Circular Shaft Under Torque
Overview
The aim of this test case is to validate the following functions:
- torque
- remote force
The simulation results of SimScale were compared to the numerical results presented in [Roark]. The meshes used in (A) and (B) were created with the parametrized-tetrahedralization-tool on the SimScale platform. The meshes used in (C) and (D) were locally created with Salome.
Import validation project into workspace
Geometry
The shaft has a radius r
= 0.1 m and a length of l
= 0.5 m.
Analysis type and Domain
Tool Type : CalculiX/Code_Aster
Analysis Type : Static
Mesh and Element types :
| Case | Mesh type | Number of nodes | Element type |
|---|---|---|---|
| (A) | linear tetrahedral | 12940 | 3D isoparametric |
| (B) | quadratic tetrahedral | 94919 | 3D isoparametric |
| (C) | linear hexahedral | 10325 | 3D isoparametric |
| (D) | quadratic hexahedral | 40935 | 3D isoparametric |
Simulation Setup
Material:
- isotropic: E = 208 GPa, ν
= 0.3, G = 80 GPa
Constraints:
- Face A is fixed
Loads:
- Torque T
of 50000 N/m on face B
Reference Solution
J=12πr4=1.57⋅10−4m4(1)
τmax=TrJ=31.847N/mm2(2)
θ=τmaxlGr=1.9904⋅10−4rad(3)
Results
Important
- The analytical solution assumes an undeformable surface on the face, wich is subject to the torque bc. This can be modelled in Code_Aster with the option ‘undeformable’ in the remote displacement bc.
- CalculiX has no such option and therefore the stresses in the entitites, which are assigned to the torque bc, are unphysical in CalculiX. So the stresses were computed at a point on the edge of face A.
Comparison of the maximum shear stress τmax
and the angle of twist θ
obtained with SimScale and the results derived from [Roark].
| Case | Tool Type | [Roark] | SimScale | Error |
|---|---|---|---|---|
| (A) | CalculiX | 31.847 | 30.212 | 5.13% |
| (A) | Code_Aster | 31.847 | 30.212 | 5.13% |
| (B) | CalculiX | 31.847 | 31.842 | 0.02% |
| (B) | Code_Aster | 31.847 | 31.838 | 0.03% |
| (C) | Code_Aster | 31.847 | 32.066 | -0.69% |
| (D) | Code_Aster | 31.847 | 31.879 | -0.10% |
| Case | Tool Type | [Roark] | SimScale | Error |
|---|---|---|---|---|
| (A) | CalculiX | 0.0019904 | 0.001953 | 1.88% |
| (A) | Code_Aster | 0.0019904 | 0.001969 | 1.08% |
| (B) | CalculiX | 0.0019904 | 0.001969 | 1.08% |
| (B) | Code_Aster | 0.0019904 | 0.001989 | 0.07% |
| (C) | Code_Aster | 0.0019904 | 0.002004 | -0.68% |
| (D) | Code_Aster | 0.0019904 | 0.00199 | 0.02% |