# Voluminal paving stone subjected to harmonic pressure¶

## Overview¶

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

- Harmonic analysis
- Harmonic pressure

The simulation results of SimScale were compared to the numerical results in [SDLV124]. The mesh used in case (A) was obtained from Code_Aster.

## Geometry¶

A | B | C | D | A’ | B’ | C’ | D’ | |
---|---|---|---|---|---|---|---|---|

x [m] | 0 | 0.35 | 0.35 | 0 | 0 | 0.35 | 0.35 | 0 |

y [m] | 0 | 0 | 0.25 | 0.25 | 0 | 0 | 0.25 | 0.25 |

z [m] | 0 | 0 | 0 | 0 | 0.01 | 0.01 | 0.01 | 0.01 |

## Analysis type and Domain¶

**Tool Type** : Code_Aster

**Analysis Type** : Harmonic analysis

**Mesh and Element types** :

Case | Mesh type | Number of nodes | Element type |
---|---|---|---|

(A) | linear hexahedral | 1764 | 3D isoparametric |

## Simulation Setup¶

Material:

- isotropic: E = 180 GPa, \(\nu\) = 0.3, \(\rho\) = 7800 kg/m³
- Rayleigh damping: \(\alpha_k\) = 3E-5 s, \(\beta_m\) = 1E-3 s⁻¹

Constraints:

- Faces ABA’B’, BCB’C’, CDC’D’ and ADA’D’ are fixed

Loads:

- Pressure of 0,5 MPa on Face ABCD

## Results¶

Comparison of displacements at point E (0.1575, 0.125, 0) obtained with SimScale with the results presented in [SDLV124]. The Error was calculated with respect to [SDLV124_N].

Case | Quantity | [SDLV124_N] | [SDLV124] | SimScale | Error (%) |
---|---|---|---|---|---|

(A) | \(d_X\) [m] | 9.0386E-007 | 9.0529E-007 | 9.0529E-007 | 0.16% |