Documentation
The aim of this test case is to validate the following functions:
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.
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Geometry of the shaft
The shaft has a radius r = 0.1 m and a length of l = 0.5 m.
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 |
Mesh used for the SimScale case (A)
Mesh used for the SimScale case (C)
Material:
Constraints:
Loads:
\[\begin{equation}\label{ref1}
J = \frac{1}{2} \pi r^4 = 1.57 \cdot 10^{-4} m^4
\end{equation}\]\[\begin{equation}\label{ref2}
\tau_{max} = \frac {T r} {J} = 31.847 N/mm^2
\end{equation}\]\[\begin{equation}\label{ref3}
\theta = \frac {\tau_{max} l} {G r} = 1.9904 \cdot 10^{-4} rad
\end{equation}\]
Important
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% |
[Roark] | (1, 2, 3, 4) (2011)”Roark’s Formulas For Stress And Strain, Eighth Edition”, W. C. Young, R. G. Budynas, A. M. Sadegh |
Last updated: January 29th, 2019
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