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CASCA: A Simple 2-D Mesh Generator

1. Menu Description Subdivide Menu Description Subdivision Menu Description Subregions CASCA User s Manual 23 9 20 20 23 6 11 16 16 23 16 16 16 11 18 18 8 12 14 19 20 19 19 8 Menu Description SubRegions T3 Menu Description T6 Menu Description Transition Menu Description Triangular Map Menu Description Tutorial UnJck Menu Description Unspecify Hole Menu Description UnSplit Menu Description W O Corner Pts Menu Description Write Menu Description Write Mesh Menu Description ZOOM Menu Description 18 11 20 23 20 10 13 14 15 21 13 15 21 5 20 18 19 13 20 3 22 3 10 21 22
2. Menu Description 22 Automatic 13 Materials Menu Description 21 Menu Description 18 auxiliary window 1 Mesh 9 10 13 14 Bilinear 3 Side 13 15 21 Menu Description 20 Menu Description 21 Mesh Boundary Bilinear 4 Side 9 14 15 21 Menu Description 21 Menu Description 20 message window 1 Construct mouse 1 Menu Description 21 Num Segments 8 coordinate system Menu Description 19 cursor 1 operations window 1 Data Size Optm 20 Menu Description 16 PAN Delete Menu Description 22 Menu Description 17 program control window 1 END Q4 Menu Description 23 Menu Description 20 Files Q8 CSC 3 Menu Description 20 inp 3 Quadratic Linear vw 3 Menu Description 19 Generate Int Pt 14 Query Geometry 7 11 18 Menu Description 18 19 Menu Description 17 Ratio 9 Get Bezier Menu Description 19 Menu Description 17 Read Get Circle 7 11 Menu Description 22 Menu Description 17 18 Read Grid Get Ellipse Menu Description 22 Menu Description 17 RESET Get Line 8 11 Menu Description 22 Menu Description 17 18 Reset All Grid Menu Description 20 Menu Description 18 22 Restore Grid Center Menu Description 16 Menu Description 16 RESTORE VIEW CASCA User s Manual Page 26 Index Menu Description Revert Ratio Menu Description Right Menu Description SAVE VIEW Menu Description Set Scale Menu Description SNAP Menu Description Spacing X Menu Description Spacing XY Menu Description Spacing Y Menu Description Specify Hole Menu Description Split
3. Type I 4 The material type 1 Linear elastic isotropic 2 Linear elastic orthotropic If Mat Type 1 Young s modulus R 8 Poisson s Ratio R 8 Thickness R 8 Fracture Toughness KIc R 8 Density R 8 If Mat Type 2 Young s modulus in the 1 direction R 8 Young s modulus in the 2 direction R 8 Young s modulus in the 3 direction R 8 Modulus of rigidity in the 12 direction R 8 Poisson s ratio in the 12 direction R 8 Poisson s ratio in the 13 direction R 8 Poisson s ratio in the 23 direction R 8 Rotation angle beta R 8 Thickness R 8 Fracture Toughness KIc in the 1 direction R 8 Fracture Toughness KIc in the 1 direction R 8 Density R 8 Card Set 4 Connectivity Number of cards in set Num Elem FORMAT 1015 Elem Num I 4 Element number Material I 4 Material number for element Elem Nodes 1 I 4 First node number Elem Nodes 8 I 4 Eighth node number Note Node numbers should be specified in a counter clockwise direction starting at any corner node If Elem Nodes has eight non zero elements a Q8 is assumed if 6 non zero elements a T6 is assumed Card Set 5 Nodal Coordinates Number of cards in set Num Nodes Node Number I 4 Node number X Coord R 4 X coordinate of node Y Coord R 4 Y coordinate of node CASCA User s Manual Tutorial Example Page 5 CASCA Examples In this portion of the manual the use of the CASCA program is illustrated The steps necessary to cre
4. default is to use T6 elements unless T3 elements are specified If NO INTERIOR PT is specified only the subdivision points on the region boundary will be used If GENERATE INT PT is specified interior points will be generated to maintain triangle sizes consistent with the segment sizes along each edge Construct Build elements manually one edge at a time May be useful for editing a transition mesh however even this is usually not needed In some versions these options are not implemented Automatic Generate elements for all regions not already meshed The default element type will be used if possible otherwise the T6 element will be used Delete Unmesh a region Point to the region to unmesh and hit Done Subdivision Pts Toggle the subdivision points on and off Mesh Boundary Display only the mesh boundary Go back into Mesh to redisplay the entire mesh Write Mesh Write the current mesh to an output file The file is formatted for FRANC input and will have a inp file extension Read Read a CASCA data file This is a restart file written with the Write option below CASCA User s Manual Page 22 Menu Description E Write Write a CASCA data file The file is formatted for CASCA input using the READ option above and will have a csc file extension Use this for periodic saves during a working session as well as for restart files for later changes Always save your work at the end of a ses
5. ensure that the material was assigned to the proper region Specify Hole Holes must be identified so that the mesh generator will not automatically fill in a hole with elements An unspecifed hole is simply another region Unspecify Hole Change the hole back to a region Grid Toggle the grid on and off Query Click on end points to get coordinates Subregions Sub regions divide regions into smaller regions Sub regions that are part of the same region cannot have different material number assignments Only regions have material assignments Sub regions simplify meshing in some cases and are especially useful for creating transition areas where element size will change significantly from one region to another Use the sub region commands in a similar manner to the Geometry commands Lines Connected See description in Geometry above Get Line See description in Geometry above Get Circle See description in Geometry above Split Divides an edge by inserting a point In most cases splitting is handled automatically for the user In some cases the user might want to control the location of a point This allows the user to do that CASCA User s Manual Menu Description Page 19 ss UnSplit Reverses the Split command Subdivision Pts If the user has already proceeded to the Subdivide menu and subdivided edges this command allows them to be displayed Grid Disp
6. recovers the previously defined number of segments Ratio Quick local change of the ratio only local All Remaining Subdivide all the edges that have not yet been subdivided Reset All Erase all of the subdivision points for all of the edges This is useful to restart the subdivision process rather than re subdividing each edge Grid Displays grid and turns on snap to Mesh After all the regions are subdivided they can be meshed Currently four elements are supported eight noded quadrilateral Q8 four noded quadrilateral Q4 six noded triangle T6 and three noded triangle T3 Q8 Q4 T6 T3 Select the desired element type as the default for mesh generation Right Left UnJck Optm Select the desired element configuration for triangle element generation W O Corner Pts Toggle corner point specification on and off for Bilinear 3 and 4 Side element generation Bilinear 4 Side Generate elements in a region using mapping to four sides of the region CASCA User s Manual Menu Description Page 21 ES Bilinear 3 Side Generate elements in a region using mapping to three sides of the region This uses Bilinear 4 Side and collapses two of the corner points on top of each other Triangular Map Generate elements in a region designed as a triangle The mapping may be better using this method than for the Bilinear 3 Side method Transition Generate elements in an arbitrary shaped region The
7. types Note FRANC2D L does not accept four noded quadrilateral Q4 or three noded triangular T3 elements Use only Q8 or T6 elements GEOCRACK accepts only T6 elements Notes on Using Bilinear 4 Side The Bilinear 4 Side meshing algorithm can be useful even for regions that have more than four edges What is important is that there be a mapping of the region into a quadrilateral with equal subdivisions on opposite edges For instance go to the Subdivide menu and change the subdivisions on the edges of region E as shown in Figure 11 Use 10 subdivisions on the arc 5 Figure 11 Bilinear 4 Side Subdivisions each on the opposite edges and 5 subdivisions with a ratio of 1 3 on the radial lines When you return to the Mesh menu use Bilinear 4 Side to mesh region E Because you changed the subdivisions for region C you will also need to remesh that region Your mesh should look like Figure 12 CASCA User s Manual Tutorial Example Page 15 The important point is that although region E has 5 edges the algorithm can recognize that the two edges with 5 subdivisions can be considered one edge with 10 sides making it possible to use the Bilinear 4 Side algorithm A similar situation can arise when a triangular region is defined by four sides two of the edges form a straight line In this case you can use either Triangular Map if the total number of subdivisions is the same on all sides or Biline
8. 1 Seb Scales eie b o DENT NO m ttu naa e 11 O M 11 SUD OO iniciada dada adan laredo 11 subdivide the EGBEes o usen sen es 12 Mesh the Regions tii A 13 Exploring other Meshing Possibilities eene 13 Other algorithms on Region A taa 13 Other algorithms om Region B sas a cie e ee au A la Coded aee eue deu 13 Other algorithms on Region DA des EOM da dE 14 Using Q6 and T6 as the Default Element Type essen 14 Notes on Using Bilinear ASE E peteret e lutte eid ase ede rada 14 ERICO NICE la N INI A AAA A A AA ARE NUS 15 O A isossa san oe aseesinaine onssas 16 A OO A 16 DAS A as 16 GR c RN TD 16 SPACING AY e 16 PACT X euro eee Ged ae tud gon dace et tte esate 16 SPACE Y MC I H 16 Din A M 16 NR 17 Eines Connecteda a dis oi 17 CASCA User s Manual Table of Contents 111 Gemelas li dash 17 Get Circle O Ies EE 17 E 17 ro Be VATS EEEE ete ite en ere ee 17 Delete eve ceca o OA A eee EY RSA 17 AttribULeS A BAe ies HR ETERNI B PERENNI A 17 Analysis DyDe umi teca ds 17 Materials e itv es oiii t e rtu es 18 NAO 18 U specity Hole e e atii 18 A P POT NOR ORE 18 QUE n 18 SUM PDE ESN OOTAS cs cas Seas enu ea qm NE 18 EME CONN CUCU ooo A s 18 A A 18 Get Circles i NN 18 SD o os
9. CASCA A Simple 2 D Mesh Generator Version 1 4 User s Guide May 1997 Manual and Code Modifications by Daniel Swenson Mark James and Brian Hardeman Kansas State University e Manhattan Kansas CASCA originally written by Paul Wawrzynek and Louis Martha Cornell University e Ithaca New York Page ii Table of Contents Table of Contents TIPO CCOO 5 555 ceessesiisecscussdesebeaiassesdssstcsseacsedscessdedess ARM NERIS 1 WAS CA E D E iae cabins svtegaasbaceecscacecosneloewsunsseseguasonsacancadecounesscoancantepncuuvenees 3 CAS CAS esc BLES AAA ARA A A 3 OV EVV A aveseavasevaacoacabscetaseosenss EE UNUS PRENNE 3 Input inp Fes iiis netten three anh r imn du iod eie hi ebd Ge r6 eo ka aha suia euk ian n quin ada Du ee dues 3 CASCA Exanipl s coe ety A AA FERE Fe Ma IQ d ev dq 5 Plate with Hole Using Symmetry ecce e eee ee eee eee ee eee eese eo setate sete ea setae seta 6 Running the CASCA Promise 6 Set Scale Setting an Appropriate Data pace oooooocnnococonncccooncnononcnonancconnnccnnnnannns 6 Geometry Creating the Problem Outline 5 aite ettet terere tren etta 7 Subregions Dividing the Geometry uie ii pd dada 8 Subdivide Specifying Nodal Points on the Edges sess 8 Mesh Mesh Generation for Plale 4 4 teris etse etas esee deve ba Eee Eo Pho ades 9 Example with Complete Hole and Different Meshing Algorithms 11 R n CASCAG as A ota a G 1
10. ample cd Example1 Then type the path to the CASCA executable for example Casca casca exe You will be asked whether you want a big or small window type s to select small At this point a new CASCA window will be created Please note that the directory in which the executable is saved can be placed in the search path so that CASCA can be run from any directory by typing only casca Aliases and paths in Unix can be used the same way Set Scale Setting an Appropriate Data Space Initially you will have only three options setting the data space Set Scale reading a restart file Read and adjusting your view RESET MAGNIFY ZOOM PAN and SNAP Because we are starting a new problem from scratch we must select Set Scale In the Set Scale page you can change the world coordinates in the operations mesh window By default the window is 12 units wide by 12 units high with a grid spacing of one unit and the center of the grid at X 0 0 Y 0 0 This is satisfactory for our problem so just select RETURN CASCA User s Manual Tutorial Example Geometry Creating the Problem Outline Grid lines are available to simplify geometry construction Select Grid from the menu The X in the middle of the screen marks the center of the grid presently X 0 0 Y 0 0 When the grid is displayed a selection near a grid point will snap to the grid In addition to grid snap to snap to is always active to the ends of lines that the us
11. ar 3 Side if only two sides have the same number of subdivisions If prompted for the corners start with the vertex opposite a side that has a different number of total subdivisions than the other two sides Figure 12 Meshed bilinear 4 side region Final Comments For triangular regions the Triangular Map algorithm requires an equal total number of subdivisions on three sides a side may be composed of more than one edge Bilinear 3 Side is most reliable predictable during automatic meshing if two of the three sides have the same number of subdivisions All three of these meshing algorithms can work on irregularly shaped regions but the user must define an appropriate discretization for each meshing algorithm The Transition meshing procedure can be used where it is impossible or difficult to define regularly shaped regions The algorithm uses a quad tree to recursively subdivide the region into smaller and smaller areas based on the subdivision density on the boundary of the region Adjust the mesh density by adjusting the number and location of segments around the region CASCA User s Manual Page 16 Menu Description Menu Description This section describes each of the menu selections in CASCA Set Scale The Set Scale initializes the scaling for the problem to be defined Initially the window is a 12 x 12 grid Each grid square is one unit wide Data Size The Data Size is the window width and hei
12. ate a mesh are described It is intended that you repeat the steps as they are described The example consists of a plate with a hole as shown in Figure 2 8 0 ay R 4 0 Figure 2 Schematic of plate with hole We will generate meshes for this problem The tutorials use only a subset of the options and features available in CASCA However the examples should give you the confidence to try other features which are described in the menu reference section In the tutorial menu options are indicated by bold text such as Data Size Text that you enter in the program control window are indicated with a typewriter font such as tutorial csc CASCA User s Manual Page 6 Tutorial Example EE Plate with Hole Using Symmetry Running the CASCA Program Begin by running the CASCA program Windows 95 NT Start an MS DOS window select the menus Start Programs MS DOS Prompt In that window go to the directory in which you want to save your analysis for example cd C My DocumentsiExamplel Then type the path to the CASCA executable for example C My DocumentsiCascalcasca exe You will be asked whether you want a big or small window type s to select small At this point a new CASCA window will be created Unix Select the window in which you will start CASCA typically an xterm window started using the command xterm amp In that window go to the directory in which you want to save your analysis for ex
13. cannot be completed at one sitting or to make modifications to an existing mesh A csc file is created when the Write option not Write Mesh is selected in CASCA VIEW vw Files The vw files are used to store views A vw file is created when the SAVE VIEW menu is selected under PAN RESTORE VIEW asks for a vw file name The user gives the vw file name no extensions in the program control window Input inp Files The inp files contain the mesh data used for input to finite element programs These are human readable ASCII files that describe a mesh using nodes and elements in a format similar to those used by most other finite element programs The inp file is written by CASCA using the Write Mesh option The file format is given below TKK KKK KK KK KK KK KK KK KK KK KKK KK OK KK OK KK kck kK OK KKK KK OK KK OK OK KKK kK KK kok INPUT FILE FORMAT TKK KK OK KK KK KKK kK KK kok KK KK KK KK KK KK KK KK KK KK KK OK KK OK KK kck kK OK Card Set 1 Title card Number of cards in set 1 Problem_title Char 40 Title of problem 40 chars Card Set 2 Control card Number of cards in set 1 Num_Nodes 1 4 Num Elem I 4 Num Mat I 4 Number of materials Prob Type 1 4 Analysis type e Axisymmetric 1 Plane Stress 2 Plane Strain 3 Linear Bending CASCA User s Manual Page 4 CASCA Files eee __ Card Set 3 Material Properties Number of cards in set Num_Mat See Card Set 2 FORMAT 15 14F10 2 Mat
14. e hole have five sides However if we think of the arc on the circle as one side the radial lines as each a side and the opposing top and right box edges as one logical side we have a four sided region with equal nodes on opposing sides We mesh this by selecting the Bilinear 4 Side option and clicking in the region A mesh is generated If the program is not able to determine the four corners of the region it prompts you to specify these points Repeat selecting the Bilinear 4 Side option and clicking on the rest of the regions The mesh is shown in Figure 7 Figure 6 After line subdivision CASCA User s Manual Page 10 Tutorial Example Figure 7 Final Mesh CASCA User s Manual Note that it is not necessary to have regions that can be meshed using the Bilinear 4side option For example the Transition mesh option allows you to mesh arbitrary regions with arbitrary subdivision on the sides This option can generate interior nodes or use only the boundary nodes Meshing of the plate is now complete you should RETURN to the main page Create a CASCA restart file by means of the Write option After you select Write you must bring the program control window to the front and type in a file name no extensions Give a name such as plate and a plate csc file will be written A inp file can also be created for FRANC2D L by selecting the Write Mesh option Again specify the name plate and a plate inp file w
15. er has defined From the main menu you should see a Geometry option Geometry is constructed by connecting edges into closed faces Presently only lines circles and arcs are available These allow you to specify the outline of your problem which is the geometry used when generating a mesh Select Page 7 Geometry You are now presented with a number of options that you can Figure 4 Completed outline Figure 3 Circle arc use to specify the outline of your object For the plate with hole problem we will begin with the hole To take advantage of symmetry we will mesh only the right half of the problem First select Get Circle By default the ARC option is active An arc is specified in the counter clockwise direction by three points beginning ending and the center Our grid spacing is one unit but want to specify the arc beginning at X 0 0 Y 0 5 Since we can not just click on the grid we will use the KEYPAD Select KEYPAD to display a numeric pad then use the mouse to input 0 0 for the X coordinate followed by ENT for enter then input 0 5 for Y and ENT again The beginning point for the arc will now be displayed with a square To enter the ending point for the arc again select KEYPAD and enter the coordinates as X 0 0 and Y 0 5 To complete the arc specification we need to indicate the center of the arc We can do this using the grid since the center point lies on the grid Just point t
16. es those in Figure 9 the mesh should look like Figure 10 The automatic meshing algorithm attempts to use the most appropriate meshing scheme for whatever subdivisions have been specified on each face In this case the algorithm has used e Triangular map for region A This is used when there are the same number of subdivisions on each edge of a triangular face e Bilinear 3 side for region B This is used when at least two sides of a triangular face have the same number of subdivisions e Bilinear 4 side for region C Used when opposite edges of a quadrilateral face have matching subdivisions e Transition for region D Transition can mesh regions with arbitrary number of edges and arbitrary subdivisions on each edge You can verify that these are in fact the algorithms that have been used by deleting using Delete each region and then manually selecting the meshing algorithm for each region Figure 10 Meshed regions This should give you identical meshes Exploring other Meshing Possibilities Other algorithms on Region A Select W O Corner Pts it changes to Prompt Corners to force CASCA to ask for a user definition of corners New remesh region A several times using Bilinear 3 Side selecting corner points in different orders Note the effect on the resulting mesh Other algorithms on Region B Try the Triangular Map algorithm on region B it won t work because the number of subdivisions is not equal
17. ght in world coordinates The default data size is 12 units The current number of grid squares remains the same when the data size is changed however the spacing described below does change For example change the data size to 24 units and the spacing changes to 2 units Change the data size to 10 units and the Spacing XY to 2 units and the number of grid squares will be 5 per side Note that the effect of an odd number of grid squares is half a square on each side of the window rather than an even number across the window Grid Center The Grid Center is the position of the center of the default window This allows more permanent mesh translation during model generation This is the reset position for the RESET menu option described below The default center is 0 0 Spacing XY Spacing XY changes the distance for one grid square while maintaining the current Data Size The default spacing is 1 unit Spacing X Spacing X changes the spacing for only the X direction Spacing Y Spacing Y changes the spacing for only the Y direction Restore Restores the default spacings CASCA User s Manual Menu Description Page 17 ee Geometry Element generation can take place only after the problem geometry has been specified Use the geometry commands to create closed geometric regions that can be meshed Different material types must have different geometric regions Lines Connected Draw multiple connected
18. he Attributes menu allows the user to define the analysis type and material properties Material properties are always attached to geometry faces The mesh that will eventually be created on each face will inherit the material property attributes RETURN to the main menu SubRegions Select SubRegions from the main menu Use Figure 8 as a reference to generate the subregions A good way to do this is to first create the three radial lines extending from the hole use Get Line and KEYPAD to give the starting points on the circle then click on a grid point for the ending points Create the horizontal line in the upper half using two Get Line commands clicking on grid points to define the lines a two step definition is needed because CASCA does not allow the insertion of crossing lines Finally complete the diagonal lines and lower horizontal line RETURN to the main menu CASCA User s Manual Page 12 Tutorial Example a Subdivide the Edges Select the Subdivide menu option We will first work only with the edges in the upper right of the figure Use Figure 9 as a reference The edges are subdivided into either 4 or 5 segments In all cases the ratio is 1 1 RETURN to the main menu Figure 8 Plate subdivisions Figure 9 Subdivided edges CASCA User s Manual Tutorial Example Page 13 Mesh the Regions Select the Mesh menu option Select the Automatic menu option If the edge subdivisions match
19. he right of the plate Use the Keypad to specify the first point at X 0 5 and Y 0 then just click on the grid at point X 2 0 and Y 0 0 Select DONE not QUIT to accept this line Repeat just clicking on the grid points to add lines above and below the hole at Y 2 0 and Y 2 0 You now have divided the patched plate into four regions The problem should look like Figure 5 This is all the division that is necessary you should now RETURN to the main menu Note that when we added the new lines we actually split the existing lines defining the geometry Subdivide Specifying Nodal Points on the Edges From the main menu select Subdivide In the subdivision page one specifies nodal densities along the boundaries for all the regions in the structure The arrow on each edge indicates its orientation and is used for a varying density along the edges We will start with the two arcs that now define the hole We will define 10 subdivisions on each quarter circle arc To do this select Num Segments and enter 10 Now click on both arcs defining the circle You should see triangles to indicate the nodal densities Also click on the three radial lines extending from the circle Next select Num Segments and enter 4 Define this nodal density for the two horizontal segments on the top and the two segments on the bottom of the plate To define the two segments on the right edge away from the circle select Num Segments and enter 6 We also want a f
20. ill be created Select END and CONFIRM EXIT to leave CASCA Tutorial Example Page 11 ET Example with Complete Hole and Different Meshing Algorithms This example shows how to define a hole in a body It also demonstrates some of the meshing options available in CASCA We mesh the same plate with a hole used in the previous example Figure 2 The steps are again given below Run CASCA Start the CASCA program Set Scale From the main page select the Set Scale menu This establishes the range of the coordinate system for the problem We will use the default scale so just select RETURN Geometry Select Grid to display the grid Next select Geometry from the main menu First use Lines Connected to generate the rectangular plate this could also be done using multiple Get Line definitions To define the hole select Get Circle click on whole ARC to define a whole circle the active option is given in capital letters We must now define a point on the circle Often the user could just click on a grid point but since we want a hole with a radius of 0 5 we will use the keypad Select KEYPAD and specify X 0 5 Y 0 0 Now define the center of the hole by clicking on the center grid point Finally select DONE to indicate the definition is complete At this time a circle has been defined but it is still necessary to define this as a hole not just a circular region To define the hole select Specify Hole and click inside the hole T
21. ily available as menu buttons for quick access RESTORE VIEW Allows user to access a saved view file The file name must be input in the program control window ZOOM See above description MAGNIFY See above description SNAP Write a PostScript output file of the current mesh or geometry model displayed The file is named grax ps where x is the number of the output file for this session Move each file to a new name or a new directory at the end of each session to prevent gra0 ps for the next session from overwriting gra0 ps from the previous session END Exit the program A restart file is NOT automatically written Use Write to save your work before hitting END if you expect to restart later CASCA User s Manual Page 24 Acknowledgments Acknowledgments CASCA was originally developed by Paul Wawrzynek and Louis Martha at Cornell University This work was done under the direction of Prof Anthony Ingraffea who has focused on numerical methods and crack growth Brian Hardeman modified the gr aphics routines so that CASCA could be ported to Windows 95 NT Mark James cleaned up some bugs and added some useful features CASCA User s Manual Acknowledgements Page 25 Index Acknowledgments 24 Introduction 1 All Remaining Left Menu Description 20 Menu Description 20 Analysis Type Lines Connected 7 11 Menu Description 17 Menu Description 17 18 Attributes 11 MAGNIFY Menu Description 17
22. iner mesh near the X axis so select Ratio and enter 1 and 2 to define a 1 2 ratio Click on the lower right line segment Next since the arrow of the upper right line segment is towards the X axis select Revert Ratio and click on that line segment Finally return the ratio to 1 1 specify 5 divisions and CASCA User s Manual Figure 5 Subregions added Tutorial Example Page 9 SS In select All Remaining to finish the subdivision of all lines The plate should now look like Figure 6 As illustrated the Ratio option can be used to specify a mesh with a density that varies along a line For instance selecting Ratio and entering 1 and 2 means the mesh size will vary a factor of two in the direction of the arrow defining the line segment The Revert Ratio option can be used to change the arrow direction Mesh Mesh Generation for Plate Return to the main page The next step is to generate meshes for the four regions Select the Mesh option to move to the mesh page The first two options on this page allow you to select element types The defaults are Q8 quadrilateral elements and T6 triangular elements You must use these second order elements with FRANC2D L All four regions of the patched plate can be meshed with the bilinear four sided meshing algorithm Bilinear 4 Side This algorithm requires a rectangular region with equal numbers of nodes on opposing sides The two regions adjacent to th
23. lays grid and turns on snap to Query Click on end points to get coordinates Subdivide Specify the distribution of elements in a region or sub region Before a region can be meshed the meshing algorithm must know the number of elements to place along each edge of a region or sub region Num Segments Number of elements along a sub region edge The default number of segments is four Ratio The ratio of the longest segment to the shortest segment along an edge The arrows on the edges denote the ratio direction The ratio is always the length of the segment at the tail of the edge to the length of the segment at the head of the edge The default ratio is one Quadratic Linear Not active Subdivide Specify one or more edges to subdivide with the current number of segments and the current ratio Use Revert Ratio to change the ratio for the next subdivision To edit the number of subdivision points for an edge simply re subdivide the edge with a different number of segments or a different ratio Use the Reset All option described below to erase all of the subdivision points CASCA User s Manual Page 20 Menu Description EE Revert Ratio If the arrow of an edge is in the opposite direction that you want the ratio to operate select revert ratio before selecting the edge for subdivision Num Segments A quick way to change the number of subdivisions The number is only local returning to the Subdivide menu
24. lines Each segment can act as a side to a geometric region Get Line Draw one line segment The line segment need not initially be attached to anything however before meshing can take place all segments must be part of some closed region Get Circle Draw an ARC or a WHOLE circle The option in all capital letters is in effect ARC specify two points on the ends of the arch then the arc center point The arc will be drawn clockwise from the first point to the second point Use the mouse to move the center point to adjust the arc radius WHOLE specify a point on the edge of the circle then specify the circle center Use the mouse to move the center point to adjust the circle orientation and size Get Ellipse Not implemented Get Bezier Not implemented Delete Select an item then hit Done Repeat for more items Attributes The analysis type and material types can be defined here Usually this will take place before meshing however region material types can be changed after meshing as long as the regions were defined before meshing Analysis Type Analysis type zero is Axisymmetric type one is Plane Stress and type two is Plane Strain CASCA User s Manual Page 18 Menu Description 5_I_R RD 2 _ DR QQ L QQQ Materials Multiple materials may be defined and may be either isotropic or orthotropic Use the Attach option to change the material definition for a given region Use the Check Region option to
25. o PS dio dita dius aat oid vases E tue mud Uma 18 UnSplt st ii seal eee aim ieee 19 S bdiyision Pis oem e E de GAS 19 Sii ML T 19 gu M 19 SUD K G eie tO E E 19 IN Segriellis c rues cieli tp e Messen die iade din itia t a t eed 19 hene E 19 Quadratic LIaneat i tbv b ettet 19 SUDO VIGO 1e ete lee a luteis Ute le cct nq 19 Revert Ratio i A debet IS E EE 20 IN ti segments ul c ee den e e Pn RI REN ta E AST E E eei Pere a 20 ROO A iio 20 All un dices 20 Reset O 20 Ss Me HMM 20 Mesias aid TETUR 20 108 0d T6 Tia ia o rbd mtis huc e i 20 Right Left Unlek OW ooa c poppe n eel sate oes UR 20 W O Corner Plica nee RW tette tede eT eri s 20 Bilincar 4 510655 e m LEM pU 20 Bilinear 3 der er tetti re ter tiet ba reet i een 21 Triangular Map e 21 o naa a nhieu ease tats uin ENS 21 Constructs AAA d a EI UN c hs 21 Alto mac e tutus 21 Delta dada TQ 21 Subdivision PIS 22 2 9 4 002 AAA SA 21 MeshborOd Vii AA A Ese oi r E Een aii 21 Write Mesina dica dal lis 21 CASCA User s Manual Page iv Table of Contents VRE A A ox ap i M wired Tc pE T B A A uieescse sedes cete esce eaa oc eee esae ce pea eee kao ao Ce aL RR Osee e asa e Re ee pa Deae ce Deos Ge SERE oL Re Ras de Nan A A O IA Iura AA A RS RR RR CASCA U
26. o the center of the grid and click with the mouse The arc will be displayed Select DONE to indicate that you are finished defining the arc If you select QUIT the circle will be ignored The display should be as shown in Figure 3 To complete the plate outline we will use the Lines Connected option Select this option To start the connected lines click on the top point of the circle arc Then move up to the grid location corresponding to X 0 0 Y 4 0 click move to the right 2 grid intersections to X 2 0 Y 4 0 click down 8 grid intersections to X 2 0 Y 4 0 click to the left 2 grid intersections to X 0 0 Y 4 0 click and finally to the lower point of the circle arc and CASCA User s Manual Page 8 Tutorial Example click To leave this mode of adding line segments select DONE The display should be like Figure 4 This completes the border definition RETURN to the main page Subregions Dividing the Geometry From the main menu you should now notice more options are available The next one we will use is Subregions This allows you to break your object up into a number of simpler regions that are more convenient for meshing In the plate problem we will divide the plate and hole into four separate regions for meshing Select Subregions and you will see a number of options that are similar to those available on the geometry page Select the Get Line option and specify a line from the right of the hole to the border on t
27. on all three edges of the region Make sure you delete the mesh in region B Now try Transition meshing with Generate Int Pt generate interior points CASCA User s Manual Page 14 Tutorial Example E_R QR RR M _QQCEEEQ This will create a mesh using triangular elements Leave the mesh and select Transition again Again select Generate Int Pt but now click at several locations inside region B then select DONE Each point you clicked on now becomes a node This allows you to refine meshes in desired areas Other algorithms on Region D Return to the Subdivide menu and change the number of subdivisions on region D so that opposite edges of the quadrilateral have an equal number of subdivisions Now remesh region D using Bilinear 4 Side Note that when the subdivisions on an edge change the mesh that depends on the subdivisions will be deleted This hierarchical dependence is also true for other entities For instance changing the geometry of the problem Before you quit try deleting a geometry or subregion edge and check the effect on the subdivisions and the mesh Using Q8 and T6 as the Default Element Type Mesh region C using Bilinear 4 Side Now change the current element type to T6 six noded triangle by selecting the T6 menu option Mesh region C again using Bilinear 4 Side Experiment with meshing region C using the Right Left UnJck and Optm menu options these only apply to regions meshed with T3 or T6 element
28. put in the program control window The coordinate system used within the program is always fixed so that the x coordinate is horizontal increasing to the right and the y coordinate is vertical increasing going up CASCA User s Manual Page 2 Introduction 5 CASCA was originally developed by Paul Wawrzynek and Louis Martha at Cornell University as a test bed for a hierarchical data base that was later implemented in FRANC3D However it has proven to be a useful tool so it has continued to live beyond its initial application The fact that CASCA was originally written in 1987 is reflected in the menu structure The menus were designed for display using low level XWindows commands A rewrite of these low level commands has allowed us to port the code to Windows 95 NT in a simple fashion The advantage is that the Unix and Windows 95 NT versions are identical the disadvantage is that the program does not use dialog boxes or pull down menus We hope you will find the interface adequate if not ideal CASCA User s Manual CASCA Files Page 3 CASCA Files Two types of files are generated or used by the CASCA program The contents of these files and their uses are discussed here The s in the text are to be replaced by file names chosen by the analyst CASCA csc Files The csc files are restart files generated by CASCA A restart file allows one to save current work and recover it later This is convenient when a mesh description
29. ser s Manual Introduction Page 1 Introduction CASCA is an interactive program for the creation of two dimensional continuum finite element meshes Its capabilities include three and six noded triangles and four and eight noded quadrilaterals This manual is intended to be a simple description of the basic features of CASCA It includes a brief tutorial hints on addressing common problems and menu descriptions Within the CASCA program all user commands are made by clicking the mouse on one of the options displayed in the menu window Figure 1 A message window is always present to prompt the user on the next step in the requested procedure Entry into CASCA and I O operations invoked during the running of CASCA are made from the program control window This is the window from which the program was started An auxiliary window is used for attribute definition auxiliary window title window command options operations window program control window Scasca Figure 1 The CASCA window system The CASCA program uses two types of cursors The normal cursor has the shape of an arrow When you see this cursor it means that the program is waiting for you to select a menu option or some other graphical input The second cursor is a stylized wristwatch When you see this cursor it means that either the program is processing data e g generating a mesh or it is waiting for in
30. sion CASCA does NOT save for you Grid Toggle the grid on and off Read Grid If the user has previously saved a mesh file this can be read in to define a grid This can be useful if the user wants to make modifications to previous work but does not have a saved csc file Reading in a mesh as a grid allows the user to quickly rebuild the geometry by taking advantage of grid snap to RESET Reset the window to the startup view after Magnify Zoom or Pan described below MAGNIFY Specify the new lower left and upper right corners of the display area The current display perspective will be retained ZOOM Magnify the display area keeping the same window center Use the to enlarge the image size and the to reduce the image size PAN The PAN menu allows the user to move the model inside the window The pointer in the window acts as a potentiometer Place the pointer just above center in the window and the viewing window will move up slightly Place the pointer near the top of the window and the viewing window will move up much farther Similar concepts apply for left right and down PAN also activates many of same view control menus available at a higher level These include RESET See above description CASCA User s Manual Menu Description Page 23 See SAVE VIEW The current view is saved in a vw file The user must type in the view file name in the program control window The views are temporar

CASCA: A Simple 2-D Mesh Generator

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