# Thick plate under pressure¶

## Overview¶

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

- distributed pressure
- nodal stresses

The simulation results of SimScale were compared to the numerical results presented in [NAFEMS]. In addition to the meshes described in [NAFEMS], the meshes used in (A) and (B) were set up using an automatically created tetrahedral mesh and a refined hexahedral mesh was used in (G).

## Geometry¶

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

x [m] | 0 | 0 | 3.25 | 2 | 0 | 0 | 3.25 | 2 |

y [m] | 1 | 2.75 | 0 | 0 | 1 | 2.75 | 0 | 0 |

z [m] | 0.6 | 0.6 | 0.6 | 0.6 | 0 | 0 | 0 | 0 |

The point B’’ is located in the middle of edge BB’. The same applies to point C’’ and edge CC’.

The gradient of edge BC is defined via equation \(\eqref{edgeBC}\) and for the edge AD via equation \(\eqref{edgeAD}\).

## Analysis type and Domain¶

**Tool Type** : Code_Aster

**Analysis Type** : Static (linear elastic)

**Mesh and Element types** :

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

(A) | quadratic tetrahedral | 26761 | 3D isoparametric |

(B) | quadratic tetrahedral | 174707 | 3D isoparametric |

(C) | linear hexahedral | 36 | 3D isoparametric |

(D) | quadratic hexahedral | 111 | 3D isoparametric |

(E) | linear hexahedral | 105 | 3D isoparametric |

(F) | quadratic hexahedral | 349 | 3D isoparametric |

(G) | quadratic hexahedral | 52941 | 3D isoparametric |

## Simulation Setup¶

Material:

- isotropic: E = 210 GPa, \(\nu\) = 0.3

Constraints:

- Face DCD’C’ zero y-displacement
- Face ABA’B’ zero x-displacement
- Face BCB’C’ x and y displacements fixed
- z-displacement fixed along the edge B’‘C’‘

Loads:

- Pressure of 1 MPa on Face ABCD

## Results¶

Comparison of the stress \(\sigma_{YY}\) at point D obtained with SimScale and the results presented in [NAFEMS].

Case | [NAFEMS] | SimScale | Error (%) |
---|---|---|---|

(A) | 5.38 | 5.44473 | 1.20% |

(B) | 5.38 | 5.39614 | 0.30% |

(C) | 5.38 | 3.98345 | -25.96% |

(D) | 5.38 | 5.47091 | 1.69% |

(E) | 5.38 | 5.10811 | -5.05% |

(F) | 5.38 | 5.71058 | 6.14% |

(G) | 5.38 | 5.38599 | 0.11% |