validations:te10-solid-twisted-beam

TE10 SOLID-ISOPARAM element twisted beam validation

This validation aims at assessing the behavior of the SesamX TE10 SOLID-ISOPARAM element against the equivalent Abaqus C3D10 element. These 2 elements implement the iso-parametric tetrahedron element. We expect the results to be identical.

A twisted 3D beam model is studied for this comparison.

 Twisted beam model

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.

The following figure gives an overview of the beam displacement.

 Twisted beam deformation

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
5 8.84E-06 3.04E-05 5.98E-06 3.22E-05 8.84E-06 3.04E-05 5.98E-06 3.22E-05 0.00%
884 6.64E-07 1.05E-06 1.71E-06 2.11E-06 6.64E-07 1.05E-06 1.71E-06 2.11E-06 0.00%
24 1.43E-06 3.51E-06 3.02E-06 4.85E-06 1.43E-06 3.51E-06 3.02E-06 4.85E-06 0.00%
201 2.44E-06 7.21E-06 3.27E-06 8.29E-06 2.44E-06 7.21E-06 3.27E-06 8.29E-06 0.00%
28 4.15E-06 1.54E-05 1.27E-06 1.60E-05 4.15E-06 1.54E-05 1.27E-06 1.60E-05 0.00%
768 5.23E-06 2.47E-05 -2.38E-06 2.53E-05 5.23E-06 2.47E-05 -2.38E-06 2.53E-05 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
119 5.47E-06 -4.67E-07 -1.21E-06 5.47E-06 -4.67E-07 -1.21E-06 0.00% 0.00% 0.00%
140 8.11E-06 -1.65E-06 -3.89E-06 8.11E-06 -1.65E-06 -3.89E-06 0.00% 0.00% 0.00%
543 5.21E-06 -1.59E-06 -1.89E-06 5.21E-06 -1.59E-06 -1.89E-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
119 1.38E-02 4.83E-03 3.71E-03 1.38E-02 4.83E-03 3.71E-03 0.00% 0.00% 0.00%
140 1.60E-02 1.27E-03 -2.11E-03 1.60E-02 1.27E-03 -2.11E-03 0.00% 0.00% 0.00%
543 1.03E-02 1.31E-04 -3.30E-04 1.03E-02 1.31E-04 -3.30E-04 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 C3D10 element and the SesamX TE10 SOLID-ISOPARAM element.

  • validations/te10-solid-twisted-beam.txt
  • Last modified: 2023/05/31 20:40
  • by Ali Baba