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Documentation

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

CircularShaftUnderTorque-geometry
CircularShaftUnderTorque-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 :

CaseMesh typeNumber of nodesElement type
(A)linear tetrahedral129403D isoparametric
(B)quadratic tetrahedral949193D isoparametric
(C)linear hexahedral103253D isoparametric
(D)quadratic hexahedral409353D isoparametric
CircularShaftUnderTorque-mesh-a
CircularShaftUnderTorque-mesh-a

Mesh used for the SimScale case (A)

CircularShaftUnderTorque-mesh-c
CircularShaftUnderTorque-mesh-c

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].

Comparison of maximum shear stress τmax in [MPa]
CaseTool Type[Roark]SimScaleError
(A)CalculiX31.84730.2125.13%
(A)Code_Aster31.84730.2125.13%
(B)CalculiX31.84731.8420.02%
(B)Code_Aster31.84731.8380.03%
(C)Code_Aster31.84732.066-0.69%
(D)Code_Aster31.84731.879-0.10%
Comparison of the angle of twist θ in [rad]
CaseTool Type[Roark]SimScaleError
(A)CalculiX0.00199040.0019531.88%
(A)Code_Aster0.00199040.0019691.08%
(B)CalculiX0.00199040.0019691.08%
(B)Code_Aster0.00199040.0019890.07%
(C)Code_Aster0.00199040.002004-0.68%
(D)Code_Aster0.00199040.001990.02%

References

[Roark](1234) (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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