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]\(^1\).
The geometry used for the case is as follows:
Figure 1: Geometrical model of the beam
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:
POINT X \([m]\) Y \([m]\) Z \([m]\) A 0 0 0 B 10 0 0 C 10 1 0 D 0 1 0 E 0 0 1 F 10 0 1 G 10 1 1 H 0 1 1 Table 1: Geometry points coordinates 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:
Case Mesh Type Number of Nodes Element Type Element Technology A Standard 1173 1st order tetrahedral Standard B Standard 7481 2nd order tetrahedral Standard Table 2: Mesh details for each case
Figure 2: Tetrahedral mesh as used in case A. Simulation Setup
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 \( s \)
Constraints: Face ADEH is fixed Face BCFG is fixed Loads: 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.
Comparison of the displacement (DZ), velocity (VZ), and acceleration (AZ) computed on the midpoint of the beam for cases A and B.
Figure 3: Displacement results comparison
Figure 4: Velocity results comparison
Figure 5: Acceleration results comparison
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 \(s\):
Figure 6: Deformed shape and contour plot at time 0.012 \(s\) for case A, with a scaling factor of 1000
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Last updated: September 28th, 2021
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