TE4 SOLID-ISOPARAM element twisted beam validation
This validation aims at assessing the behavior of the SesamX TE4 SOLID-ISOPARAM element against the equivalent Abaqus C3D4 element. These 2 elements implement the iso-parametric tetrahedron element. We expect the results to be identical.
Validation model
A twisted 3D beam model is studied for this comparison.
The beam is clamped at one end and subjected to an arbitrary load at the other end. A linear elastic material is applied with $E = 200 GPa$ and $\nu = 0.33$.
This case is solved as a linear static resolution.
Validation results
The following figure gives an overview of the beam displacement.
The following table gives the comparison of the nodal translations between Abaqus and SesamX.
| Abaqus | SesamX | Comparison | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Node id | $u_x (m)$ | $u_y (m)$ | $u_z (m)$ | Magnitude $(m)$ | $u_x (m)$ | $u_y (m)$ | $u_z (m)$ | Magnitude $(m)$ | Magnitude error |
| 2 | 6.63E-06 | 2.75E-05 | 4.42E-06 | 2.86E-05 | 6.63E-06 | 2.75E-05 | 4.42E-06 | 2.86E-05 | 0.00% |
| 70 | 4.49E-06 | 2.60E-05 | -3.83E-06 | 2.66E-05 | 4.49E-06 | 2.60E-05 | -3.83E-06 | 2.66E-05 | 0.00% |
| 140 | 1.05E-06 | 4.94E-06 | -7.79E-07 | 5.11E-06 | 1.05E-06 | 4.94E-06 | -7.79E-07 | 5.11E-06 | 0.00% |
| 210 | 1.29E-06 | 7.19E-06 | -2.70E-06 | 7.79E-06 | 1.29E-06 | 7.19E-06 | -2.70E-06 | 7.79E-06 | 0.00% |
| 280 | 2.98E-06 | 1.23E-05 | 1.07E-07 | 1.26E-05 | 2.98E-06 | 1.23E-05 | 1.07E-07 | 1.26E-05 | 0.00% |
| 360 | 4.87E-08 | 6.67E-08 | 5.34E-08 | 9.83E-08 | 4.87E-08 | 6.67E-08 | 5.34E-08 | 9.83E-08 | 0.00% |
The nodal translations are identical between Abaqus and SesamX.
The following table gives the comparison of the principal strains between Abaqus and SesamX.
| Abaqus | SesamX | Comparison | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Element id | $\varepsilon_{11} (\%)$ | $\varepsilon_{22} (\%)$ | $\varepsilon_{33} (\%)$ | $\varepsilon_{11} (\%)$ | $\varepsilon_{22} (\%)$ | $\varepsilon_{33} (\%)$ | $\varepsilon_{11}$ error | $\varepsilon_{22}$ error | $\varepsilon_{33}$ error |
| 519 | 3.72E-06 | -8.52E-07 | -1.32E-06 | 3.72E-06 | -8.52E-07 | -1.32E-06 | 0.00% | 0.00% | 0.00% |
| 836 | 1.02E-05 | -1.31E-06 | -4.73E-06 | 1.02E-05 | -1.31E-06 | -4.73E-06 | 0.00% | 0.00% | 0.00% |
| 1285 | 8.27E-06 | -3.52E-07 | -3.38E-06 | 8.27E-06 | -3.52E-07 | -3.38E-06 | 0.00% | 0.00% | 0.00% |
The strain values are identical between Abaqus and SesamX.
The following table gives the comparison of the principal stresses between Abaqus and SesamX.
| Abaqus | SesamX | Comparison | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Element id | $\sigma_{11} (MPa)$ | $\sigma_{22} (MPa)$ | $\sigma_{33} (MPa)$ | $\sigma_{11} (MPa)$ | $\sigma_{22} (MPa)$ | $\sigma_{33} (MPa)$ | $\sigma_{11}$ error | $\sigma_{22}$ error | $\sigma_{33}$ error |
| 519 | 7.85E-03 | 9.75E-04 | 2.68E-04 | 7.85E-03 | 9.75E-04 | 2.68E-04 | 0.00% | 0.00% | 0.00% |
| 836 | 2.14E-02 | 4.09E-03 | -1.05E-03 | 2.14E-02 | 4.09E-03 | -1.05E-03 | 0.00% | 0.00% | 0.00% |
| 1285 | 1.90E-02 | 6.09E-03 | 1.54E-03 | 1.90E-02 | 6.09E-03 | 1.54E-03 | 0.00% | 0.00% | 0.00% |
The stress values are identical between Abaqus and SesamX.
As expected, due to identical element formulation the results are the same between the Abaqus C3D4 element and the SesamX TE4 SOLID-ISOPARAM element.