The aim of this test case is to validate the following functions:
The simulation results of SimScale were compared to the analytical results in [Roark]. The meshes used in (A) and (B) were created with the parametrized-tetrahedralization-tool on the SimScale platform and the meshes used in (C) and (D) were meshed with Salome.
Import validation project into workspace
The bar has a cross section A
of 0.05 x 0.05 m² and a length l
= 1.0 m.
Tool Type : Calculix, Code_Aster
Analysis Type : Thermomechanical
Mesh and Element types :
| Case | Mesh type | Number of nodes | Element type | Tool type |
|---|---|---|---|---|
| (A) | linear tetrahedral | 84 | 3D isoparametric | Calculix |
| (B) | quadratic tetrahedral | 369 | 3D isoparametric | Calculix |
| (C) | linear hexahedral | 369 | 3D isoparametric | Calculix |
| (D) | quadratic hexahedral | 1221 | 3D isoparametric | Calculix |
| (E) | linear tetrahedral | 84 | 3D isoparametric | Code_Aster |
| (F) | quadratic tetrahedral | 369 | 3D isoparametric | Code_Aster |
| (G) | linear hexahedral | 369 | 3D isoparametric | Code_Aster |
| (H) | quadratic hexahedral | 1221 | 3D isoparametric | Code_Aster |
Material:
= 0.3
= 12E-6 1/K
Constraints (Boundary Conditions):
Loads:
= 10 K on the outer surface
σ=ΔTγE(1)
The equation (1)
used to solve the problem is derived in [Roark]. Inserting the values described in the previous chapter results in the unit stress σ
= 24.6 Mpa in the whole beam.
Comparison of the unit stress σ
in the beam obtained with SimScale with the results derived from the equations presented in [Roark].
| Case | [Roark] | SimScale | Error (%) |
|---|---|---|---|
| (A) | 24.6 | 24.6 | 0.00% |
| (B) | 24.6 | 24.6 | 0.00% |
| (C) | 24.6 | 24.599 | 0.004% |
| (D) | 24.6 | 24.599-24.601 | ±
0.004% |
| (E) | 24.6 | 24.6 | 0.00% |
| (F) | 24.6 | 24.6 | 0.00% |
| (G) | 24.6 | 24.6 | 0.00% |
| (H) | 24.6 | 24.6 | 0.00% |
Note: The worst results was obtained with mesh (D). This was due to an interpolation error and is shown in the picture below.
