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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.

CaseElement TypeNumber of NodesElement Technology
A1st Order Tetrahedral8682Standard
B2nd Order Tetrahedral 63084Standard
C2nd Order Tetrahedral 63084 Reduced Integration
Table 1: Mesh and element overview
first order standard mesh generated with simscale's standard mesher which has 8682 nodes
Figure 2: Generated standard mesh used for cases A

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: September 24th, 2021