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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]$$^1$$.

## 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.

## 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:

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

Note

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

Last updated: September 24th, 2021