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]\(^1\).

Geometry

The geometry used for the case is as follows:

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.

Case	Element Type	Number of Nodes	Element Technology
A	1st Order Tetrahedral	8682	Standard
B	2nd Order Tetrahedral	63084	Standard
C	2nd Order Tetrahedral	63084	Reduced Integration

Simulation Setup

Material/Fluid:

• 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

Contacts

• 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]	SimScale	Error [%]
A	32	31.794	-0.643
B	32	31.564	-1.360
C	32	31.565	-1.360

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

Last updated: September 24th, 2021