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Circular Shaft Under Torque


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 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

Mesh used for the SimScale case (A)


Mesh used for the SimScale case (C)

Simulation Setup


  • isotropic: E = 208 GPa, ν = 0.3, G = 80 GPa


  • Face A is fixed


  • Torque T of 50000 N/m on face B

Reference Solution

J = \frac{1}{2} \pi r^4 = 1.57 \cdot 10^{-4} m^4
\tau_{max} = \frac {T r} {J} = 31.847 N/mm^2
\theta = \frac {\tau_{max} l} {G r} = 1.9904 \cdot 10^{-4} rad



  • 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
Comparison of the angle of twist θ in [rad]
CaseTool Type[Roark]SimScaleError


[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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