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.

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Geometry

Geometry of the shaft

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 :

Mesh used for the SimScale case (A)

Mesh used for the SimScale case (C)

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

\[\begin{equation}\label{ref1}
J = \frac{1}{2} \pi r^4 = 1.57 \cdot 10^{-4} m^4
\end{equation}\]\[\begin{equation}\label{ref2}
\tau_{max} = \frac {T r} {J} = 31.847 N/mm^2
\end{equation}\]\[\begin{equation}\label{ref3}
\theta = \frac {\tau_{max} l} {G r} = 1.9904 \cdot 10^{-4} rad
\end{equation}\]

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].

References

Last updated: January 29th, 2019

What's Next

part of: Compressible Flow: de Laval Nozzle