Required field
Required field
Required field

# Straight Beam with Damping of Rayleigh

## Overview

The aim of this test case is to validate the following functions:

• Dynamic analysis
• Material Rayleigh damping

The simulation results of SimScale were compared to the results presented in case A and case B of [SDLS123].

Import validation project into workspace

## Geometry

A B C D E F G H
x [m] 0 10 10 0 0 10 10 0
y [m] 0 0 1 1 0 0 1 1
z [m] 0 0 0 0 1 1 1 1

## Analysis type and Domain

Tool Type : Code_Aster

Analysis Type : Dynamic (linear)

Mesh and Element types :

Case Mesh type Number of nodes Number of 3D elements Element type Analysis type
(A) linear hexahedrals 496 270 3D isoparametric Explicit
(B) quadratic hexahedral 1720 270 3D isoparametric Explicit
(C) linear tetrahedrals 1637 5596 3D isoparametric Explicit
(D) quadratic tetrahedrals 1268 542 3D isoparametric Explicit
(E) quadratic hexahedral 1720 270 3D isoparametric Implicit
(F) quadratic tetrahedrals 1268 542 3D isoparametric Implicit

## Simulation Setup

Material:

• isotropic: E = 35 GPa, ν
$\nu$

= 0.22, ρ

$\rho$

= 2500 Kg/m³, α

$\alpha$

= 6.69e-5 1/s, β

$\beta$

= 20.06 s

Constraints:

• Face BCFG zero x-y-z-displacement

• Linear pressure increment of 1e5 Pa on face EFGH until 1e-4 s and than constant afterwards

## Results

Comparison of the displacement (Dz), velocity (Vz) and acceleration (Az) computed on mid point of the beam for case A,B,E (left) and case C,D,F (right) with the results presented in case A and case B of [SDLS123] respectively.

Comparison of the displacement result for case A,B,E (left) and case C,D,F (right) with [SDLS123] case A and case B respectively

Comparison of the velocity result for case A,B,E (left) and case C,D,F (right) with [SDLS123] case A and case B respectively

Comparison of the acceleration result for case A,B,E (left) and case C,D,F (right) with [SDLS123] case A and case B respectively

The results produced are in good agreement with the reference except case C due to the nature of linear tetrahedral elements.

## References

 [SDLS123] (1, 2, 3, 4, 5) SDLS123 – Poutre droite avec amortissement de Rayleigh (comportement élastique)