Quarter shaft subjected to a fixed rotation¶
Overview¶
The aim of this test case is to validate the following functions:
- cyclic symmetry
- rotating motion
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.
Geometry¶
The shaft has a radius \(r\) = 0.1 m and a length \(l\) = 0.5 m, but only one quarter is being modelled.
Analysis type and Domain¶
Tool Type : Code_Aster
Analysis Type : Static
Mesh and Element types :
Case | Mesh type | Number of nodes | Element type |
---|---|---|---|
(A) | quadratic tetrahedral | 2866 | 3D isoparametric |
(B) | quadratic tetrahedral | 19243 | 3D isoparametric |
(C) | linear hexahedral | 2730 | 3D isoparametric |
(D) | quadratic hexahedral | 10527 | 3D isoparametric |
(a) Mesh used for the SimScale case (A) |
(b) Mesh used for the SimScale case (C) |
Simulation Setup¶
Material:
- isotropic: E = 208 GPa, \(\nu\) = 0.3, G = 80 GPa
Constraints (Boundary Conditions):
- Face ABC is fixed
- Face A’B’C’ is rotated with an angle \(\theta\) = 2*10⁻³ rad around the z-axis
Contacts:
- Cyclic symmetry, face AA’BB’ is tied to face AA’CC’
- rotation axis: z-axis
- Sector angle: 90°
Reference Solution¶
Results¶
Comparison of the maximum shear stress \(\tau_{max}\) obtained with SimScale and the results derived from [Roark].
Case | [Roark] | SimScale | Error |
---|---|---|---|
(A) | 32 | 30.454 | 4.83% |
(B) | 32 | 32.1978 | -0.62% |
(C) | 32 | 32 | 0.00% |
(D) | 32 | 32.059 | -0.18% |