1. Problème de référence#
1.1. Géométrie#
On considère deux cubes \(A\) et \(B\) de coté \(a=2\mathit{mmm}\) . Les deux cubes sont initialement en contact (pas de jeu entre \(A\) et \(B\) ).
Voici la position des points de référence (\(\mathit{mm}\) ):
Cube |
Point |
\(x\) |
\(y\) |
\(z\) |
\(A\) |
\(\mathit{NH1}\) |
2 |
0 |
2 |
\(A\) |
\(\mathit{NH2}\) |
2 |
2 |
2 |
\(A\) |
\(\mathit{NH3}\) |
0 |
2 |
2 |
\(A\) |
\(\mathit{NH4}\) |
0 |
0 |
2 |
\(A\) |
\(\mathit{NH5}\) |
2 |
0 |
4 |
\(A\) |
\(\mathit{NH6}\) |
2 |
2 |
4 |
\(A\) |
\(\mathit{NH7}\) |
0 |
2 |
4 |
\(A\) |
\(\mathit{NH8}\) |
0 |
0 |
4 |
\(A\) |
\(\mathit{NH9}\) |
2 |
1 |
2 |
\(A\) |
\(\mathit{NH10}\) |
1 |
2 |
2 |
\(A\) |
\(\mathit{NH11}\) |
0 |
1 |
2 |
\(A\) |
\(\mathit{NH12}\) |
1 |
0 |
2 |
\(A\) |
\(\mathit{NH17}\) |
2 |
1 |
4 |
\(A\) |
\(\mathit{NH18}\) |
1 |
2 |
4 |
\(A\) |
\(\mathit{NH19}\) |
0 |
1 |
4 |
\(A\) |
\(\mathit{NH20}\) |
1 |
0 |
4 |
\(A\) |
\(\mathit{NH26}\) |
1 |
1 |
4 |
\(A\) |
\(\mathit{NH21}\) |
1 |
1 |
2 |
\(B\) |
\(\mathit{NB1}\) |
2 |
0 |
0 |
\(B\) |
\(\mathit{NB2}\) |
2 |
2 |
0 |
\(B\) |
\(\mathit{NB3}\) |
0 |
2 |
0 |
\(B\) |
\(\mathit{NB4}\) |
0 |
0 |
0 |
\(B\) |
\(\mathit{NB5}\) |
2 |
0 |
2 |
\(B\) |
\(\mathit{NB6}\) |
2 |
2 |
2 |
\(B\) |
\(\mathit{NB7}\) |
0 |
2 |
2 |
\(B\) |
\(\mathit{NB8}\) |
0 |
0 |
2 |
\(B\) |
\(\mathit{NB17}\) |
2 |
1 |
2 |
\(B\) |
\(\mathit{NB18}\) |
1 |
2 |
2 |
\(B\) |
\(\mathit{NB19}\) |
0 |
1 |
2 |
\(B\) |
\(\mathit{NB20}\) |
1 |
0 |
2 |
\(B\) |
\(\mathit{NB26}\) |
1 |
1 |
2 |
\(B\) |
\(\mathit{NB9}\) |
2 |
1 |
0 |
\(B\) |
\(\mathit{NB10}\) |
1 |
2 |
0 |
\(B\) |
\(\mathit{NB11}\) |
0 |
1 |
0 |
\(B\) |
\(\mathit{NB12}\) |
1 |
0 |
0 |
\(B\) |
\(\mathit{NB21}\) |
1 |
1 |
0 |
1.2. Propriétés des matériaux#
Les deux cubes sont élastiques avec:
Coefficient de Poisson: \(0\)
Module d’Young: \(200\mathit{GPa}\)
1.3. Conditions aux limites et chargements#
On impose un déplacement \(\mathit{DZ}=-\mathrm{0.2mm}\) sur le cube \(A\) . Les deux cubes sont en contact sans frottement.