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# Validation Case: Straight Beam with Damping of Rayleigh

This validation case belongs to the material damping of the Rayleigh model in solid mechanics. The aim of this test case is to validate the following parameters on the middle point of the beam:

• Acceleration;
• Velocity;
• Displacement.

The simulation results from SimScale were compared to the Europlexus and Code Aster results presented in [SDLS123]$$^1$$.

## Geometry

The geometry used for the case is as follows:

The beam has a length of 10 $$m$$ and a square cross-section with a side length of 1 $$m$$. The coordinates of each point can be found in the following table:

## Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Dynamic

Mesh and Element Types:

Tetrahedral meshes were computed using SimScale’s Standard mesh algorithm and manual sizing:

## Simulation Setup

Material:

• Linear Elastic Isotropic with Damping of Rayleigh:
• $$E =$$ 35 $$GPa$$
• $$\nu =$$ 0.22
• $$\rho =$$ 2500 $$kg/m^3$$
• $$\alpha =$$ 6.69e-5 $$1/s$$
• $$\beta =$$ 20.06 $$s$$

Boundary Conditions:

• Constraints:
• Face BCFG is fixed
• Linear pressure increment of 1e5 $$Pa$$ on face EFGH until $$t =$$ 1e-4 $$s$$ and constant afterwards

## Reference Solution

The reference solution is of numerical type as presented in cases A and B of [SDLS123]$$^1$$. The Europlexus and Code Aster results for the same linear triangular mesh were used for the comparison.

## Result Comparison

Comparison of the displacement (DZ), velocity (VZ), and acceleration (AZ) computed on the midpoint of the beam for cases A and B.

The results produced are in good agreement with the reference. Higher deviations are blamed on the nature of linear tetrahedral elements.

Following is a deformed shape of the beam for case A at time $$t =$$ 0.012 $$s$$:

Note

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

Last updated: September 28th, 2021