LN2 TRUSS-STANDARD element assembly validation
This validation aims at assessing the behavior of the SesamX LN2 TRUSS-STANDARD element against the equivalent Abaqus T3D2 element.
Validation model
The model studied for this comparison is made of a the following truss assembly.
It consists of a truss assembly clamped on one end subjected to a vertical load on the second end, where:
- each truss element is 1 $m$ long,
- each truss element has an area of 40 $mm^2$,
- a linear elastic material is applied with $E = 200GPa$ and $\nu = 0.33$.
This case is solved as a linear static resolution.
Validation results
The following figure gives an overview of the truss assembly displacements, as well as the node numbers.
The following table gives the comparison of the nodal displacements between Abaqus and SesamX.
| Abaqus | SesamX | Comparison | |||||
|---|---|---|---|---|---|---|---|
| Node id | $u_{x} (m)$ | $u_{y} (m)$ | Magnitude $(m)$ | $u_{x} (m)$ | $u_{y} (m)$ | Magnitude $(m)$ | Magnitude error |
| 1 | -1.75E-03 | -9.29E-03 | 9.45E-03 | -1.75E-03 | -9.29E-03 | 9.45E-03 | 0.00% |
| 2 | -1.88E-03 | -1.29E-02 | 1.30E-02 | -1.88E-03 | -1.29E-02 | 1.30E-02 | 0.00% |
| 3 | 1.25E-03 | -1.29E-02 | 1.30E-02 | 1.25E-03 | -1.29E-02 | 1.30E-02 | 0.00% |
| 4 | 1.25E-03 | -9.41E-03 | 9.50E-03 | 1.25E-03 | -9.41E-03 | 9.50E-03 | 0.00% |
| 5 | -1.50E-03 | -5.94E-03 | 6.12E-03 | -1.50E-03 | -5.94E-03 | 6.12E-03 | 0.00% |
| 6 | -1.13E-03 | -3.08E-03 | 3.28E-03 | -1.13E-03 | -3.08E-03 | 3.28E-03 | 0.00% |
| 7 | -6.25E-04 | -9.79E-04 | 1.16E-03 | -6.25E-04 | -9.79E-04 | 1.16E-03 | 0.00% |
| 8 | -5.00E-33 | 0.00E+00 | 5.00E-33 | 0.00E+00 | 0.00E+00 | 0.00E+00 | - |
| 9 | 1.13E-03 | -6.06E-03 | 6.16E-03 | 1.13E-03 | -6.06E-03 | 6.16E-03 | 0.00% |
| 10 | 8.75E-04 | -3.21E-03 | 3.32E-03 | 8.75E-04 | -3.21E-03 | 3.32E-03 | 0.00% |
| 11 | 5.00E-04 | -1.10E-03 | 1.21E-03 | 5.00E-04 | -1.10E-03 | 1.21E-03 | 0.00% |
| 12 | 5.00E-33 | -1.00E-33 | 5.10E-33 | 0.00E+00 | 0.00E+00 | 0.00E+00 | - |
The following table gives the comparison of the strain between Abaqus and SesamX.
| Abaqus | SesamX | Comparison | |
|---|---|---|---|
| Element id | $\varepsilon_{11}(\%)$ | $\varepsilon_{11}(\%)$ | $\varepsilon_{11}$ error |
| 1 | -1.25E-02 | -1.25E-02 | 0.00% |
| 2 | 0.00E+00 | -1.73E-16 | - |
| 3 | 0.00E+00 | 2.17E-17 | - |
| 4 | 1.77E-02 | 1.77E-02 | 0.00% |
| 5 | -2.50E-02 | -2.50E-02 | 0.00% |
| 6 | -3.75E-02 | -3.75E-02 | 0.00% |
| 7 | -5.00E-02 | -5.00E-02 | 0.00% |
| 8 | -6.25E-02 | -6.25E-02 | 0.00% |
| 9 | 1.25E-02 | 1.25E-02 | 0.00% |
| 10 | -1.25E-02 | -1.25E-02 | 0.00% |
| 11 | 1.77E-02 | 1.77E-02 | 0.00% |
| 12 | 2.50E-02 | 2.50E-02 | 0.00% |
| 13 | 1.77E-02 | 1.77E-02 | 0.00% |
| 14 | -1.25E-02 | -1.25E-02 | 0.00% |
| 15 | -1.25E-02 | -1.25E-02 | 0.00% |
| 16 | 1.77E-02 | 1.77E-02 | 0.00% |
| 17 | 5.00E-02 | 5.00E-02 | 0.00% |
| 18 | 1.77E-02 | 1.77E-02 | 0.00% |
| 19 | -1.25E-02 | -1.25E-02 | 0.00% |
| 20 | 3.75E-02 | 3.75E-02 | 0.00% |
The following table gives the comparison of the stress between Abaqus and SesamX.
| Abaqus | SesamX | ||
|---|---|---|---|
| Elem id | $\sigma_{11}(MPa)$ | $\sigma_{11}(MPa)$ | $\sigma_{11}$ error |
| 1 | -2.50E+01 | -2.50E+01 | 0.00% |
| 2 | 0.00E+00 | -3.47E-13 | - |
| 3 | 0.00E+00 | 4.34E-14 | - |
| 4 | 3.54E+01 | 3.54E+01 | 0.00% |
| 5 | -5.00E+01 | -5.00E+01 | 0.00% |
| 6 | -7.50E+01 | -7.50E+01 | 0.00% |
| 7 | -1.00E+02 | -1.00E+02 | 0.00% |
| 8 | -1.25E+02 | -1.25E+02 | 0.00% |
| 9 | 2.50E+01 | 2.50E+01 | 0.00% |
| 10 | -2.50E+01 | -2.50E+01 | 0.00% |
| 11 | 3.54E+01 | 3.54E+01 | 0.00% |
| 12 | 5.00E+01 | 5.00E+01 | 0.00% |
| 13 | 3.54E+01 | 3.54E+01 | 0.00% |
| 14 | -2.50E+01 | -2.50E+01 | 0.00% |
| 15 | -2.50E+01 | -2.50E+01 | 0.00% |
| 16 | 3.54E+01 | 3.54E+01 | 0.00% |
| 17 | 1.00E+02 | 1.00E+02 | 0.00% |
| 18 | 3.54E+01 | 3.54E+01 | 0.00% |
| 19 | -2.50E+01 | -2.50E+01 | 0.00% |
| 20 | 7.50E+01 | 7.50E+01 | 0.00% |
The results are identical between SesamX and Abaqus. The SesamX LN2 TRUSS-STANDARD element implementation is the same as the Abaqus T3D2 implementation.