Pyramid elements C3D5 & C3D13

fgr · October 20, 2023, 9:19am

I have been fiddling with implementing pyramid elements into ccx_2.21 so it would be nice if anybody would help with any kind of testing of the elements. So far it’s only pure mechanical functionality in some unknown limited range due to the complexity of testing any different combination.

How to install

Make a backup of the files “Makefile.inc” & “gauss.f” in your ccx_2.21 source directory/folder. These files are the only files which will be overwritten.
Delete all object files “*.o” in your source folder
Copy all files from the pyramid source folder into your source folder and recompile your CCX program

PyramidSource_ccx_2.21.zip

The source files have been compiled and tested in both environment, Debian Linux and Window 10, so case of any problems in compiling I’ll will not be able to help.

How to uninstall

Delete all object files “*.o” in your source folder
Delete source files with the “+” sign, “+.”
Restore your original “Makefile.inc” & “gauss.f” files
Recompile the original CCX program

Pyramid elements installed

C3D5, a 5 node element based on the Bergot shape formulation with full integration.
C3D13 a 13 node element based on Bedrosian shape formulation with full integration.
C3D13F a 13 node element based on Felippa shape formulation also with full integration.

One could ask, why both Bedrosian and Felippa shape formulation for the 13 node pyramid, why my answer would be, since the stiffness are slightly different between them I found it interesting to have the ability to test against each other and since the time consumption adding an extra nearly similar element was minimal compared to total time consumption tracing through hole program finding places to engaged I choose to implement both type.

The zip file contains a source folder with all the changed ccx source files plus test_tool folder with some ccx input files used for test/validation and comparison between standard ccx elements and the pyramid elements. Further the folder also holding a modification of the python script “ccx2paraview.py” capable of export pyramid ccx output to paraview input ex. “python ccx2paraview.py C3D13beam.frd vtu”

The fully functionality of the pyramid elements are a little difficult to describe since it’s only the datasets in the test_tool folder which have been tested.

For a general test and use with contact and friction it’s important to ensure that sufficient contact elements/nodes are engaged to having the friction force to converge so to obtain converged friction in the used dataset it will be necessary to subdivide elements for having sufficient elements/nodes engaged.

The folder test_tools hold different simple pyramid dataset for test and compare with standard ccx element. Following have been tested:

C3D13beam.inp , nlgeom, *cload, perturbation, *frequency
C3D13Fbeam.inp , nlgeom, *cload, perturbation, *frequency
C3D13beamG.inp , nlgeom, *dload, gravity
C3D13cubeC.inp, static, *dload, centrifugal
C3D13pendul.inp, nlgeom, *dynamic, *dload, gravity
C3D13dload.inp, static, *dload, uniform_pressure
C3D13frictionNS.inp, static, *dload, uniform_pressure, linear contact node to surface
C3D13frictionNS.inp, static, *dload, uniform_pressure, linear contact surface to surface
dynC3D13exp.inp, *dynamic, explicit, *cload

topology
PyramidCube
Bending

lucas_bueno · October 20, 2023, 10:56pm

Thanks for sharing! Adding new elements is very interesting and I would really like to test them in the future. For this, I have some questions:

Which mesh software can be used to create this type of element?
Is there any executable file available? I am not familiar with such a compiling process myself.

I want to test them in buckling cases with analytical solutions that I’ve been testing in the last few months.

fgr · October 21, 2023, 2:51am

@lucas_bueno , Thanks for your reply

In fact it’s only in some special cases it can be a huge advantage to use the pyramid as a connection between the brick and the tetrahedron so it will probably only be some few high end commercial mesher programs which are capable of doing this automatic.
I’ll need generate a buckling test case to trace and observe if it should be necessary to apply additional code for handling this case also before. After then I’ll could supply with a windows version running the spooles solver if you still should be interested in doing test with the pyramid elements.

vicmw · October 21, 2023, 9:12am

Great work!

If you publish a Windows Spooles .exe, I’m happy to make some test cases and can generate meshes with refined pyramids (mixed with tets), mesh transitions, and on-axis triangles revolved into solids (another useful application).

Perhaps you could identify a list of features that whose cases would provide full code coverage? It’s a shame when good features have bugs in combination with random other features.

Did you know you can already do pyramids in CCX by collapsing one face of a hex element? They won’t be as good as these though.

NorbertH · October 21, 2023, 3:01pm

@fgr ohhhh yeah! that’s one thing i planned to implement for calculix if no one does it. so i can remove this from my bucket list. i will test this as soon as i can. if you need help with mesh creation for testing, just write me.

do you plan to make a pull request on github to get this into the official calculix?

@lucas_bueno for mesh creation you could use cubit. its easy to make mesh transition vom hex to tet with pyramids. i will see to implement the pyramids export into the calculix plugin with the next update.

jbr · October 21, 2023, 3:10pm

Gmsh may also have the capability to create pyramids from their manual:

Gmsh’s mesh module regroups several 1D, 2D and 3D meshing algorithms:

The 2D unstructured algorithms generate triangles and/or quadrangles (when recombination commands or options are used). The 3D unstructured algorithms generate tetrahedra, or tetrahedra and pyramids (when the boundary mesh contains quadrangles).

The 2D structured algorithms (transfinite and extrusion) generate triangles by default, but quadrangles can be obtained by using the recombination commands or options. The 3D structured algorithms generate tetrahedra, hexahedra, prisms and pyramids, depending on the type of the surface meshes they are based on.

SergioP · October 21, 2023, 10:52pm

That’s interesting. I´m not a fan of pyramids elements, have never used in the past but I know that can be used to create a transition from hexas to tets. Siemens NX and Salome can create such kind of transitions

Attached an example mesh in med and other formats available from Salome including pyramids in case you want to try it. I just noticed that when the mesh is exported in unv format, pyramids elements are skipped

You could use Meshio to translate from med to inp maybe.

https://drive.google.com/file/d/15hfopD8DIvv3oYJYtE5ppIltBfHH86-H/view?usp=share_link

rafal.brzegowy · October 22, 2023, 6:19pm

Exe file from @fgr source, (spooles, PRADISO, PaStiX):

fgr · October 23, 2023, 2:45pm

@rafal.brzegowy
Thanks for distribute a version including the pyramid elements I have also include a version in my link, but this version does only include the spooles an pardiso solvers.

@vicmw
When I have traced through the code ex. for the functionality of the wedge elements, it seems like the fully functionality hasn’t been implemented form the start but have been added stepwise and probably of more than one person, so what I would like to have tested are all functionality within the mechanical area which not already have been tested in my small test described by input files and included in the test_tool folder.

What I have tested so far have only been based on pyramid with a normalized size of 2x2x1 where the performance seem to be not that bad at all compared to the C3D20 but it would nice to know a little about the performance away from the normalized dimensions.

I didn’t know it was possible to collapse a C3D8 or C3D20 into a pyramid in ccx. Carlos Felippa’s shape formulation is based on a collapsed brick so based on this it could make sense the problem consist in that the integration points and weights aren’t changed in ccx in according to the reduced brick.

I know that ANSYS use same input card for both brick and pyramid with the topology expectation that index 5-8 & 13-16 should hold the same node number. I’m not any Knowles about why ANSYS is using 14 integration points nor the shape formulation in the ANSYS theory manual which obviously is missing some brackets.

@NorbertH
I’m from another decade Learned and wrote my first program on a teletyper terminal with paper roll, so I don’t very much about github and push request but if anyone find my code worthy for the official calculix I will be happy just to know that other finds it usefull.

vicmw · October 24, 2023, 6:38am

C3D5 doesn’t seem to work right with *DSLOAD.

It should be uniform tension in the Y direction, with some Poisson effect, but instead it bends in the Z direction.

This is with @ rafal.brzegowy 's build

*NODE
1,0,0,0
2,1,0,0
3,1,1,0
4,0,1,0
5,0,0,1
6,1,0,1
7,1,1,1
8,0,1,1
9,0.5,0.5,0.5
*ELEMENT,TYPE=C3D5
1,1,4,8,5,9
2,1,2,3,4,9
3,6,5,8,7,9
4,2,1,5,6,9
5,3,2,6,7,9
6,4,3,7,8,9
*ELSET,ELSET=Default
1
2
3
4
5
6
*SURFACE,NAME=pressure_faces
6,S5
*MATERIAL,NAME=Material
*ELASTIC,TYPE=ISOTROPIC
200000000000,0.3
*SOLID SECTION,ELSET=Default,MATERIAL=Material
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
2,1,,0
2,2,,0
2,3,,0
5,1,,0
5,2,,0
5,3,,0
6,1,,0
6,2,,0
6,3,,0
*STEP
*STATIC
*DSLOAD
pressure_faces,P,-1000000
*NODE FILE
U
*END STEP

vicmw · October 24, 2023, 9:28am

Tests with C3D13 in linear static with curved and high aspect ratio elements. It looks very good, similar to C3D20 and much better than collapsed C3D20 pyramids.

C3D13_thin.inp

*NODE
1,0,0,0
2,0.001,0,0
3,0.001,0.001,0
4,0,0.001,0
5,0,0,5E-05
6,0.001,0,5E-05
7,0.001,0.001,5E-05
8,0,0.001,5E-05
9,0.0005,0.0005,2.5E-05
10,0.0005,0,0
11,0.001,0.0005,0
12,0.0005,0.001,0
13,0,0.0005,0
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29,0,0.001,2.5E-05
30,0.002,0,0
31,0.003,0,0
32,0.003,0.001,0
33,0.002,0.001,0
34,0.002,0,5E-05
35,0.003,0,5E-05
36,0.003,0.001,5E-05
37,0.002,0.001,5E-05
38,0.0025,0,0
39,0.003,0.0005,0
40,0.0025,0.001,0
41,0.002,0.0005,0
42,0.002,0,2.5E-05
43,0.003,0,2.5E-05
44,0.003,0.001,2.5E-05
45,0.002,0.001,2.5E-05
46,0.0025,0,5E-05
47,0.003,0.0005,5E-05
48,0.0025,0.001,5E-05
49,0.002,0.0005,5E-05
*ELEMENT,TYPE=C3D13
1,1,4,8,5,9,13,29,19,26,14,17,24,23
2,1,2,3,4,9,10,11,12,13,14,15,16,17
3,6,5,8,7,9,18,19,20,21,22,23,24,25
4,2,1,5,6,9,10,26,18,27,15,14,23,22
5,3,2,6,7,9,11,27,21,28,16,15,22,25
6,4,3,7,8,9,12,28,20,29,17,16,25,24
*ELEMENT,TYPE=C3D20
7,30,31,32,33,34,35,36,37,38,39,40,41,46,47,48,
49,42,43,44,45
*ELSET,ELSET=Default
1
2
3
4
5
6
7
*MATERIAL,NAME=Material
*ELASTIC,TYPE=ISOTROPIC
50000000000,0.4
*SOLID SECTION,ELSET=Default,MATERIAL=Material
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
4,1,,0
4,2,,0
4,3,,0
5,1,,0
5,2,,0
5,3,,0
8,1,,0
8,2,,0
8,3,,0
13,1,,0
13,2,,0
13,3,,0
19,1,,0
19,2,,0
19,3,,0
26,1,,0
26,2,,0
26,3,,0
29,1,,0
29,2,,0
29,3,,0
30,1,,0
30,2,,0
30,3,,0
33,1,,0
33,2,,0
33,3,,0
34,1,,0
34,2,,0
34,3,,0
37,1,,0
37,2,,0
37,3,,0
41,1,,0
41,2,,0
41,3,,0
42,1,,0
42,2,,0
42,3,,0
45,1,,0
45,2,,0
45,3,,0
49,1,,0
49,2,,0
49,3,,0
*STEP
*STATIC
*CLOAD
3,3,-0.004166666666667
2,3,-0.004166666666667
6,3,-0.004166666666667
7,3,-0.004166666666667
11,3,0.01666666666667
27,3,0.01666666666667
21,3,0.01666666666667
28,3,0.01666666666667
31,3,-0.004166666666667
32,3,-0.004166666666667
35,3,-0.004166666666667
36,3,-0.004166666666667
39,3,0.01666666666667
43,3,0.01666666666667
44,3,0.01666666666667
47,3,0.01666666666667
*NODE FILE,GLOBAL=YES
U
*EL FILE
S,NOE
*END STEP

C3D13_curved.inp

*NODE
1,0.5,0,0
2,0.6,0,0
3,0.4242640687119,0.4242640687119,0
4,0.3535533905933,0.3535533905933,0
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6,0.6,0,0.05
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27,0.478095027074,0.3194528839863,0.0375
28,0.6,0,0.025
29,0.4242640687119,0.4242640687119,0.025
30,0.1121769351593,0.5639515362319,0.0125
31,3.673819061467E-17,0.6,0.025
32,3.673819061467E-17,0.6,0
33,3.061515884556E-17,0.5,0
34,3.367667473012E-17,0.55,0.05
35,0.2296100594191,0.5543277195068,0.05
36,3.673819061467E-17,0.6,0.05
37,3.061515884556E-17,0.5,0.05
38,0.2104758878008,0.5081337428812,0.025
39,0.1913417161825,0.4619397662556,0
40,3.061515884556E-17,0.5,0.025
41,0.1913417161825,0.4619397662556,0.05
42,0.3194528839863,0.478095027074,0.0375
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45,0.1024224190585,0.5149122722117,0.0375
46,0.2916743723353,0.4365215464588,0.0375
47,0.1121769351593,0.5639515362319,0.0375
48,0.2296100594191,0.5543277195068,0
49,3.367667473012E-17,0.55,0
50,0.3194528839863,0.478095027074,0.0125
51,0.5,0,0.2
52,0.6,0,0.2
53,0.4242640687119,0.4242640687119,0.2
54,0.3535533905933,0.3535533905933,0.2
55,0.5,0,0.25
56,0.6,0,0.25
57,0.4242640687119,0.4242640687119,0.25
58,0.3535533905933,0.3535533905933,0.25
59,0.55,0,0.2
60,0.5543277195068,0.2296100594191,0.2
61,0.3889087296526,0.3889087296526,0.2
62,0.4619397662556,0.1913417161825,0.2
63,0.5,0,0.225
64,0.6,0,0.225
65,0.4242640687119,0.4242640687119,0.225
66,0.3535533905933,0.3535533905933,0.225
67,0.55,0,0.25
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69,0.3889087296526,0.3889087296526,0.25
70,0.4619397662556,0.1913417161825,0.25
71,0.2296100594191,0.5543277195068,0.25
72,3.367667473012E-17,0.55,0.25
73,3.673819061467E-17,0.6,0.2
74,3.061515884556E-17,0.5,0.2
75,3.673819061467E-17,0.6,0.225
76,3.061515884556E-17,0.5,0.225
77,3.673819061467E-17,0.6,0.25
78,3.061515884556E-17,0.5,0.25
79,0.1913417161825,0.4619397662556,0.25
80,0.2296100594191,0.5543277195068,0.2
81,3.367667473012E-17,0.55,0.2
82,0.1913417161825,0.4619397662556,0.2
*ELEMENT,TYPE=C3D13
1,1,4,8,5,9,10,11,12,13,14,15,16,17
2,1,2,3,4,9,18,19,20,10,14,21,22,15
3,6,5,8,7,9,23,12,24,25,26,17,16,27
4,2,1,5,6,9,18,13,23,28,21,14,17,26
5,3,2,6,7,9,19,28,25,29,22,21,26,27
6,4,3,7,8,9,20,29,24,11,15,22,27,16
7,4,33,37,8,38,39,40,41,11,43,44,45,46
8,4,3,32,33,38,20,48,49,39,43,50,30,44
9,7,8,37,36,38,24,41,34,35,42,46,45,47
10,3,4,8,7,38,20,11,24,29,50,43,46,42
11,32,3,7,36,38,48,29,35,31,30,50,42,47
12,33,32,36,37,38,49,31,34,40,44,30,47,45
*ELEMENT,TYPE=C3D20
13,51,52,53,54,55,56,57,58,59,60,61,62,67,68,69,
70,63,64,65,66
14,54,53,73,74,58,57,77,78,61,80,81,82,69,71,72,
79,66,65,75,76
*ELSET,ELSET=Default
1
2
3
4
5
6
7
8
9
10
11
12
13
14
*MATERIAL,NAME=Material
*ELASTIC,TYPE=ISOTROPIC
200000000000,0.3
*SOLID SECTION,ELSET=Default,MATERIAL=Material
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
2,1,,0
2,2,,0
2,3,,0
5,1,,0
5,2,,0
5,3,,0
6,1,,0
6,2,,0
6,3,,0
13,1,,0
13,2,,0
13,3,,0
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63,1,,0
63,2,,0
63,3,,0
64,1,,0
64,2,,0
64,3,,0
67,1,,0
67,2,,0
67,3,,0
*STEP
*STATIC
*CLOAD
33,3,-416.6666666667
32,3,-416.6666666667
36,3,-416.6666666667
37,3,-416.6666666667
49,3,1666.666666667
31,3,1666.666666667
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40,3,1666.666666667
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74,3,-416.6666666667
77,3,-416.6666666667
78,3,-416.6666666667
81,3,1666.666666667
75,3,1666.666666667
76,3,1666.666666667
72,3,1666.666666667
*NODE FILE,GLOBAL=YES
U
*EL FILE
S,NOE
*END STEP

fgr · October 24, 2023, 2:12pm

@vicmw , thanks for your input, it really helps a lot.
I have updated the original link with the new modified code additional I have also include an executable ccx.
I need to admire, that quite early lost focus on the C3D5 and concentrated on the C3D13 instead. I was a little impressed when I experienced that the Bedrosian C3D13 performed a little better compared to C3D20 than the similarity I got tested in ANSYS
Hereby a comparison of C3D5 vs C3D8 for *DLOAD/DSLOAD

Which software are You using for the graphics ?

vicmw · October 25, 2023, 1:25am

Quick fix @fgr!

Here’s another test of large rotations with nonlinear. I wanted to make sure the stress rotates properly, which it does. Each beam has a 1 GN force on it’s 1m^2 end face and we correctly get a 1 GPa stress in the Y direction, even though it’s rotated 90 degrees from the undeformed orientation. The new pyramids are have better displacement than collapsed hex pyramids.

I’m using a modified version of Mecway that can read and write these pyramid elements.

*NODE
1,0,0,0
2,2,0,0
3,2,1,0
4,0,1,0
5,0,0,1
6,2,0,1
7,2,1,1
8,0,1,1
9,1,0.5,0.5
10,0,0.5,0
11,0,1,0.5
12,0,0.5,1
13,0,0,0.5
14,0.5,0.25,0.25
15,0.5,0.75,0.25
16,0.5,0.75,0.75
17,0.5,0.25,0.75
18,1,0,0
19,2,0.5,0
20,1,1,0
21,1.5,0.25,0.25
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23,1,0,1
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28,2,0,0.5
29,2,1,0.5
30,23.5,0.25,0.75
31,4,0,0
32,4,1,0
33,23.5,0.75,0.75
34,24,0,0.5
35,4,0,1
36,4,1,1
37,24,1,0.5
38,3,0.5,0.5
39,29.5,0.75,0.75
40,26,0,0
41,26,1,0
42,30,0,0.5
43,2.5,0.25,0.25
44,2.5,0.75,0.25
45,2.5,0.75,0.75
46,2.5,0.25,0.75
47,3,0,0
48,4,0.5,0
49,3,1,0
50,3.5,0.25,0.25
51,3.5,0.75,0.25
52,3,0,1
53,3,1,1
54,4,0.5,1
55,3.5,0.25,0.75
56,3.5,0.75,0.75
57,4,0,0.5
58,4,1,0.5
59,30,1,0.5
60,6,0,0
61,6,1,0
62,26,0,1
63,26,1,1
64,6,0,1
65,6,1,1
66,31.5,0.75,0.25
67,5,0.5,0.5
68,25,0.5,0.5
69,32,0,0
70,32,1,0
71,31,0,1
72,4.5,0.25,0.25
73,4.5,0.75,0.25
74,4.5,0.75,0.75
75,4.5,0.25,0.75
76,5,0,0
77,6,0.5,0
78,5,1,0
79,5.5,0.25,0.25
80,5.5,0.75,0.25
81,5,0,1
82,5,1,1
83,6,0.5,1
84,5.5,0.25,0.75
85,5.5,0.75,0.75
86,6,0,0.5
87,6,1,0.5
88,31,1,1
89,8,0,0
90,8,1,0
91,24.5,0.25,0.25
92,24.5,0.75,0.25
93,8,0,1
94,8,1,1
95,24.5,0.75,0.75
96,7,0.5,0.5
97,24.5,0.25,0.75
98,25,0,0
99,26,0.5,0
100,25,1,0
101,6.5,0.25,0.25
102,6.5,0.75,0.25
103,6.5,0.75,0.75
104,6.5,0.25,0.75
105,7,0,0
106,8,0.5,0
107,7,1,0
108,7.5,0.25,0.25
109,7.5,0.75,0.25
110,7,0,1
111,7,1,1
112,8,0.5,1
113,7.5,0.25,0.75
114,7.5,0.75,0.75
115,8,0,0.5
116,8,1,0.5
117,25.5,0.25,0.25
118,10,0,0
119,10,1,0
120,25.5,0.75,0.25
121,25,0,1
122,10,0,1
123,10,1,1
124,25,1,1
125,9,0.5,0.5
126,26,0.5,1
127,25.5,0.25,0.75
128,25.5,0.75,0.75
129,26,0,0.5
130,8.5,0.25,0.25
131,8.5,0.75,0.25
132,8.5,0.75,0.75
133,8.5,0.25,0.75
134,9,0,0
135,10,0.5,0
136,9,1,0
137,9.5,0.25,0.25
138,9.5,0.75,0.25
139,9,0,1
140,9,1,1
141,10,0.5,1
142,9.5,0.25,0.75
143,9.5,0.75,0.75
144,10,0,0.5
145,10,1,0.5
146,26,1,0.5
147,12,0,0
148,12,1,0
149,32,0,1
150,28,0,0
151,12,0,1
152,12,1,1
153,28,1,0
154,11,0.5,0.5
155,32,1,1
156,32,0.5,1
157,28,0,1
158,28,1,1
159,10.5,0.25,0.25
160,10.5,0.75,0.25
161,10.5,0.75,0.75
162,10.5,0.25,0.75
163,11,0,0
164,12,0.5,0
165,11,1,0
166,11.5,0.25,0.25
167,11.5,0.75,0.25
168,11,0,1
169,11,1,1
170,12,0.5,1
171,11.5,0.25,0.75
172,11.5,0.75,0.75
173,12,0,0.5
174,12,1,0.5
175,31,0.5,0.5
176,14,0,0
177,14,1,0
178,27,0.5,0.5
179,31.5,0.25,0.75
180,14,0,1
181,14,1,1
182,31.5,0.75,0.75
183,13,0.5,0.5
184,32,0,0.5
185,32,1,0.5
186,26.5,0.25,0.25
187,26.5,0.75,0.25
188,12.5,0.25,0.25
189,12.5,0.75,0.25
190,12.5,0.75,0.75
191,12.5,0.25,0.75
192,13,0,0
193,14,0.5,0
194,13,1,0
195,13.5,0.25,0.25
196,13.5,0.75,0.25
197,13,0,1
198,13,1,1
199,14,0.5,1
200,13.5,0.25,0.75
201,13.5,0.75,0.75
202,14,0,0.5
203,14,1,0.5
204,26.5,0.75,0.75
205,16,0,0
206,16,1,0
207,26.5,0.25,0.75
208,27,0,0
209,16,0,1
210,16,1,1
211,28,0.5,0
212,15,0.5,0.5
213,27,1,0
214,27.5,0.25,0.25
215,27.5,0.75,0.25
216,27,0,1
217,14.5,0.25,0.25
218,14.5,0.75,0.25
219,14.5,0.75,0.75
220,14.5,0.25,0.75
221,15,0,0
222,16,0.5,0
223,15,1,0
224,15.5,0.25,0.25
225,15.5,0.75,0.25
226,15,0,1
227,15,1,1
228,16,0.5,1
229,15.5,0.25,0.75
230,15.5,0.75,0.75
231,16,0,0.5
232,16,1,0.5
233,27,1,1
234,18,0,0
235,18,1,0
236,28,0.5,1
237,27.5,0.25,0.75
238,18,0,1
239,18,1,1
240,27.5,0.75,0.75
241,17,0.5,0.5
242,28,0,0.5
243,28,1,0.5
244,30.5,0.25,0.25
245,30,0,0
246,16.5,0.25,0.25
247,16.5,0.75,0.25
248,16.5,0.75,0.75
249,16.5,0.25,0.75
250,17,0,0
251,18,0.5,0
252,17,1,0
253,17.5,0.25,0.25
254,17.5,0.75,0.25
255,17,0,1
256,17,1,1
257,18,0.5,1
258,17.5,0.25,0.75
259,17.5,0.75,0.75
260,18,0,0.5
261,18,1,0.5
262,30,1,0
263,20,0,0
264,20,1,0
265,30.5,0.75,0.25
266,30.5,0.75,0.75
267,20,0,1
268,20,1,1
269,30,0,1
270,19,0.5,0.5
271,30,1,1
272,30.5,0.25,0.75
273,29,0.5,0.5
274,31,0,0
275,18.5,0.25,0.25
276,18.5,0.75,0.25
277,18.5,0.75,0.75
278,18.5,0.25,0.75
279,19,0,0
280,20,0.5,0
281,19,1,0
282,19.5,0.25,0.25
283,19.5,0.75,0.25
284,19,0,1
285,19,1,1
286,20,0.5,1
287,19.5,0.25,0.75
288,19.5,0.75,0.75
289,20,0,0.5
290,20,1,0.5
291,32,0.5,0
292,22,0,0
293,22,1,0
294,31,1,0
295,31.5,0.25,0.25
296,22,0,1
297,22,1,1
298,28.5,0.25,0.25
299,21,0.5,0.5
300,28.5,0.75,0.25
301,28.5,0.75,0.75
302,28.5,0.25,0.75
303,29,0,0
304,20.5,0.25,0.25
305,20.5,0.75,0.25
306,20.5,0.75,0.75
307,20.5,0.25,0.75
308,21,0,0
309,22,0.5,0
310,21,1,0
311,21.5,0.25,0.25
312,21.5,0.75,0.25
313,21,0,1
314,21,1,1
315,22,0.5,1
316,21.5,0.25,0.75
317,21.5,0.75,0.75
318,22,0,0.5
319,22,1,0.5
320,30,0.5,0
321,24,0,0
322,24,1,0
323,29,1,0
324,29.5,0.25,0.25
325,24,0,1
326,24,1,1
327,29.5,0.75,0.25
328,23,0.5,0.5
329,29,0,1
330,29,1,1
331,30,0.5,1
332,29.5,0.25,0.75
333,22.5,0.25,0.25
334,22.5,0.75,0.25
335,22.5,0.75,0.75
336,22.5,0.25,0.75
337,23,0,0
338,24,0.5,0
339,23,1,0
340,23.5,0.25,0.25
341,23.5,0.75,0.25
342,23,0,1
343,23,1,1
344,24,0.5,1
345,0,0,2
346,2,0,2
347,2,1,2
348,0,1,2
349,0,0,3
350,2,0,3
351,2,1,3
352,0,1,3
353,26,1,2
354,4,0,2
355,4,1,2
356,18,0,3
357,18,1,3
358,4,0,3
359,4,1,3
360,30,0,2
361,30,1,2
362,6,0,2
363,6,1,2
364,20,0,2
365,20,1,2
366,6,0,3
367,6,1,3
368,26,0,3
369,26,1,3
370,8,0,2
371,8,1,2
372,20,0,3
373,20,1,3
374,8,0,3
375,8,1,3
376,32,0,2
377,32,1,2
378,10,0,2
379,10,1,2
380,22,0,2
381,22,1,2
382,10,0,3
383,10,1,3
384,28,0,2
385,28,1,2
386,12,0,2
387,12,1,2
388,22,0,3
389,22,1,3
390,12,0,3
391,12,1,3
392,30,0,3
393,30,1,3
394,14,0,2
395,14,1,2
396,24,0,2
397,24,1,2
398,14,0,3
399,14,1,3
400,28,0,3
401,28,1,3
402,16,0,2
403,16,1,2
404,24,0,3
405,24,1,3
406,16,0,3
407,16,1,3
408,32,0,3
409,32,1,3
410,18,0,2
411,18,1,2
412,26,0,2
413,1,0,2
414,2,0.5,2
415,1,1,2
416,0,0.5,2
417,0,0,2.5
418,2,0,2.5
419,2,1,2.5
420,0,1,2.5
421,1,0,3
422,2,0.5,3
423,1,1,3
424,0,0.5,3
425,3,0,2
426,4,0.5,2
427,3,1,2
428,4,0,2.5
429,4,1,2.5
430,3,0,3
431,4,0.5,3
432,3,1,3
433,5,0,2
434,6,0.5,2
435,5,1,2
436,6,0,2.5
437,6,1,2.5
438,5,0,3
439,6,0.5,3
440,5,1,3
441,7,0,2
442,8,0.5,2
443,7,1,2
444,8,0,2.5
445,8,1,2.5
446,7,0,3
447,8,0.5,3
448,7,1,3
449,9,0,2
450,10,0.5,2
451,9,1,2
452,10,0,2.5
453,10,1,2.5
454,9,0,3
455,10,0.5,3
456,9,1,3
457,11,0,2
458,12,0.5,2
459,11,1,2
460,12,0,2.5
461,12,1,2.5
462,11,0,3
463,12,0.5,3
464,11,1,3
465,13,0,2
466,14,0.5,2
467,13,1,2
468,14,0,2.5
469,14,1,2.5
470,13,0,3
471,14,0.5,3
472,13,1,3
473,15,0,2
474,16,0.5,2
475,15,1,2
476,16,0,2.5
477,16,1,2.5
478,15,0,3
479,16,0.5,3
480,15,1,3
481,17,0,2
482,18,0.5,2
483,17,1,2
484,18,0,2.5
485,18,1,2.5
486,17,0,3
487,18,0.5,3
488,17,1,3
489,19,0,2
490,20,0.5,2
491,19,1,2
492,20,0,2.5
493,20,1,2.5
494,19,0,3
495,20,0.5,3
496,19,1,3
497,21,0,2
498,22,0.5,2
499,21,1,2
500,22,0,2.5
501,22,1,2.5
502,21,0,3
503,22,0.5,3
504,21,1,3
505,23,0,2
506,24,0.5,2
507,23,1,2
508,24,0,2.5
509,24,1,2.5
510,23,0,3
511,24,0.5,3
512,23,1,3
513,25,0,2
514,26,0.5,2
515,25,1,2
516,26,0,2.5
517,26,1,2.5
518,25,0,3
519,26,0.5,3
520,25,1,3
521,27,0,2
522,28,0.5,2
523,27,1,2
524,28,0,2.5
525,28,1,2.5
526,27,0,3
527,28,0.5,3
528,27,1,3
529,29,0,2
530,30,0.5,2
531,29,1,2
532,30,0,2.5
533,30,1,2.5
534,29,0,3
535,30,0.5,3
536,29,1,3
537,31,0,2
538,32,0.5,2
539,31,1,2
540,32,0,2.5
541,32,1,2.5
542,31,0,3
543,32,0.5,3
544,31,1,3
545,0,0,4
546,2,0,4
547,2,1,4
548,0,1,4
549,0,0,5
550,2,0,5
551,2,1,5
552,0,1,5
553,1,0.5,4.5
554,28,1,4
555,11,0.5,4.5
556,32,1,5
557,6,0,6
558,28,0,5
559,28,1,5
560,18,0,5
561,18,1,5
562,28,0,7
563,14,1,7
564,18,1,4
565,8,1,7
566,12,0,6
567,20,0,6
568,18,0,6
569,17,0.5,4.5
570,28,1,6
571,18,1,6
572,28,1,7
573,14,1,5
574,26,0,7
575,4,0,4
576,4,1,4
577,30,1,6
578,4,0,6
579,4,0,5
580,4,1,5
581,0,0,6
582,3,0.5,4.5
583,12,0,7
584,26,0,4
585,26,1,4
586,10,1,6
587,30,1,7
588,31,0.5,4.5
589,22,0,5
590,10,1,7
591,22,1,7
592,24,1,6
593,14,0,4
594,13,0.5,4.5
595,14,1,4
596,27,0.5,4.5
597,24,1,5
598,22,1,5
599,24,0,5
600,14,0,5
601,20,1,6
602,12,1,6
603,22,1,4
604,6,0,4
605,6,1,4
606,26,0,5
607,26,1,5
608,6,0,5
609,6,1,5
610,8,0,6
611,5,0.5,4.5
612,25,0.5,4.5
613,32,0,4
614,32,1,4
615,22,0,7
616,30,1,4
617,32,0,7
618,20,1,4
619,10,0,7
620,32,1,6
621,16,0,4
622,26,0,6
623,24,0,4
624,30,0,5
625,16,0,7
626,22,0,4
627,16,0,6
628,20,0,4
629,16,1,7
630,21,0.5,4.5
631,22,1,6
632,10,0,6
633,8,0,4
634,8,1,4
635,4,1,6
636,2,0,6
637,8,0,5
638,8,1,5
639,2,1,6
640,7,0.5,4.5
641,18,0,7
642,18,1,7
643,4,1,7
644,0,1,6
645,16,1,4
646,26,1,7
647,20,0,7
648,14,1,6
649,28,0,6
650,20,1,5
651,6,0,7
652,8,1,6
653,16,0,5
654,16,1,5
655,8,0,7
656,19,0.5,4.5
657,23,0.5,4.5
658,15,0.5,4.5
659,30,1,5
660,16,1,6
661,0,1,7
662,10,0,4
663,10,1,4
664,0,0,7
665,4,0,7
666,10,0,5
667,10,1,5
668,2,0,7
669,9,0.5,4.5
670,6,1,7
671,26,1,6
672,2,1,7
673,30,0,6
674,14,0,7
675,32,0,6
676,14,0,6
677,24,0,7
678,20,0,5
679,20,1,7
680,24,1,7
681,24,0,6
682,29,0.5,4.5
683,22,0,6
684,32,1,7
685,6,1,6
686,30,0,7
687,12,1,7
688,18,0,4
689,30,0,4
690,24,1,4
691,12,0,4
692,12,1,4
693,32,0,5
694,28,0,4
695,12,0,5
696,12,1,5
*ELEMENT,TYPE=C3D13
1,1,4,8,5,9,10,11,12,13,14,15,16,17
2,1,2,3,4,9,18,19,20,10,14,21,22,15
3,6,5,8,7,9,23,12,24,25,26,17,16,27
4,2,1,5,6,9,18,13,23,28,21,14,17,26
5,3,2,6,7,9,19,28,25,29,22,21,26,27
6,4,3,7,8,9,20,29,24,11,15,22,27,16
7,2,3,7,6,38,19,29,25,28,43,44,45,46
8,2,31,32,3,38,47,48,49,19,43,50,51,44
9,35,6,7,36,38,52,25,53,54,55,46,45,56
10,31,2,6,35,38,47,28,52,57,50,43,46,55
11,32,31,35,36,38,48,57,54,58,51,50,55,56
12,3,32,36,7,38,49,58,53,29,44,51,56,45
13,31,32,36,35,67,48,58,54,57,72,73,74,75
14,31,60,61,32,67,76,77,78,48,72,79,80,73
15,64,35,36,65,67,81,54,82,83,84,75,74,85
16,60,31,35,64,67,76,57,81,86,79,72,75,84
17,61,60,64,65,67,77,86,83,87,80,79,84,85
18,32,61,65,36,67,78,87,82,58,73,80,85,74
19,60,61,65,64,96,77,87,83,86,101,102,103,104
20,60,89,90,61,96,105,106,107,77,101,108,109,102
21,93,64,65,94,96,110,83,111,112,113,104,103,114
22,89,60,64,93,96,105,86,110,115,108,101,104,113
23,90,89,93,94,96,106,115,112,116,109,108,113,114
24,61,90,94,65,96,107,116,111,87,102,109,114,103
25,89,90,94,93,125,106,116,112,115,130,131,132,133
26,89,118,119,90,125,134,135,136,106,130,137,138,131
27,122,93,94,123,125,139,112,140,141,142,133,132,143
28,118,89,93,122,125,134,115,139,144,137,130,133,142
29,119,118,122,123,125,135,144,141,145,138,137,142,143
30,90,119,123,94,125,136,145,140,116,131,138,143,132
31,118,119,123,122,154,135,145,141,144,159,160,161,162
32,118,147,148,119,154,163,164,165,135,159,166,167,160
33,151,122,123,152,154,168,141,169,170,171,162,161,172
34,147,118,122,151,154,163,144,168,173,166,159,162,171
35,148,147,151,152,154,164,173,170,174,167,166,171,172
36,119,148,152,123,154,165,174,169,145,160,167,172,161
37,147,148,152,151,183,164,174,170,173,188,189,190,191
38,147,176,177,148,183,192,193,194,164,188,195,196,189
39,180,151,152,181,183,197,170,198,199,200,191,190,201
40,176,147,151,180,183,192,173,197,202,195,188,191,200
41,177,176,180,181,183,193,202,199,203,196,195,200,201
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211,578,557,685,635,665,651,670,643
212,557,610,652,685,651,655,565,670
213,610,632,586,652,655,619,590,565
214,632,566,602,586,619,583,687,590
215,566,676,648,602,583,674,563,687
216,676,627,660,648,674,625,629,563
217,627,568,571,660,625,641,642,629
218,568,567,601,571,641,647,679,642
219,567,683,631,601,647,615,591,679
220,683,681,592,631,615,677,680,591
221,681,622,671,592,677,574,646,680
222,622,649,570,671,574,562,572,646
223,649,673,577,570,562,686,587,572
224,673,675,620,577,686,617,684,587
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xyont · October 25, 2023, 4:59am

Gnsh developer also notified, Hex-Dominant algorithm (R-tree) may generate pyramid element at transition. CalculiX user need to check mesh result and make it sure all element type is supported.

Matej · November 2, 2023, 2:28pm

Since I am integrating Gmsh into PrePoMax, I can confirm that Gmsh can produce pyramid elements, which can often happen when the user requires transfinite and recombined mesh on the surfaces of the tetrahedral domain. I had no idea collapsed elements are even possible, so that is great news for me, but adding full support for the pyramid elements is even better.

rafal.brzegowy · February 9, 2024, 10:15am

Info, experimental support for the four-sided pyramid elements was added (C3D5 and C3D13) in PrePoMax:

Calc_em · February 9, 2024, 10:29am

Indeed, but let’s keep in mind that those aren’t true pyramid elements:

since pyramid elements are not yet supported by the CalculiX solver they are exported as collapsed wedges or collapsed hexahedrons

So the development of pyramid elements for CalculiX is still needed.

vicmw · February 12, 2024, 6:39pm

@fgr, it seems that Abaqus doesn’t have quadratic pyramid elements (C3D13). I wonder if in CCX, it should be treated as C3D20 with repeated node numbers for better compatibility?

I really hope Guido will incorporate your changes because it’s quite an inconvenient gap without them. Rafal has made an issue on Github for it. Pyramid elements C3D5 and C3D13 · Issue #76 · Dhondtguido/CalculiX · GitHub

It look like you had to modify a lot of files so I worry that as time goes on, your code will become too difficult to integrate back into main CCX If I was to diff your source files with the 2.21 release’s source, would all the changes be for the pyramids?

Calc_em · February 12, 2024, 7:33pm

I plan to contact Guido about other issues soon so I will mention this one as well and ask him to take a look at this code.

fgr · February 12, 2024, 9:32pm

@vicmw

Honestly , ccx has a huge number of code lines and from I can recognize from the code, then the ccx code also has a touch from many different programmers, so for sure I have probably implemented code where it’s useless and other places the implementing still could be missing.

I read the PHD of Robert Browning about the second order19-node pyramid element and got curious if the pyramid element really was as poor as the rumor and convinced myself that if it was an element, I was gone to use I needed to make a full implementation. I was also a little curious about the difference between the Bedrosian and Filippa shape formulation why I also implemented a C3D15F element for the Filippa. In Ansys the data card for the pyramid element is similar to a brick except for the top vertex node are repeated just like the top surface was collapsed, but in according to the Ansys theory manual it looks like they are using their own shape function or the formulation needs a reader review,

I quickly realized that the wedge element C3D15 was one of the latest elements implemented, so I made some few test cases with the C3D15 element and run them in Linux under the GNU profiler to recognize in which routines the C3D15 have been used, further I also did a complete search for all places where C3D15 had been implemented in where I believed it must be connected to pure mechanics and put in code for the C3D13 beside the code for the C3D15.

Off course the right way to do it had been to check every single implementation of code separately but that would have a huge work and many places in the ccx code has been built in such manner that you even will not get a warning but only a wrong result if the element is missing the specific location so for me it made most sense just to put beside the C3D15 element.

Hopefully this will make it easier for everyone to decide if they should use my code changes or not.

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Pyramid elements C3D5 & C3D13

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