem 1034396 O Nu 3 000e 01 8 000e 01 7 000e 01
4. 6 000e 01 5 000e 01 4 000e 01 Figure 5 23 Evolution of the geometry for multiple load case structure using dynamic scaling of the weights The design is improved with respect to not using dynamic weighing by strengthening the portion of the structure carrying the center load 57 5 7 Surface Design of a Beam This example demonstrates 1 Free surface design for solids 2 Geometry constraints for free surface design 5 7 1 Problem Definition The geometry and loading conditions for the example are shown in Figure 5 24 Figure 5 24 Beam model for free surface design 5 7 2 Results with four surfaces All four sides of the beam were selected for shape design The convergence tolerance for this example is a 5096 smoothing The problem converged in 8 iterations 58 LS DYNA keyword deck by LS PrePost Time 1 Fringe Levels Contours of Effective Stress v m 1 000e 02 min 3 06253 at elem 1593 max 54 5524 at elem 1252 9 031e 01 8 061e 01 7 092e 01 6 123e 01 5 153e 01 4 184e 01 3 214e 01 2 245e 01 1 276e 01 3 063e 00 1 Figure 5 25 Final design for four surfaces back Smoothing 0 bottom_surf Smoothing front Smoothing top_surf Smoothing 0 4 0 2 Multiple histories 0 1 Iteration Figure 5 26 Convergence history 59 5 7 3 Results with extrusion and symmetry geometry definitions The front and back side of the beam were selected for shape design The convergence toleran
5. A e Raa a a A A a oca T a aM 6 Table f COMES y E e o tl e E a 7 TED A inanis ei aani eee eh T A EE DA ake 10 1 1 Classification of Structural Optimization Techniques esses 10 1 1 1 Topology Optimization vita iia 10 1 1 2 Topometry Optimization entierement ee tot eide s Used sese d eo derit ena 10 1 1 3 Size CUMIN AU OM RE CET TER 10 1 1 4 Shape punt 7 atl Oi os 10 1 2 Bref OVerviQw uus rU id 11 1 3 Topology Optimization Method in LS TaSC esee 11 LE Finding Information tit p Can deeds editi oe e eei A A qus 12 Oe ioi MATE PT es nuns 12 Za Topology Optimization ce oues o DR REM e gens NOM UN ENSIS SS QNSESU t VM S ERSTER EAE ria 14 2 1 The Design Parts sesion dis 14 2 IDGSI GI OT SOUS xcu tau E tete tat uvae ttd ess 14 Z1 Desenot SES A A 14 2 1 3 El ment DY POS Larva XV AREA TT GPS A de Gia 15 2 1 4 NIsteriabd3E uite ca bacca A A dnce 15 2 2 Geometry and Manufacturing Definitions essere 15 DoS E 17 24o Design AA sete aai ues Bie aca feo 17 2 4 1 Mapping Elements to the Design Variables ooonononnnnccnnoncccnoncninnnncinnnnnos 17 242 Filtering or Results so 17 2 4 3 Initialization Deletion and Regeneration of the Design Variables 18 2 5 LS DYNA Modeling Specifics eerte 18 2 5 1 The Contact DS MAIO ta dica 18 29 2 Part Dent A E M oU MC 19 2 5 3 P rt Set Der lobe 2 6 emu a dia E NA 19 2 5 4 Elem
6. Default Neighbor radius Default Geometry definitions Name Definition Symmetryl Symmetry about x y plane in global coordinate system Symmetry2 Symmetry about y z plane in global coordinate system AQ a Castingl Two way casting along z axis in global coordinate system ivi Im on Be lt i ui X cancel ok Figure 4 6 The panel to create part and geometry 4 3 5 The Surface Panel The shape definition panel contains information about the surfaces to be designed such as the geometry It is similar in function and layout to the parts panel shown in Figure 4 5 Surface data Segment ID Objective Target value Neighbor Radius The ID of the solid surface that must redesigned The objective for the redesign of the surface One of Match average will smooth out the surface stress by considering the average stress over the surface Minimum stress will use the minimum stress on the surface as a target Minimum volume will use the maximum stress on the surface as a target For Match target the target value must be specified If the objective is set to a target value then the target value must be specified using this parameter Otherwise this value will be ignored All nodes within a sphere of radius of this value are considered the neighbors of a node The design variable at a node is updated using the result at the node averaged together with that of its neighbors The d
7. but not for major changes to nodes and elements of design part like re meshing The st binout file is used for the restart if it exists but it can be corrupted It contains 1 the values of the design variables computed and ii results stored for plotting such as histories and constraint values It is safe to delete the file The values will be extracted again from the d3plot files and the design variables computed So the restart will be done without rerunning LS DYNA The restart will take longer though specifically if the advanced options are set not to store filters in memory An LS DYNA job will be restarted for a specific iteration if the finished file in the run directory is deleted or missing for this iteration You cannot use restart to change the bound on a constraint This will change the designs computed and analyzed In this case begin in a clean directory You can add a constraint with neither a lower bound nor an upper bound and use restart to extract the constraint values purely for monitoring because this does not affect the design computed Restart can be used to write out the lt SOLVER_NAME gt OptDesign lt iteration gt k file at an earlier iteration 4 8 Script Commands The script commands issued to create the database can be viewed from the View pulldown menu Use these commands as a template for scripts 42 5 EXAMPLE PROBLEMS The application of the topology code is demonstrated with the help of a
8. DYNA MPP version and hence using a script named submit pbs for the PBS queuing system 5 1 3 Output The output of the code is written in the file named Ist_output txt The error and warning messages are echoed in Ist error and Ist Warning files respectively The typical output in the Ist output txt is ls dyna analysis time 161s it 1 total IED 9 933e 03 Mf 0 250 ls dyna analysis time 177s rt 2 total IED 9 495e 03 Mf 0 250 dX 0 074627 target 0 001 ls dyna analysis time 183s xt 3 total IED 8 983e 03 Mf 0 250 dX 0 077542 target 0 001 ls dyna analysis time 187s it 4 total IED 9 252e 03 Mf 0 250 dX 0 072176 target 0 001 ls dyna analysis time 193s i 5 total IED 9 156e 03 Mf 0 250 dX 0 063345 target 0 001 ls dyna analysis time 193s a Convergence History The convergence is quantified using the change in topology characterized by the normalized density redistribution and the total internal energy density as shown in Figure 5 2 Density_Redistribution 20 40 Iteration Figure 5 2 Convergence history of the mass redistribution The simulation converged after 57 iterations It was observed that initially there were significant changes in the topology upto 30 iterations Afterwards small changes were made in the topology There was a drop in the total internal energy density during the early phase of the optimization but it increased dur
9. Fraction Material utilization The value of the design variable for the element The extent to which the material in the element is used in the application These are the values actually used in the redesign and consider multiple load cases and geometry definitions such symmetry The value is high for parts of the structure heavily used and low for structural elements not useful in the application This information is only 39 Solid density Solid IED Shell IED Shell thickness available after the design has been analyzed using LS Dyna The material density in a solid element This is related to the Variable Fraction field The Internal Energy Density for solid elements This is related to the material utilization The Internal Energy Density for shell elements This is related to the material utilization The shell thicknesses This is related to the Variable Fraction field a willem on dellwr File Edit View Terminal Tabs Help 1 willem staff 45360 1 willem staff 150936 srwxr xr x 1 willem staff 0 willem l willem TOPO EXAMPLES SM willem_1 willem TOPO EXAMPLES S willem_1 willem TOPO EXAMPLES S willem 1 willem TOPO EXAMPLES SM lst binout lst inp nexti lst errors txt lst mat k willem 1 willem TOPO EXAMPLES SM willem 1 willem TOPO EXAMPLES S Ele View Plot Info Cases Problem Method Run View Y Topology histories Matrix size Density Redistribution 2 T
10. Mostly oscillations indicate that there is more than one possible optimal solution One fix is to reduce the move limit on the design variables using the advanced settings 6 7 LS PREPOST You may need to install another version of LS PREPOST into the LS TaSC installation directory Please follow the instructions on the LS PREPOST web site The name of the executable must be sprepost Do not use a symbolic link You may need to investigate the latest version of LS Prepost 2 4 and 3 1 6 8 Casting definitions Using the Advanced Options in the File pull down menu you can set a debug flag which will dump a definition of the faces to a file for display in LS PREPOST 6 9 Mysterious Error when after calling LS DYNA and or Errors involving the LSOPT Environment Variable Make sure the queuing is set correctly Specifying the use of a queuing system when none is available may cause i mysterious errors or ii the LS DYNA execution not to return after finishing Make sure the LSOPT environment variable is not set 65 66 7 OTHER LS TASC MANUALS The functioning of LS TaSC is described in a number of manuals The standard user will only be interested in the users s manual The more advanced topic are therefore supplied as separate manuals to keep the size of this manual down to what the normal user will require 7 1 Theory manual The theory manual is available in the same location as your LS TaSC executable 7 2 Scripting m
11. Neighbor Radius Minimum variable fraction All elements within a sphere of radius of this value are considered the neighbors of an element The design variable at an element is updated using the result at the element averaged together with that of its neighbors Smaller values of this parameter yield finer grained structures The default value depends on the average element size If the design variable value associated with and elements is too small then that element is deleted to preserve the stability of the model An appropriate value 0 05 x 0 95 is supplied here The default is 0 05 for non linear problems and 0 001 for linear problems 3l 102 TOPO mass fraction 0 3 E a l Say d 9 mass fraction 0 2 AAS ee E Constrain Post uo Weight OK Accept New Edit Delete Done 35 Run ew Design part ID 102 v Mass fraction between 0 0 and 1 0 e w Minimum variable fraction for deleting element Default Neighbor radius Default Geometry definitions Name Definition Extrusionl Extrusion using set 1 Castingl One way casting along negative y axis in global coordinate system 1 t H 2 ASS q 4 uj Cancel OK daGeo ShaGeo WirGeo ShfCtr Clear AutCen Zoln ZoOut PicCen vcr Top Figure 4 5 The parts panel 32 Design part ID 10 Edit Part x Mass fraction between 0 0 and 1 0 10 3 Minimum variable fraction for deleting element
12. Satisfying the global constraints is actually a search for the mass of the structure If the displacements are too large then mass are added to the structure to increase the stiffness If the reaction forces are too large then mass is removed from the structure to reduce the force Multiple global constraints may be specified If the constraints are in conflict then a trade off is done and a design is selected resulting in the minimum violation of any given constraint The global constraint handling considers only active constraints If none of global constraints is active anymore then the algorithm will slowly return to the user specified mass fraction Other user defined responses can be defined by specifying a string The only allowable commands are the D3PlotResponse and BinoutResponse commands as defined in the LS OPT manual Use LS OPT to create these strings Local effects such as stress concentrations are not handled by this algorithm 2 7 Dynamic Load Cases Weighing It may happen that a single load case dominates the topology of the final design making the structure perform badly for the other load cases This can be resolved by assigning different weights to the load cases but it is difficult to know good weighing values in advance Dynamic weighing of the load cases is used to select the load case weights based on the responses of the structure as the design evolves thereby resulting in a design that performs well for all
13. by the user through the mass fraction parameter Each solid element is controlled by changing the amount of material in the element This is achieved by assigning a design variable to the density of each element The design variable x also known as relative density varies from O to 1 where 0 indicates void and 1 represents the full material The upper bound on the design variable is 1 while elements with design variable value less than a user defined minimum value 0 05 for dynamic problems and 0 001 for linear are deleted to improve numerical stability In this approach the design variable is linked to a material with the desired density The material properties are obtained using an appropriate interpolation model as described in the theoretical manual The final design variable value for each element will be driven to full use of the element the maximum value of 1 or deletion of the element values below the user defined minimum using the SIMP algorithm described in the theoretical manual The use of the SIMP algorithm can however be de activated using the advanced options described later in this chapter in which case the design variables will have intermediate values selected to achieve a uniform internal energy density in the part 2 1 2 Design of Shells For shells the thicknesses are changed to achieve a uniform internal energy density in the part The upper bound on the design variables is the original shell thicknesses while el
14. field value A value larger than 1 indicates that an element is highly used while a value smaller than 1 indicates that an element is lightly used e Existing Ist_output txt files will be copied to a new name instead of being appended to if the environment variable LSTASC SEPARATE OUTPUT is set Many thanks are due to Luo Liangfeng who did the integration with LS PrePost and the latest GUI development Luo had to master many topics in order to achieve this At the Livermore office thanks are due to Philip Ho for managerial inputs regarding the LS PrePost integration and to Yanhua Zhao for overseeing a smooth interaction with the China office Valuable feedback from customers and co workers is also acknowledged Willem Roux Livermore CA July 2013 PREFACE TO VERSION 2 1 Version 2 1 started in spring of 2011 is a refinement of version 2 It contains the following major new features Dynamic load case weighting This algorithm obtains a design equally relevant for all design load cases Forging geometry definition This geometry definition is similar to a two sided casting except that a forging thickness is introduced New minor features are Castings can have interior holes Pentahedral elements are supported The memory footprint is reduced more than a factor of 2 and an option is provided which can be set to reduce memory use by a further factor of 2 MAT ELASTIC is supported for the design part Lightly used elements
15. finalized the configuration of the system but improvements are sought by changing the thickness of members of the structure on a part basis instead of an element by element basis as done for topometry optimization There is usually no need to re mesh the geometry This class of optimization problems is the most amenable to meta model based optimization The LS OPT program should be used for this instead of this program 1 1 4 Shape Optimization Shape optimization further expands the scope of design domain by allowing changes in the geometry of the structure for example the radius of a hole While there is more freedom to explore the design space the complexity of optimization increases due to the possible need to mesh different candidate optimum designs We distinguish between two methods of doing shape design using free surface shape design and using parameters Firstly you can do free surfaces shape design as with this program This approach is very easy to use but has the drawback of not being very general Secondly you can do shape design using parameters such the radius of a hole or shape vector magnitude This is a very general approach able to consider all crash specific 10 constraints Use the LS OPT program together with a preprocessor such as LS PREPOST instead of this program 1 2 Brief Overview Topology optimization in structures has been studied since the 1970s resulting in many books and numerous papers The bo
16. load cases The dynamic weighing is done by defining a desired relationship between the responses of all the load cases The algorithm will scale the load case weights to achieve this relationship Say we have constraint C from the first load case and constraint C from the second load case then we write our desired behavior as KC offset k C offset with C the constraint value k a scale factor and an offset added The final weights found are not suitable for restarting They can be examined though for an indication of good values of the weights but usually the final weights found using dynamic weighing are too large 21 3 FREE SURFACE DESIGN Free surface design revises a solid surface shape to have a uniform surface stress for the given loads 3 1 The Design Surfaces The surface of a solid part can be redesigned to reduce stress concentrations There is no restriction on the element type The surface is defined using a SET_SEGMENT definition in the LS DYNA input deck Shells structures cannot be designed in this version of LS TaSC 3 2 Geometry and manufacturing definitions For each surface geometry and manufacturing definitions such as being an extrusion may be specified The geometry definitions as shown in Figure 2 1 are e Symmetry For these the geometry is duplicated across a symmetry plane The part as supplied by the user must be symmetric an element must have a matching element on the other side of the
17. of elements 2 4 2 Filtering of Results Structured grids are not always possible for industrial applications and the results should be mesh independent A radius based strategy is therefore used to identify neighbors In this strategy a virtual sphere of default or user defined radius is placed at the center of an element All elements that are within this sphere are considered the neighbors of the corresponding element The result at an element is computed scaled from its own value and of its neighbors 17 For dynamic problems it was observed that accounting for the history of evolution induces stability by reducing the element deletion rate Hence the field variable internal energy density of i cell at iteration t is updated by defining a weighted sum on the field variable of three previous iterations 2 4 3 Initialization Deletion and Regeneration of the Design Variables The design variables are initialized to satisfy the mass fraction All variables in a part are assigned the same initial value All associated field variables are also initialized to zero The variable value of the element depends on its loading together with that of its neighbors due to filtering If the variable value is too low then the element is removed from the model once the variable value is smaller than the minimum allowable value The element can be kept in the model in later or all iterations by decreasing this minimum allowable value of the varia
18. pulldown menu e The histories can be printed or saved to file using the Plot pulldown menu e The history data can be exported and postprocessed using the scripting interface The available history variables are given in the following table Histories Case Constraint This is the value of the Constraint of the named Case Case Weight This is the weighing applied to the named load Case If 38 Mass Redistribution P123 ElFrac P123 MassFrac dynamic load cases weighing is set then this value is changed to that effect This convergence criterion is the fraction of the total mass of the structure that has been redistributed per iteration This is the element fraction for part 723 This value only relevant for solids is the fraction of elements in use not deleted At convergence this will be close to the mass fraction value for solids This is the mass fraction for part 723 This value is constant if no constraint bounds were set If constraint bounds were set then the part mass fraction will be adjusted to satisfy the constraints info Cases Parts Constraints Completion Run View Multiple histories 1 Iteration Figure 4 12 The view panel with histories For the LS PrePost plots you can plot either the design of a single iteration or a matrix plot showing the evolution of the design over several iterations The available field variables are giving in the following table Field Variable
19. structure The evolution of the topology under the static loading conditions is shown in Figure 5 13 While the final form of the structure was largely evolved by 17 iteration first structure in the second row the material was re distributed to remove the low density elements that were not contributing sufficiently to support the load and obtain a homogenous material distribution such that the simulation converged after 28 iterations 51 5 5 Shell Example This example shows how to work with shell structures 5 5 1 Problem Definition Figure 5 14 The geometry and loading conditions of the shell example The left side is built in while a downward load is applied to the right back corner The geometry and loading conditions for the example are shown in Figure 5 14 5 5 2 Input The project input data is saved to the file Shell lstasc as provided in the examples distribution Additionally scripts to recreate the database are also provided The project database can be investigated using the scripts use the script in example Error eference source not found to print the project data 5 5 3 Output a Convergence History 52 Mass_Redistribution Iteration Figure 5 15 Convergence history for the shell example The convergence history for the shell example is shown in Figure 5 15 The simulation converged after 14 iterations There was largely monotonic reduction in the density redistribut
20. E Total_IED Case Max nodal displacemer 2012441 Model plots Single Matrix Hide Shad View BDC View top Front Right Bottom Back teft Wire LS PREPOST 2 4 Beta 19Feb2009 14 49 BEAM 50 1 d3plot chiste File Misc Toggle Background Applications Settings Help Follow Splitw Particle Output Trace Xyplot Anno Light FLD SPlane Setting State Range Vector Measur Find Ident ASCII Fcomp History Views Appear Color Model Group Blank SelPar 1 2 3 41 5 1 7 D Title Off Tims Triad Beolr Unode Frin Isos Leon Acen Zin 10 Rx Deon REM Top Front Right Redw Home Feat Edge Grid Mesh Shrn Peen Zout Cip Au ETE Bottm Back Left Anim Reset Fist Y Last 202 Ine 1 M Loop sF lid Time 0 4 a gt 4 y NoofDiv States 1 Ey 2 Done Finished reading command filet Show Figure 4 13 Viewing the model evolution in LS PREPOST 4 5 Databases and Files The important files and directories are shown in the figure below Four files are important to know about e The project database e The project results in the st binout binary file e The optimal design in the case directory e The d3plot files in the run directory inside the case directory 40 Work Directory database Istasc Ist output txt Ist_error txt Ist_errors txt Ist binout CASE 1 CASE 2
21. IN 52 ST Problem DeftioEi oo E eiut dies A es 52 3 5 2 PUE A aba ccn ed eiu AEN 32 5 5 3 A O a aan 52 a Convergence History iia A 52 b Final Shell Thicknesses oooononononocononononononononononononononononononononononononononononos 53 240 3 MU Eoad Cases ne ii 53 5 6 1 Probl m Definition iei i Rec e eterne eR eae debated 54 5 6 2 pit em 54 5 6 3 Results with constant Wells 54 5 6 4 Results with dynamic Weighing oooooonnocccnnncccnonnncnonnnononcncnnnccononcnnonncnnnnnnno 56 3s Surface Design OF Beanie eina is 58 5 7 1 Probl m Definition ue ie erectas dal 58 ATP Results with four surfaces opto loa ie 58 5 7 3 Results with extrusion and symmetry geometry definitions 60 5 7 4 Results with smooth transition geometry definition 61 6 WrOUBIESHOGUINE pino tp 64 6 1 Executable failing or no Output ee epe dread on Dee ea Ed ce end nae dun 64 6 2 NESTE Patto oco alio ERAN OUR M ad M sabes EM MM e EE 64 MEI A Cm 64 64 Negative Volumes sisse ine te tdi 64 6 5 The LS DYNA analysis fails if a smaller mass fraction is requested 64 6 0 CODVEDPEHOO cuatro OG ENTIER eS eb eft hU NOM ELE 65 6 1 LS PRBPONST cista nasan n is 65 GO Casting de TIED sedeo qup O A 65 6 9 Mysterious Error when after calling LS DYNA and or Errors involving the LSOPT Environment Vartable oe DI eoe es ee 65 d Other ES FaSC MANUALS costs 67 Ta The
22. The LS TaSC M Software TOPOLOGY AND SHAPE COMPUTATIONS USING THE LS DYNA SOFTWARE USER S MANUAL July 2013 Version 3 0 Copyright O 2009 2013 LIVERMORE SOFTWARE TECHNOLOGY CORPORATION All Rights Reserved Corporate Address Livermore Software Technology Corporation P O Box 712 Livermore California 94551 0712 Support Addresses Livermore Software Technology Corporation Livermore Software Technology Corporation 7374 Las Positas Road 1740 West Big Beaver Road Livermore California 94551 Suite 100 Tel 925 449 2500 Fax 925 449 2507 Troy Michigan 48084 Email sales Istc com Tel 248 649 4728 Fax 248 649 6328 Website www lstc com Disclaimer Copyright 2009 2013 Livermore Software Technology Corporation All Rights Reserved LS DYNA LS OPT and LS PrePost are registered trademarks of Livermore Software Technology Corporation in the United States All other trademarks product names and brand names belong to their respective owners LSTC reserves the right to modify the material contained within this manual without prior notice The information and examples included herein are for illustrative purposes only and are not intended to be exhaustive or all inclusive LSTC assumes no liability or responsibility whatsoever for any direct of indirect damages or inaccuracies of any type or nature that could be deemed to have resulted from the use of this manual Any reproduction in whole or in part of this
23. anual The scripting manual is available in the same location as your LS TaSC executable 7 3 Queueing system installation The queuing system installation manual is available in the same location as your LS TaSC executable 67
24. ata 13 showed potential in handling topology 11 optimization problem for crashworthiness problems This method updates the density of elements based on the information from its neighbors No gradient information was required The simplicity and effectiveness of this method for both two and three dimensional problems made it an attractive choice for our initial implementation The methodology has however been enhanced using more general approaches as well currently amongst others it gives mesh independent results Our methodology is therefore best referred to as simply the LS TaSC 3 0 methodology the product name together with the version number 1 4 Finding Information This manual is divided into parts The user s manual describes how to do topology optimization using LS TaSC A few examples are provided to cover different options in the topology optimization program Some common errors and tips on troubleshooting are provided in a separate chapter The scripting manual lists the command language used to interact with the topology optimization code together with some examples In the theory manual the method for topology optimization is described Setting up queuing systems is described yet another manual All manuals are bundled with the executables and can be found in the same location after installation 1 5 References GIN Rozvany Structural Design via Optimality Criteria Kluwer London 1989 MP Bendsge O Sigmund Topolog
25. ble fraction but this may result in instability of the FE model The element will be regenerated if its neighbors are highly stressed in a later generation If the neighborhood radius is set to O then it won t be regenerated because it does not receive any information from its neighbors 2 5 LS DYNA Modeling Specifics The portions of the FE model related to the design parts are extensively edited by the optimization algorithm In these segments of the FE model only specific versions of PART SET and CONTACT keywords may be used as described in the relevant sections Portions of the model not edited by the optimization algorithm are not subjected to this rule 2 5 1 The Contact Definition This discussion applies only to solid structures For the design of shell structures no action is required because the part and contact definitions will not be edited by LS TaSC Contact involving a solid design part requires special handling because a design part ID is changed by the topology algorithm There are two options to model contact involving the solid design parts defining contact using part sets or using specific CONTACT AUTOMATIC OPTION definitions Firstly the contact can be defined using part sets containing the design part LS TaSC will rewrite part sets to reflect changes to the design part This will allow any CONTACT definition to be used The alternative option is modeling the contacts involving the design parts using
26. can be kept instead of deleted The SIMP algorithm can be switched on and off Coordinate systems are no longer limited to DIRZX Restarting was improved to be faster by using more archived results A fringe plot of the material utilization as considered in the design process can be viewed The fraction of the original number of elements used in the design can be viewed as a history The global constraint handling has been changed to consider only active constraints If no global constraints are active anymore then the algorithm will slowly return to the user specified mass fraction Many thanks are due to David Bj rkevik for the GUI design and implementation Valuable feedback from customers and co workers is also acknowledged Willem Roux Livermore CA November 2011 PREFACE TO VERSION 2 Version 2 was started in spring of 2010 in response to industrial feedback regarding version 1 Version 2 is an important step forward containing the following major new features e Shell structure support Global constraints Multiple parts Symmetry definitions Casting direction definitions Some minor features are e Tetrahedral solid element and triangular shell element support e The speed of some algorithms was improved e Improved integration with LS DYNA Many thanks are due to David Bj rkevik for the GUI design and implementation Tushar Goel for the initial global constraints implementation and Trent Eggleston for assistance with distribu
27. ce for this example is a 50 smoothing The problem converged in 27 iterations The final design is shown in Figure 5 27 Note that for an extrusion such as this a complete smoothing of the stress is not possible because the loading varies along the extrusion direction while the geometry does not LS DYNA keyword deck by LS PrePost Time 1 Fringe Levels Contours of Effective Stress v m 1 000e 02 min 0 807878 at elem 1691 max 50 1228 at elem 1772 9 000e 01 8 000e 01 7 000e 01 6 000e 01 5 000e 01 4 000e 01 3 000e 01 2 000e 01 1 000e 01 0 000e 00 Figure 5 27 Final design of beam with extrusion and symmetry geometry definitions 60 back Smoothing front Smoothing 0 4 0 3 0 2 Multiple histories 0 1 20 Iteration Figure 5 28 Convergence history of beam with extrusion and symmetry geometry definitions 5 7 4 Results with smooth transition geometry definition The front half of the beam was selected for shape design A node set was defined on the center edge and used to define the smooth transition Use LS TaSC to investigate the problem definition visually The objective was the minimum volume of the part The convergence tolerance for this example is a 50 smoothing with a maximum of 30 iterations allowed The final design is as shown in Figure 5 29 The design without the smooth transition is shown in Figure 5 31 the resulting poor mesh quality can be seen 61 Figure 5 29 Final d
28. e details 4 3 9 Setting advanced options Advanced options can be set as shown in Figure 4 10 This is accessed through the Settings pulldown menu 36 Delete elements True Invert SIMP use False Store filters in memory True Dump casting faces False Face direction tolerance 0 258 Number of discrete parts 1 Delete unreferenced nodes True Use d3part database False Design Field IED Figure 4 10 Options panel The available options are described in the following table Option Delete elements Invert SIMP use Dump casting faces Store filters in memory Face direction tolerance Delete unreferenced nodes Description Normally the program delete elements below a certain variable value but the elements can be set to have a value of the minimum allowable The normal SIMP use can be inverted such that it is not used for solids but used for shells This advanced options dumps files showing the casting faces which can be viewed in LS PrePost This option can reduce memory use by a factor two but extend the time required to extract results The option is useful can cases where the elements have many neighbors such as tetrahedral models For casting definitions this is used to decide whether two elements face in the same direction It is the sine of the allowable angle The MPP LS DYNA execution speed can be slowed down in later iterations because of the presence of many unreferenced nodes Use this option t
29. efault value depends on the 33 average element size Move limit This is the maximum distance a node will be moved in an iteration Remesh depth This the number of elements that should be considered in remeshing after a shape change was done Segment Set ID Move Limit E SY Default Objective Neigbor Radius Match Average Default Target Field Remesh Depth Default Default Surface definitions Name Definition symmetry1 Symmetry about z x plane in global coordinate system SmoothTransition1 Smooth transition using set 2 e 10 Match Average Cancel OK A EJ New Edit Delete Done Figure 4 7 The surface panel 4 3 6 Part and Surface Geometry The geometric properties can be defined for every part and surface See the following table and Figure 4 8 for more details Geometry data Name The geometric property can assigned a name or a default name can be used Extrusion Set ID To define an extruded part the user firstly creates a set of all elements that would be extruded Allowable set definitions are SSET SOLID SET SOLID LIST SET SHELL and SET SHELL LIST Smooth transition To define a smooth transition the user firstly creates a node Set ID set definition defining the edge Allowable set definitions are 34 Symmetry Plane Cast direction Coordinate System ID SET NODE and SET NODE LIST Specify a symmetry plane to define symmetry A cast directio
30. efinition The sets involving the design parts should be defined using SET SOLID SET SHELL or SET SHELL LIST Neither the generate general list generate nor the column options are edited by LS TaSC do not use these options to include the design part 2 5 5 Unsupported Keywords The INCLUDE keyword is not supported in the current version It may be used but LS TaSC will not follow the link 2 5 6 Disallowed Keywords In general all keywords are allowed but LS TaSC will only edit the listed keywords to reflect changes to the design part 19 2 5 7 Automatic Keyword Edits by LS TaSC Automatic keyword edits preserve the stability of the LS DYNA simulation by deleting elements that are inverting or have a very small timestep The values of variables are reset as in the following table The user can override the values supplied by LS TaSC using the information in the table Keyword Variable LS TaSC Auto Set User override CONTROL ERODE 1 erode elements Set to 1 to force of value TIMESTEP of 0 no erosion CONTROL DTMIN 0 01 if less than or equal Set to a positive value to TERMINATION to 0 force the use of this positive value Remarks 1 DTMIN was set to 0 001 in versions before version 3 0 but this value was increased on the basis that larger values should be more useful for topology design Aggressively large values in topology design may results in critical load paths being deleted during the evoluti
31. either the CONTACT AUTOMATIC SURFACE TO SURFACE ID Or the CONTACT AUTOMATIC SINGLE SURFACE ID options These automatic 18 contact options are general enough to accommodate the changes in the geometry of the design parts during the optimization to maintain valid contacts Other contact types are not edited by LS TaSC They can be used i if the contact does not involve the design part or ii if the contact is defined for a part set containing the design part because LS TaSC will rewrite part sets to reflect changes to the design part It is also recommended to specify the contact options e g friction coefficients appropriately accounting for the changes in the geometry may result in significantly different material properties for some elements near the contacts Too restrictive values may cause instabilities in the LS DYNA simulations for intermediate geometries LS TaSC will set the SOFT 2 on the optional card A to improve contact behavior if the optional card A is not specified for the contact types named in the first paragraph This can be overridden by specifying the optional card A 2 5 2 Part Definition The part must be defined using PART not PART OPTION 2 5 3 Part Set Definition The part sets involving the design parts should be defined using SET PART or SET PART LIST Neither the generate nor the column options are edited by LS TaSC do not use these options to include the design part 2 5 4 Element Set D
32. ements with shell thicknesses less than a user defined minimum value 0 05 for dynamic problems and 0 001 for linear are deleted to improve numerical stability 14 The final shell thicknesses will have values varying between the original shell thickness the maximum value and the user defined minimum value if not deleted for stability reasons The shell thicknesses will not be driven to the maximum or minimum values using the SIMP algorithm described in the theoretical manual The SIMP algorithm can however be activated using the advanced options described later in this chapter in which case the behavior will be similar the default behavior for solids 2 1 3 Element types Solid elements must be eight noded solid elements four noded tetrahedral elements or six noded pentahedral elements Elements shapes close to perfectly cubic are the best for the current neighbor selection algorithm Shell elements may be four noded shell elements or three noded shell elements The triangular elements must be specified as four noded shell elements by specifying the last node twice Elements shapes close to perfectly square or an equilateral triangle are the best for the current neighbor selection algorithm Tetrahedral and triangular elements cannot be extruded 2 1 4 Material data For the design of a shell structure any material can be used while the design of solid structures 1s limited to the use of certain materials for the design part Fo
33. ent Set DEMO A ici 19 2 5 5 Unsupported Keywords visi inner 19 2 5 6 Disallowed KOVO dS iso 19 2 5 7 Automatic Keyword Edits by LS TaSC seen 20 25m EAN Sitti Ato ns sent Diu s dic acies etas nea 20 Zi Global Constraints ii cu octaua pedis 20 2 7 Dynamic Load Cases Welghtnlg sud a Qin 21 Dio E SUT ACS a ad nica 22 S bs Th D sisn UA ri ida 22 3 2 Geometry and manufacturing definitions oooocnnncccnoncccnonnncnnnnnnnnnaninnnanonnnccinnnos 22 3 37 A S 23 SA Design Variables iii iii illa 23 3 a ees wt peine us a LEE d 23 3 6 LS DYNA Modeling Specifics eeeetete entes 24 3 6 1 o utface Definition an ss 24 3 6 2 Smooth Transition oer Sotto fis eue oot ing eiecit a a e iuis ame Use AR 24 3 6 3 Disallowed Ke Vey OS usos eie du die vede E E ene ee 24 3 7 Automatic mesh smoothing iiunii bs ho ond Sis uus inh rediere buie 24 PRO STATE Executions TP 25 41 Running the Prost ii ida scans 25 42 DR este Ma RR 25 ADA ES SUDUIAIOIGS e echec a toes e aar ae 25 4 3 Setting up the Problem eese see teo Ua c ER RETIA TUN ORae Fe nd et e 26 4 3 1 The POpleve UL is ts fado Des es do 26 4 3 2 The Cases Panel suo ds 27 4 3 3 THeConstraitits Pa dd RET 28 4 3 4 Th Parts Panel ote or eto lo 30 4 3 5 The Surface Panel eet pd 33 4 3 6 Part and Surface SOM 34 4 3 7 The Compl tion Panels oeste Ads 35 4 3 8 The Run Panel eine aos 36 4 3 9 Setting advanced options cep
34. esign of beam with smooth transition geometry definition front_front_half RangeReduction front_front_half Smoothing Multiple histories Iteration Figure 5 30 Convergence history of beam with smooth transition geometry definition 62 became awe TON NTH Figure 5 31Design of beam without smooth transition geometry definition 63 6 TROUBLESHOOTING This chapter lists some of the most common errors and suggested remedies 6 1 Executable failing or no output For the example problems check that you changed the name of the LS DYNA executable in the example problem to what is used on your computer Provide the complete path for the solver command instead of using alias You may also specify necessary DYNA options in the command e g home Tushar bin 1s971 single memory 100m 6 2 Design Part The design part is not found check that the DYNA input deck has the same part id for the design part as specified in the input file In the case of the multiple load cases the design domain must remain the same 6 3 Extrusion Set The extrusion set is not found check that the set of elements on the extruded face are grouped under the SET SOLID option in the DYNA input deck The ID of the set is same for all load cases as specified in the input file Unable to find all the slaved elements if the node numbering order is different for some elements are not the same then the algorithm may fa
35. few test examples below The examples are supplied together with the software executables 5 1 Fixed Beam with Central Load This example demonstrates 1 how to define a problem 2 howto add a case 3 how to optimize the topology for a non extrusion example and the 4 analysis of output 5 1 1 Problem Description This example simulates a beam that is fixed on both ends A pole with assigned initial velocity of 10m s hits the beam in the center The design part is meshed using 5mm brick elements The symmetry of the problem is used to design only half section of the beam The geometry and loading conditions of the beam are shown in Figure 5 1 The material model used in this example is defined previously L 400mm H 80mm Symmetry W 100mm Figure 5 1 Geometry and loading condition of a single load case example 5 1 2 Input The problem has a case named BEAM The name of the DYNA input deck file is Beam dyn Part 101 is the design part A maximum of 100 iterations are used to find the optimal topology The desired mass fraction is 0 25 The project input data is saved to the file st_project lstasc as provided in the examples distribution Additionally scripts to recreate the database are also provided The project database can be investigated using the scripts use the script in example Error eference source not found to print the project data The advanced user can conduct the 43 simulations using the LS
36. his capability is available only for solids e Forging This is similar to a two sided casting except that a minimum thickness of material will be preserved The geometry definition will therefore not create holes through the structure Extrusion Symmetry ME 2 One sided Casting d Estos Figure 2 1 Geometry definitions Multiple geometry constraints can be specified for each part Some combinations of geometry constraints may however not be possible A maximum of three geometry definitions per part is possible The symmetry planes must be orthogonal to each other the extrusion direction must be on the symmetry planes the casting direction must be on the symmetry planes and the extrusion directions must be orthogonal to casting directions Only one casting definition may be defined per part The symmetry and extrusion definitions are implemented by assigning multiple elements to a variable while the casting definitions are implemented as inequality constraints requiring certain variables to be larger than others according to the cast direction For a casting definition the free faces are selected as shown in Figure 2 2 It can be seen that that free faces can occur in many places for example inside a hole which cannot be created using a casting manufacturing process In version 2 1 onward the algorithm will ignore the internal cavities in the selection of the free surface This is to allow an analyst to have cavities introduced say b
37. iated with a case is defined here This enables the user to specify non uniform importance while running multiple cases This parameter indicates the number of processes to be run simultaneously A value of zero indicates all processes would be run simultaneously This parameter only makes sense if multiple cases must be evaluated The program will allow as many processes as defined for the current case being evaluated This parameter is used to indicate the queuing system The options are Isf loadleveler pbs nqs user aqs slurm blackbox msccp pbspro Honda By default no queuing system would be used See the appendix for a description of setting up the queuing systems The system is the same as used in LS OPT so a queuing system definition is the same 27 Input file Weight Queuer compone 1 none AID compone 1 none Surface EleTol Constrain Post ES Weight OK Accept Edit Copy Delete Done 4 Run ss View General Scheduling Name Weight MID 1 Input file name component k Browse Execution command without i parameter Isdyna Edit Cancel Figure 4 2 The cases panel 4 3 3 The Constraints Panel The constraint panel contains the global constraints on the structure See the following table and Figure 4 2 for more details Constraint data Name Each constraint is identified with a unique name e g MAX DISP Case Each co
38. il Using a different node number will for example cause face 1 to be the top face on one element and to be the left face on another element the algorithm depends on this not happening 6 4 Negative Volumes While care has been taken to avoid running into negative volume errors sometimes the simulation terminates due to negative volume errors A user can take several actions to correct this error 1 Check the CONTACT cards Note that the failed run probably has elements with soft material interface with elements with harder material hence care must be exercised in defining master and slave penalty stiffness factors 2 Specify SOFT 2 option on the control card 3 Increase minimum density fraction default 0 05 for dynamic problems 6 5 The LS DYNA analysis fails if a smaller mass fraction is requested Possibly the structure is not strong enough to support the load 64 Inspect the d3plot results in the failed iteration to understand what happens in the LS DYNA analysis Fixes are to reduce the load increasing the mass fraction changing the FE model to be more robust using a finer mesh modify your approach keeping in mind that you cannot get a solution from that starting mass fraction or accepting that a design does not exist at that mass fraction 6 6 Convergence For some problems the code does not converge instead oscillations set in The user must look at the geometry to understand why oscillations are observed
39. ing a line on the edge of the surface 3 6 3 Disallowed Keywords The INCLUDE and PARAMETER keywords are not supported in the current version All other keywords are allowed but LS TaSC will only edit the nodal locations to reflect changes to the design 3 7 Automatic mesh smoothing The interior nodes of the FE model related to the design surfaces are smoothed by the design algorithm The mesh is smooth for a certain depth below the surface The default value of the remesh depth defined in the number of elements should be fine for most problems but problems with few elements in the depth direction will require this value to be reduced 24 4 PROGRAM EXECUTION Both topology and shape design consist of describing the topology design problem together with the solution methodology the scheduling the automated design and the evaluation of the results 4 1 Running the Program The LS TaSC GUI is launched from the command prompt by running the executable Istasc If a project already exists then the project database name stasc can be supplied in two ways 1 With the execution command lstasc myProject lstasc 2 The file open dialogue available from the File pulldown menu LS TaSC can be run without the GUI from the command line using the command lstasc script myDataBaseFile lstasc Oras lstasc script myScriptFile with the script commands as described in the scripting manual 4 2 Problem Definition The topology de
40. ing the later iterations The final topology is visualized in LS PREPOST 44 b Density Contours The initial and final topologies are shown in Figure 5 3 and the topologies at different iterations during the evolution process are shown in Figure 5 4 Figure 5 3 Initial and final density contours The final topology evolved in a truss like structure Many holes were carved to satisfy the mass constraint while reducing the non uniformity in the distribution of the internal energy density The final structure was also found to have a reasonably homogenous distribution of the material as was desired Figure 5 4 Evolution of the geometry shown using density contours Topologies at different stages of the evolution process show that the main features of the structure were evolved by iteration 20 row 2 column 1 Further iterations were necessary to bolster the structure by removing the material from relatively non contributing zones and redistributing it to the desirable sections such as a 0 1 type topology was evolved 5 2 Beam using geometry definitions This example demonstrates how to set up a problem with geometry definitions The same fixed beam with a central load example is analyzed with an extrusion and two casting definitions The symmetry face is also defined as the extruded face In the input deck file the elements on the extrusion face were grouped in a solid set SET SOLID Two different casting conditions were a
41. ion b Final Shell Thicknesses The final design is shown in Figure 5 16 The final structure had many cutouts and resembled an optimized truss like structure Lu Figure 5 16 Final geometry and thicknesses for the shell problem 5 6 Multiple Load Cases This example demonstrates 1 multiple load cases 2 dynamic weighing of load cases 3 constraints and a 53 4 symmetry geometry definition 5 6 1 Problem Definition I Fixed N o 3 Z lt ES 2 Fixed 2 L 800mm 2 Figure 5 17 The geometry and loading conditions of the multiple load case example The geometry and loading conditions for the example are shown in Figure 5 17 This is a fixed fixed beam with three loads The three load cases were identified according to the location of the pole hitting the beam The design part was meshed with 10mm elements 5 6 2 Input The problem is symmetric so symmetry is defined and only two load cases are therefore used The desired mass fraction for this example is 0 3 A maximum of 50 iterations are allowed All simulations are run simultaneously The displacements for both load cases are constrained to be less than 110 The locations are the center of impact and the maximum value over time was selected The problem is analyzed using with and without dynamic scaling of results For the use of the dynamic scaling the two selected maximum displacements are required to be the same With dynamic scaling
42. manual is prohibited without the prior written approval of LSTC All requests to reproduce the contents hereof should be sent to sales stc com 18 Dec 13 PREFACE TO VERSION 3 Version 3 was started in spring of 2012 focusing on free surface design as well as imbedding the LS TaSC product into the LS PrePost framework Version 3 is an important step forward containing the following major new features e Free surface design of solids including o Geometry definitions Extrusions Symmetry Edge smoothing o Automatic mesh smoothing e Integration into the LS Prepost framework This is a long term project which at this stage includes o Expanding the previous GUI capabilities for free surface design o The model tree on the left on the screen allowing quick navigation of the LS TaSC model o Picking of parts and surfaces o Integrated editing of the LS DYNA FE model to create surfaces coordinates systems and other entities required for the LS TaSC design Some minor features are e Support of MAT ORTHOTROPIC ELASTIC for the topology design of solids e Support of the d3part database for reading field results e The LCSS curve option of MAT PIECEWISE LINEAR PLASTICITY is now supported e Checking and adding the LS Dyna binary output requests required for constraints e The iteration count now starts at 0 with iteration O being the initial design provided by the user e The Material Utilization plot is now scaled with the value of the target
43. n Crashworthiness Design Structural and Multidisciplinary Optimization 33 1 12 2007 12 MK Shin KJ Park GJ Park Optimization of Structures with Nonlinear Behavior Using Equivalent Loads Computer Methods in Applied Mechanics and Engineering 196 1154 1167 2007 13 A Tovar Bone Remodeling as a Hybrid Cellular Automaton Optimization Process PhD Thesis University of Notre Dame 2004 13 2 TOPOLOGY OPTIMIZATION Topology optimization computes the lay out of a structure where material should be located to provide a loadbearing structure The criterion is that the material should be fully used this is implemented by designing for a uniform internal energy density in the structure while keeping the mass constrained The outcome is typically the stiffest structure for the given weight minimum compliance design but with an upper bound on the stress 2 1 The Design Parts The design domain is specified by selecting parts the optimum parts computed will be inside the boundaries delimited by these parts The part must be defined using PART not PART OPTION The parts may contain holes a structured mesh is accordingly not required 2 1 1 Design of Solids The designed topology of a solid part is described by the subset of the initial elements used Unused material will be removed during the design process thereby revealing the structural shape that can bear the loads efficiently The amount of material removed is specified
44. n is required for a casting constraint The direction can be negative This is the direction in which the material will be removed It is the opposite of the direction in which a casting die will be removed The geometric property can be defined in a specific coordinate system or the default Cartesian system can be used Geometric Constraint Name for constraint Coordinate system Symmetry plane Global w cs J jJ Figure 4 8 Creating a geometry constraint 4 3 7 The Completion Panel The completion panel specifies how the optimization problem will be solved See the following table and Figure 4 9 for more details Completion data Number of design iterations Minimum mass redistribution This is the maximum number of iterations allowed The default value is 30 The minimum mass redistribution is the termination criterion used to stop the search when the topology has evolved sufficiently This value is compared with the Mass Redistribution history variable displayed in the view panel The default value is 0 002 35 ES Case D gt Part Model Surface EleTol Constrain Post Weight Figure 4 9 The completion panel 4 3 8 The Run Panel The control panel is used to submit the design problem In addition the LS DYNA jobs can also be stopped and old results deleted Use this panel and the Viewer panel to monitor job execution See Figure 4 11 for mor
45. nstraint 1s associated with a load case Constraint Type One of NODOUT stiffness RCFORC compliance or USERDEFINED see text Lower and upper The weight associated with a case is defined here This enables bound the user to specify non uniform importance while running multiple cases ID This is the ID of the node in the FE model at which the results must be collected Select This parameter indicates which value over time must be selected It can be the last value the maximum value the minimum value or at a specific time A time or a time interval can also be specified 28 Filtering If filtering is desired select the type of filter frequency and time units LS PREPOST can be used to investigate the effects of filtering NODOUTI 30 SOLVER 1 Case HODOUT Last registered Resultant of displacement of node with ID 777 D ContactForce gt 15 SOLVER_1 Part Model RCFORC Max Y master force of interface 9 rz 15 lt Disp 8 lt 10 SOLVER_1 zur NODOUT Last registered X Component of displacement of node with ID 8 Surface EleTol Post c Weight OK Accept Run lt View Figure 4 3 The constraints overview panel The USERDEFINED responses require a string to be specified The only allowable commands are the D3PlotResponse and BinoutResponse commands as defined in the LS OPT manual for example D3PlotResponse pids 101 res_type stress cmp von_mises select MAX start_time 0 0000 Easiest is t
46. o correct this This option will delete unreferenced nodes in the interior of the design part Note that a check is only done whether the design part still use these nodes if these interior nodes are referenced by other FE parts or entities then the LS DYNA run will fail due to the absence of these nodes 37 Use d3part database The field results IED values will be read from the d3part database instead of the d3plot database Use this option to save disk space Design field This is the criteria used to decide whether an element is utilized One of Internal Energy Density or Von Mises E LSTOPO EE Ele View Plot Help Info Cases Parts Constraints Completion Run view Job status Job ID PID Iter Case Status 1 10618 1 SOLVER 1 2 10622 2 SOLVER 1 3 10626 3 SOLVER 1 4 10630 4 SOLVER 1 5 10634 5 SOLVER 1 6 10638 6 SOLVER 1 7 10642 7 SOIVFR 1 E Engine output Optimimum design input deck written to SOLVER_1 SOLVER_1_OptDesign9 k Optimization con JMPLETED Wed Dec 15 14 33 44 2010 Run Q stop Clear results Figure 4 11 The run panel 4 4 Viewing Results The view panel can be used to monitor both optimization progress and optimization results Both histories and plots in LS PREPOST are possible See Figure 4 12 and Figure 4 13 for more details For the histories note that e Multiple histories can be plotted simultaneously by holding down the Control key e The plot ranges can be set under the View
47. o use LS OPT to create these strings You also need to specify whether an increase of weight of the structure will increase or decrease this response 29 Tem x Edit Constraint x Constraint type USERDEFINED IdentifierType ID NODOUT lip gt 88 RCFORC Displacement direction X Component D Y Component Z Component D Resultant Select Last value s Filtering None 2 Case Name for constraint DYN LOAD 2 15 NODOUTI lt 10 X cancel gx Figure 4 4 The constraints creation panel 4 3 4 The Parts Panel The part definition panel contains information about the parts to be designed such as the geometry and mass fraction See the following table Figure 4 5 and Figure 4 6 for more details Part data Design Part ID The user needs to specify the design domain for topology optimization To facilitate the identification of design domain all elements in the design domain are put in a single part in the LS DYNA input deck The information about the design domain is then communicated through the corresponding part id Note For multiple load cases the user must ensure that the design domain mesh and the part id remain the same in all input decks Mass Fraction This parameter describes the fraction of the mass of the part to be retained The rest will be removed A part with an initial weight of 5 designed using a Mass Fraction of 0 3 will have a final weight of 1 5 30
48. oks by Rozvany 1 and Bendsge and Sigmund 2 provide a very comprehensive and contemporary survey of optimization techniques used in topology optimization Most previous studies 3 4 in topology optimization have focused on designing structures with static loading conditions but there is relatively little work on handling problems involving dynamic loads like those observed in crashworthiness optimization 5 The topology optimization in the context of crashworthiness is a very complex problem due to non linear interactions among material non linearities geometry and transient nature of boundary conditions The most efficient topology optimization methods use sensitivity information optimality criterion based methods Rozvany 1 Bendsge and Kikuchi 6 to drive the search for an optimum Sensitivity calculations are computationally inexpensive for linear static problems but not for the problems that involve non linearities To use the same set of topology optimization methods one needs to explicitly calculate sensitivities which is practically infeasible due to very high computational cost involved with simulations Thus the theory used to solve the linear static load cases though quite mature is not practical for the crashworthiness problems and alternate methods need to be explored Previously different approaches have been adopted by authors to solve topology optimization with nonlinearities Pedersen used the Method of Moving Asymptotes f
49. on of the structure 2 TSMIN DTMIN DTSTART with TSMIN the minimum timestep and DTSTART the initial timestep Elements with a smaller timestep will be eroded Alternatively the analysis terminates if element erosion is inactive and the timestep falls below TSMIN 3 In version 2 1 and earlier the value of TSSFAC in CONTROL TIMESTEP was set to 0 9 The default for TSSFAC is 0 9 or 67 for high explosives so setting it to 0 9 was discontinued 4 The use of PSFAIL on CONTROL SOLID overrides the ERODE setting 2 5 8 LS DYNA Simulation The modified input deck is analyzed using LS DYNA One can take advantage of multiple processors using the MPP version of LS DYNA by specifying the simulation options as part of the command Queuing system can also be used as described in Section 4 3 2 If you desire to use less disc space then the options are to reduce the LS Dyna output or to create a file named clean clean bat in Windows in the directory containing the database This clean file must be set to be executable and can contain lines such as rm rf d3hsp scr00 LS TaSC will execute this clean script in every directory where LS DYNA ran successfully 2 6 Global Constraints Global responses depend on the design of the whole structure Two types of global responses are 20 e Stiffness This is specified as displacement constraint e Compliance This is specified as a reaction force constraint
50. or crashworthiness optimization of two dimension structures 7 They used a quasi static nonlinear FEA to account for geometric nonlinearities to handle large deformation and rotation of plastic beam elements However the method ignored the contact between elements arising due to nonlinear behavior of the structures Soto 8 9 presented a heuristics based method using a prescribed plastic strain or stress criterion to vary the density to achieve the desired stress or strains with a constraint on mass However this method could not be generalized to solid structures Pedersen 10 used beam elements to handle topology in crashworthiness optimization Forsberg and Nilsson 11 proposed two algorithms to get a uniform distribution of the internal energy density in the structure In the first method they deleted inefficient elements and in the second method they updated the thicknesses of the shell elements This method also was limited to a small set of optimization problems Shin et al 12 proposed an equivalent static load method where they calculated an equivalent static load for the dynamic problem and then used the linear static topology optimization techniques to find the optimal topology The main difficulty in this method is the requirement to accurately compute the equivalent loads 1 3 Topology Optimization Method in LS TaSC A heuristic topology optimization method developed at the University of Notre Dame known as hybrid cellular autom
51. ory tnanu al ec RI o dai DES A RE Lea 67 qo CAPAS MAMMAL uo rope ndr PR neci e 67 7 3 Queueing system installatlOm z ge eode ou Er eb peri idea acaltedeniasc 67 1 INTRODUCTION 1 1 Classification of Structural Optimization Techniques Engineering optimization finds new designs that satisfy the system specifications at a minimal cost Different types of structural optimization are 1 1 1 Topology Optimization This is a first principle based approach to develop optimal designs In this method the user needs to provide the design domain load and boundary conditions only The optimal shape including the shape size and location of gaps in the domain is derived by the optimizer While the most flexible method topology optimization is indeed the most complex optimization method due to a multitude of reasons like large number of design variables ill posed nature of the problem etc Nevertheless the benefits of using topology optimization include the possibility of finding new concept designs that have become feasible due to recent advances in technology e g new materials The LS TaSC program can be used to this design work 1 1 2 Topometry Optimization Topometry optimization a methodology closely related to topology optimization changes the element properties on an element by element basis With the LS TaSC program the shell thicknesses can be designed 1 1 3 Size Optimization In this mode the designer has already
52. pplied in two separate design runs i in the first run casting definition was applied in the Z direction and 11 in the second run a two 45 sided casting definition was applied in the Z direction All other parameters were kept the same 5 2 1 Input The main differences in this example compared to the non extrusion example are e An extrusion definition is provided e A casting definition in Z direction is provided The project input data is saved to the file Extr Cast lstasc and Extr Cast2 lstasc as provided in the examples distribution in the directory Beam extr cast Additionally scripts to recreate the database are also provided The project database can be investigated using the GUI or a script use the script in example Error Reference ource not found to print the project data 5 2 2 Output a Extrusion and Casting Figure 5 5 Evolution of the beam using extrusion and single sided casting constraints Different phases in the evolution are depicted in Figure 5 5 One can see that a lot of material was removed early The final geometry evolved by considering the geometry definitions was significantly different than the case when no manufacturing constraints were considered The C section evolved makes intuitively sense 46 b Extrusion and two sided casting Different phases in the evolution are depicted in Figure 5 5 One can see that a lot of material was removed early The final geometry evolved by considering
53. r the topology design of solids the design parts must be modeled using MAT ELASTIC Or MAT ORTOTROPIC ELASTIC Or MAT PIECEWISE LINEAR PLASTICITY For some MAT PIECEWISE LINEAR PLASTICITY material data the topology algorithm SIMP algorithm will create materials for which the slope of the stress strain curve is higher in plastic regime than in the elastic one in this case the errors and warnings should be consulted for feedback on how to modify the material stress strain curve in the input deck 2 2 Geometry and Manufacturing Definitions For each part several geometry and manufacturing definitions such as being an extrusion may be specified The geometry definitions as shown in Figure 2 1 are e Symmetry For these the geometry is duplicated across a symmetry plane The part as supplied by the user must be symmetric an element must have a matching element on the other side of the symmetry plane e Extrusion An element set is extruded in a certain direction Allowable set definitions are SET SOLID SET SOLID LIST SET SHELL and 15 SET_SHELL_LIST The part as supplied by the user must be an extrusion with every element in the elements set must have the same number of extruded elements Only hexahedrons and quadrilateral elements can be extruded e Casting Material is removed only from a given side of the structure The structure therefore will have no internal holes The casting constraints can be one sided or two sided T
54. raction was fairly close to the desired value b Density Contours The evolution of the topology of the clamped beam with multiple constraints is shown in Figure 5 9 The final structure had many cavities and resembled an optimized truss like structure The main cavities in the structure were formulated by the 15 iteration and the structure was fully developed in a largely 0 1 type structure by the 30 iteration Further redistribution of the material refined this structure between the 30 and the 40 iteration vete It 38 lt 1 pp It 30 Figure 5 9 Evolution of the geometry for multiple constrained clamped beam 5 4 Linear Static Loading The next example demonstrates the topology optimization of a statically loaded structure 5 4 1 Problem Definition 52 5mm H P L 52 5mm ni Figure 5 10 The geometry and loading conditions of a statically loaded structure 49 The geometry and loading conditions for the example are shown in Figure 5 23 The design part was meshed with 1 05mm elements such that there were approximately 125 000 elements 5 4 2 Input In this example a unit load is applied in the center of the structure The structure was fixed on the bottom The problem has a case named TopLoad The simulations are carried out using the double precision SMP version of LS DYNA 15971_double The name of the DYNA input deck file is LinearStructure dyn Part 102 is the design part A maxim
55. sign problem is defined by 1 the allowable geometric domain ii how the part will be used and iii properties of the part such as manufacturing constraints Additionally you have to specify methodology requirements such as termination criteria and management of the LS DYNA evaluations In the GUI provide this information using the following headings e Cases These store the load case data such as the LS DYNA input deck and executable to use The Cases data therefore contain the information on how to simulate the use of the part e Parts The properties of the parts such as the part ID mass reduction and geometric definitions are given here This is only required for topology optimization e Surfaces The properties of the surfaces such as the segment set ID and geometric definitions are given here This is only required for free surface design e Constraints This optional information prescribes the stiffness or compliance of the whole structure e Completion These are methodology data such as the convergence criterions 4 2 1 LS DYNA Simulation The modified input deck is analyzed using LS DYNA One can take advantage of multiple processors using the MPP version of LS DYNA by specifying the simulation options as part of the command Queuing system can also be used as described in Section 4 3 2 25 If you desire to use less disc space then the options are to reduce the LS Dyna output or to create a file named clean
56. symmetry plane e Extrusion The surface is extruded in a certain direction The initial surface as supplied by the user must already be an extrusion e Smooth transition A smooth transition between the free surface and the surrounding material is achieved by gradually smoothing out the transition between the modified and unmodified surface at a surface edge specified using a node set Smooth Transition Symmetry Extrusion Figure 3 1 Geometry definitions Multiple geometry constraints can be specified for each part Some combinations of geometry constraints may however not be possible The symmetry planes must be orthogonal to each other and the extrusion direction must be on the symmetry planes The symmetry and extrusion definitions are implemented using equality constraints while the smooth transition is imposed scaling the design variables at the nodes considering their distance from the transition 22 3 3 Convergence For shape computations the objective is to have a constant stress over the design surface The convergence is defined relative to how much of an improvement in the objective was achieved with respect to the initial design Consider Figure 3 2 showing both the stress range and the integral defining the smoothness of the stress Stress Target stress N Stress Range Lack of smoothness Distance Figure 3 2 Convergence for shape design Four strategies of setting the target stress are allo
57. t pbs for the PBS queuing system 5 3 3 Output a Convergence History 324 2 2E 06 2 1E 06 4 34 2E 06 19E 06 3 S 1 8E 06 2 E a a ul 38 ul gt amp 1 7E 06 3 SET E 1 6E 06 1 5E 06 42 1 4E 06 1 3E 06 44 i 10 20 30 40 10 20 30 40 Iteration Iteration 024 023 a 022 E 5 e 4 a 2 a 0 21 E E 9 E x E 0 2 E 5 0 1 0 18 047 D 10 20 30 40 10 20 30 40 Iteration Iteration Figure 5 8 Convergence history for the example with multiple constraints The convergence history for the multiple constraints example is shown in Figure 5 8 There were minimal changes in the geometry after 25 iterations and the simulation converged after 40 iterations While there was largely monotonic reduction in the density redistribution the constraints and IED were oscillatory in the behavior The oscillatory behavior of the constraints was due to their conflicting nature where an increase in 48 displacement required an increase in the mass fraction which resulted in higher forces At optimum a balance between the two quantities was obtained It is important to note that the mass fraction for this example was not held constant Instead it was automatically adjusted to satisfy the force and displacement constraints though the final mass f
58. ted computing Valuable feedback from customers and co workers is also acknowledged Willem Roux Livermore CA January 2011 PREFACE TO VERSION 1 The development of the topology code started in the fall of 2007 in response to a request from a vehicle company research group The alpha version was released in the spring of 2009 to allow the vehicle company research groups to give feedback from an industrial perspective while the beta version was released in November 2009 Most of the methodology developments in version 1 0 are due to Tushar Goel who worked on the engine implementation and algorithm design Additionally he also wrote the manual together with Willem Roux The project architecture was the responsibilities of Willem Roux and David Bj rkevik David had the lead role with regard to the graphical user interface aspects while Willem had the senior role looking after the overall project and the project management Thanks are also due to Nielen Stander from LSTC who helped to coordinate the efforts in the LS OPT group and sourced the initial version of the technology John Renaud and Neal Patel for discussion regarding topology optimization Kishore Pydimarry and Ofir Shor for evaluating the alpha version and Fabio Mantovani and Stefano Mazzalai for their help with LS DYNA simulations Willem Roux Livermore CA January 2010 TABLE OF CONTENTS Prefaceto Version a a 3 Prerdoe to Version diia 4 Prefacento VERSO 2 A A ave as 5
59. the all load cases are assigned a unit weight All of the details can be found in in the examples distribution in the MLC directory 5 6 3 Results with constant weights The results are as shown in Figure 5 18 to Figure 5 20 The resulting structure is much stronger in supporting the side loads than the center load with the resulting poor outcome for the constraint values as shown in Figure 5 18 54 LEFT NODOUT L MID NODOUT M 15 14 13 12 11 10 Multiple histories 10 20 30 Iteration Figure 5 18 Constraint convergence history for multiple load case example with constant weights 1 Mass_Redistribution P101_ElFrac P101_MassFrac 0 84 v 0 67 E 5 E E ed v amp 0 4 d 2 0 2 10 20 30 Iteration Figure 5 19 Various histories of the load case weight for multiple load case example using with constant weights mass redistribution the fraction of elements kept and the mass fraction 55 PTA Figure 5 20 Evolution of the geometry for multiple load case structure using constant weights 5 6 4 Results with dynamic weighing The convergence history for the multiple load example is shown in Figure 5 21 The simulation converged after 46 iterations Results are much improved by the dynamic weighing The constraints are reasonably close to the bound as shown in Figure 5 21 due to the load case weighing computed also shown
60. the geometry definitions was significantly different than the case when no manufacturing constraints were considered The I section evolved makes intuitively sense Figure 5 6 Evolution of the beam using extrusion and two sided casting constraints 5 3 Force Displacement Constraints The next example demonstrates a simulation with multiple constraints 5 3 1 Problem Definition S z S e 3 eo 3 3 3 Fixed L 800mm Figure 5 7 The geometry and loading conditions of the multiple constraints example The geometry and loading conditions for the example are shown in Figure 5 7 This is a fixed fixed beam with a central load The design part was meshed with 10mm elements 5 3 2 Input The center load was assigned at the location of the pole hitting the beam The desired mass fraction for this example was 0 25 A maximum of 100 iterations were allowed The 47 maximum displacement of the indenter was constrained at 34 units and the maximum y component of the interface force was limited at 1 45e6 units The project input data is saved to the file st_project lstasc as provided in the examples distribution Additionally scripts to recreate the database are also provided The project database can be investigated using the scripts use the script in example Error eference source not found to print the project data The advanced user can conduct the simulations using the LS DYNA MPP version and hence using a script named submi
61. to aene xod ge egeris Po CU od ape dedegen 36 O A dua aud tun eus eaae bau ad aT see 38 45 Databases and rio 40 4 6 Opening and Saving Projects eo e os qna IR pense sara eee e inn 41 Alle A seal eased oes eer ld a ae ees 41 45 MOTTE COomntandss oe onerosa ey ai hae ena tue ctii esas ea tud bere 42 Example Problems nss cease a C m SE 43 5 1 Fixed Beam with Central Load e ec et eee etin 43 5 1 1 Problem Description si A VARRO URN D REN ED 43 9 152 A vato erie e edens tal tea ote tM Ned Me UE 43 3 13 UNE D10 i EETA EE eve aet dte EEE A EEEE EET E ttu Eee 44 a CONVEESENCE Historicas 44 b Density COntOUEIS i itecto ec diarias ES EN PROS A ERU de i n 45 5 4 Beam using geometry definitions tii t estin Elo go Te gets isa reins 45 321s DUN secede tee eerta eia oce edenda aie tetas tena lenius a 46 5 2 2 iii E S 46 av Bxtr siomand dSUms eerte ietet od deve opti t ida 46 b Extrusion and two sided casting id adios 47 3 9 Borce Displacerient Constraints race cer oho ti 47 5 3 1 Problem Dent e e a AR 47 5 3 2 PU 47 209 95 A ede M ER UBER Se deo n e edit E Ld eM 48 a MOOSE OCICS History M yo isa M TE 48 b Density CODtOUEIS aniio icto pidio cidad 49 O Pi A A A A 49 5 4 1 Problem Det ia 49 5 4 2 iM HR 50 5 4 3 RO 50 a Conyersence Ord a defessi 50 b Density CODIQUES h iie Go er EY P ooa VU DRIN ES eaea E ONT Send ERE E ee TN 5 22
62. um of 100 iterations are used to find the optimal topology and the desired mass fraction is 0 30 The project input data is saved to the file st_project lstasc as provided in the examples distribution Additionally scripts to recreate the database are also provided The project database can be investigated using the scripts use the script in example Error eference source not found to print the project data 5 4 3 Output a Convergence History The convergence history for the statically loaded structure topology optimization example is shown in Figure 5 11 The simulation converged after 28 iterations though only minor changes were noted after 20 iterations As observed before monotonic reduction in the change in topology was observed The total internal energy of the structure also decreased with topology evolution 0 0 Density_Redistribution 0 0 T T 10 20 Iteration Figure 5 11 Convergence history for linear static example 50 b Density Contours The initial and final structures are shown in Figure 5 12 The final structure evolved in a column like structure with wider supports on the faces The shape of the structure also resembled the best stress design LA Figure 5 12 Initial and final density contours Fringe Levels 8201e 10 8201e 10 8 201e 10 8201e 10 8201e 10 8201e 10 8201e 10 8201e 10 8201e 10 8201e 10 8201e 10 Figure 5 13 Evolution of the geometry for statically loaded
63. wed e Match average This is the recommended default which uses the average stress over the surface as the new target stress This results in the removal of stress concentrations e Minimize volume The maximum value on the surface will be selected In this case the weight will be reduced e Minimize stress The minimum value on the surface of the surface will be used as the new target In this case the average stress will be reduced e A user defined value 3 4 Design Variables A design variable is assigned to every node in the design surface 3 5 Filtering of Results A radius based strategy 1s used to identify neighbors In this strategy a virtual sphere of default or user defined radius is placed at the center of an element All elements that are within this sphere are considered the neighbors of the corresponding element The result at an element is computed scaled from its own value and of its neighbors 23 For dynamic problems it was observed that accounting for the history of evolution induces stability Hence the field variable internal energy density of i cell at iteration f is updated by defining a weighted sum on the field variable of three previous iterations 3 6 LS DYNA Modeling Specifics 3 6 1 Surface Definition The design surfaces for shape optimization must be defined using SET SEGMENT 3 6 2 Smooth Transition The transition is defined using node set definitions SET NODE and SET NODE LIST defin
64. y Optimization Theory Methods and Applications Springer Verlag Heidelberg 2003 3 HA Eschenaur N Olhoff Topology Optimization of Continuum Structures A Review Applied Mechanics Review 54 4 331 390 2001 4 GIN Rozvany Topology Optimization in Structural Mechanics Springer Verlag Vienna 1997 5 CA Soto Applications of Structural Topology Optimization in the Automotive Industry Past Present and Future in HA Mang FG Rammerstorfer J Eberhardsteiner eds Proceedings of the Fifth World Congress on Computational Mechanics Vienna 2002 6 MP Bendsoe N Kikuchi Generating Optimal Topologies in Optimal Design using a Homogenization Method Computer Methods in Applied Mechanics and Engineering 71 2 197 224 1988 7 CBW Pedersen Topology Optimization Design of Crushed 2d Frames for Desired Energy Absorption Structural and Multidisciplinary Optimization 25 368 282 2003 8 CA Soto Structural topology optimization from minimizing compliance to maximizing energy absorption International Journal of Vehicle Design 25 1 2 142 163 2001 9 CA Soto Structural Topology Optimization for Crashworthiness International Journal of Numerical Methods in Engineering 9 3 277 283 2004 pau 12 10 CBW Pedersen Crashworthiness Design of Transient Frame Structures Using Topology Optimization Computer Methods in Applied Mechanics in Engineering 193 653 678 2004 11 J Forsberg L Nilsson Topology Optimization i
65. y drilling into a cast part All of the material shown can be considered to be defined using a single PART definition from which it can be noted that the object to the right is considered for design even though it is in the shadow of the 16 object to the left An analyst can enforce a complex behavior by breaking the part up in smaller parts and applying the casting definition only where desired Je Material removal direction Faces selected for material removal Figure 2 2 The faces selected for design in a casting definition are all the faces facing the material removal direction The algorithm will not consider the faces shown in blue Faces not selected 2 3 Convergence The algorithm monitors the mass redistributed per iteration for convergence Ideally this number will be zero for a converged design but in practice it goes down to a small number For solids considering that the SIMP model drives the element to an either fully used or deleted state it is useful to monitor the fraction of elements used for convergence This will converge to the mass fraction of the part if the elements are of uniform size Typically the problem is converged in less than 30 iterations but this is not guaranteed 2 4 Design Variables 2 4 1 Mapping Elements to the Design Variables A design variable is assigned to every finite element in the design parts For geometry constraints the variables are defined only on a subset

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