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Validation Case: Quarter Shaft Subjected to a Fixed Rotation

This validation case belongs to solid mechanics. The aim of this test case is to validate the following parameters:

  • Cyclic symmetry
  • Rotating motion

The simulation results of SimScale were compared to the results presented in [Roark’s]\(^1\).


The geometry used for the case is as follows:

sketch of a quarter shaft used for validating simscale with bottom edges labeled a to c and top surface a' to c'
Figure 1: Sketch of a quarter shaft

The quarter shaft has a radius (\(r\)) of 0.1 \(m\) and a length (\(l\)) of 0.5 \(m\).

Analysis Type and Mesh

Tool Type: Code_Aster

Analysis Type: Static – linear

Mesh and Element Types:

The standard mesh was created with the Standard meshing algorithm in SimScale.

CaseMesh TypeNumber of NodesElement Type
A1st order standard8682Standard
B2nd order standard63084Standard
C1st order hexahedral2730Standard
D2nd order hexahedral10527Standard
Table 1: Mesh used for simulation of all cases
first order standard mesh generated with simscale's standard mesher which has 8682 nodes
Figure 2: Generated standard mesh used for cases A and B
uploaded mesh which has 2730 nodes
Figure 3: Uploaded hexahedral mesh used for case C and D

Simulation Setup


  • Steel (linear elastic)
    • Isotropic: \(E\) = 205 \(GPa\), \(\nu\) = 0.3 , \(G\) = 80 \(GPa\)

Boundary Conditions:

  • Constraints:
    • Fixed: Face ABC
    • Fixed rotation:
      • Face A’B’C’: rotation with an angle of (\(\theta\)) 2e-3 \(rad\) around the z-axis


  • Cyclic Symmetry
    • Face AA’BB’ tied to face AA’CC’
    • Rotation axis: z-axis
    • Sector angle: 90°

Reference Solution

The reference solution for maximum stress etc. is given by the following equation:

$$\tau_{max} = \theta.G.r.l = 32\ GPa$$

Result Comparison

Comparison of the maximum shear stress (\(\tau_{max}\)) obtained from SimScale against the reference results obtained from [Roark] is given below:

Case[Roark]SimScaleError [%]
Table 2: Comparison of shear stress.

The visualization of the cauchy shear stress [SIYZ] contours in Pascals as in the SimScale post-processor:

visualization of cauchy stress after rotation is applied to the shaft
Figure 4: Cauchy shear stress distribution contours across the quarter shaft


If you still encounter problems validating you simulation, then please post the issue on our forum or contact us.

Last updated: June 14th, 2021

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