Required field
Required field
Not a valid email address
Required field

Validation Case: Straight Beam with Damping of Rayleigh

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

• Dynamic analysis
• Material with Rayleigh damping model

The simulation results of SimScale were compared to the 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. Hexahedral meshes were locally computed and imported into the project.

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 ADEH is fixed
• 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]$$^1$$.

Result Comparison

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

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 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: February 20th, 2021