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# Validation Case: Cylinder Under Rotational Force

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

• Centrifugal force

The simulation results of the cloud-based simulation platform SimScale were compared to the results presented in [HPLA100]$$^1$$.

## Geometry

The geometry used for the case is as follows:

The solid body is created by rotating face ABCD by 45° and due to the symmetry of the cylinder, only one-quarter of the cylinder is modeled.

The coordinates of points A, B, C, and D can be seen below:

## Analysis Type and Mesh

Tool Type: Code_Aster

Analysis Type: Static

Mesh and Element Types:

The mesh was created with the Standard meshing algorithm in SimScale.

## Simulation Setup

Material:

• Steel (linear elastic)
• Isotropic: $$E$$ = 200 $$GPa$$
• $$\nu$$ = 0.3
• $$\rho$$ = 8000 $$kg/m^3$$

Initial and/or Boundary Conditions:

• Constraints:
• $$d_z$$ = 0:
• Face AA’BB’
• Face CC’DD’
• Symmetry:
• Face ABCD
• Face A’B’C’D’
• Centrifugal force with a rotational speed $$\omega$$ of 1 $$rad/s$$ around the z-axis applied to the whole body.

## Reference Solution

The reference solutions for stress and displacement is calculated with the equations below:

$$u(r)=\frac{−(1+\nu)(1−2\nu)}{(1−\nu)E}\rho\Omega^2\frac{r^3}{8}+Ar+\frac{B}{r}\tag{1}$$

$$\sigma_{zz}(r) = \frac{-\nu}{1-\nu}\rho\Omega^2\frac{r^2}{2}+\frac{2 \nu E}{(1+\nu)(1-2\nu)}A\tag{2}$$

$$A = \frac{(3-2\nu)(1+\nu)(1-2\nu)}{4(1-\nu)E}\rho\Omega^2R^2(1-x^2) = 7.13588\times 10^{-12} \ mm^2\tag{3}$$

$$B = \frac{(3-2\nu)(1+\nu)(1-2\nu)}{8(1-\nu)E}\rho\Omega^2R^4(1-x^2)^2 = 3.561258\times 10^{-15} \ mm^2\tag{4}$$

$$x = \frac{h}{2R} =\frac{0.001 \ m}{2\times0.02 \ m} = 0.025\tag{5}$$

Term $$h$$ is the thickness of the cross-section and $$R$$ is the radius of the middle surface of the cylinder and both are in meters ($$m$$).

## Result Comparison

The rotational force is validated by comparing the displacement $$u_r$$ in meters $$m$$ and Cauchy stresses $$\sigma_{zz}$$ in $$N/m^2$$ obtained from SimScale against the reference results obtained from [HPLA100] is given below:

The stress experienced by the cylinder under the rotational force can be seen below:

Note