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: Static Linear

Mesh and Element Types:

Tetrahedral meshes were computed using SimScale’s standard mesh algorithm and manual sizing. Hexahedral meshes were locally computed and imported into the project.

Case

Mesh Type

Number of Nodes

Element Type

A

1st order Tetrahedral

191965

Standard

B

2nd order Tetrahedral

189630

Standard

C

1st order Hexahedral

10325

Standard

D

2nd order Hexahedral

40935

Standard

Table 1: Mesh details for each case

Simulation Setup

Material:

Linear Elastic Isotropic:

\(E = \) 208 \(GPa\)

\(\nu = \) 0.3

\(G = \) 80 \(GPa \)

Boundary Conditions:

Constraints:

Face A is fixed.

Loads:

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):

This website uses cookies so that we can provide you with the best user experience possible. Cookie information is stored in your browser and performs functions such as recognising you when you return to our website and helping our team to understand which sections of the website you find most interesting and useful.

Strictly Necessary Cookies

Strictly Necessary Cookie should be enabled at all times so that we can save your preferences for cookie settings.

If you disable this cookie, we will not be able to save your preferences. This means that every time you visit this website you will need to enable or disable cookies again.