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# Validation Case: Circular Shaft Under Torque Load

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

• Torque load applied through remote force boundary condition
• Shear stress distribution and maximum value
• Rotational deformation magnitude

The simulation results of SimScale were compared to the results presented in [Roark]$$^1$$

## Geometry

The geometry used for the case is below:

The axis of the shaft cylinder is aligned with the $$Z$$ axis, with a length $$L =$$ 0.5 $$m$$ and a radius $$r =$$ 0.1 $$m$$.

## Analysis Type and Mesh

Tool Type: Code_Aster

Analysis Type: Linear Static

Mesh and Element Types:

Tetrahedral meshes were computed using SimScale’s standard meshing algorithm and manual sizing. Table 1 shows an overview of the meshes in the validation project.

The second order tetrahedral mesh from case B is shown in Figure 2:

## Simulation Setup

Material:

• Linear Elastic Isotropic:
• $$E =$$ 208 $$GPa$$
• $$\nu =$$ 0.3
• $$G =$$ 80 $$GPa$$

Boundary Conditions:

• Constraints:
• Face A is fixed.
• Torque $$T =$$ 50000 $$Nm$$ on face B.

## Reference Solution

The analytical solutions for the rotation angle $$\theta_B$$ and maximum shear stress $$\tau_{max}$$ are given by the following equations:

$$\theta_B = \frac{ T L }{G J} \tag{1}$$

$$\tau_{max} = \frac{T R}{J} \tag{2}$$

$$J = \frac{\pi R^4}{2} \tag{3}$$

The computed reference solution is:

$$\theta_B = 1.9894×10^{-3}\ Rad$$

$$\tau_{max} = 31.847\ MPa$$

## Result Comparison

The plane maximum displacement $$U$$ is used to compute the rotation angle through equation 4 (obtained through the cosines law):

$$\theta = ArcCos[ 1- \frac{U^2}{2R^2} ] \tag{4}$$

The maximum shear stress is taken from the Cauchy stress tensor, component [SIYZ]:

For both 1st order and 2nd order meshes, the results show good agreement with the analytical solution. Find below an image showing the displacement magnitude on the cylinder, for case B:

References

• (2011) “Roark’s Formulas For Stress And Strain, Eighth Edition”, W. C. Young, R. G. Budynas, A. M. Sadegh.

Note

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

Last updated: July 21st, 2021