4. B modeling#
4.1. Characteristics of modeling#
We use a D_ PLAN modeling.
4.2. Characteristics of the mesh#
A convergence study is carried out with the fineness of the mesh from the calculated solution to the analytical solution. A series of meshes obtained by uniform refinement using the MACR_ADAP_MAIL command is used:
mesh 0:5 SEG3, 1 QUAD8
mesh 1:9 SEG3, 4 QUAD8
mesh 2:17 SEG3, 16 QUAD8
mesh 3:32 SEG3, 64 QUAD8
mesh 4:64 SEG3, 256 QUAD8
The curved master surface is represented by a single SEG3.
4.3. Tested sizes and results#
The convergence speed is tested with the fineness of the mesh from the calculated solution to the analytical solution in standard \({L}_{2}\):
the largest real \({\mathrm{\alpha }}_{U}>0\) such as \({\Vert {\underline{U}}^{\text{calc}}-{\underline{U}}^{\text{ref}}\Vert }_{0,\mathrm{\Omega }}<{C}_{U}\times {h}^{{\mathrm{\alpha }}_{U}}\) where \({C}_{U}\) is independent of \(h\) for displacement;
the largest real \({\mathrm{\alpha }}_{p}>0\) such as \({\Vert {p}^{\text{calc}}-{p}^{\text{ref}}\Vert }_{0,{\mathrm{\Gamma }}_{C}}<{C}_{p}\times {h}^{{\mathrm{\alpha }}_{p}}\) where \({C}_{p}\) is independent of \(h\) for contact pressure.
The sum of the absolute values of the difference between the calculated solution and the analytical solution for the displacement is also tested.
Identification |
Reference type |
Reference value |
|
“NON_REGRESSION” |
6.62799356621E-07 |
\({\mathrm{\alpha }}_{U}\) |
“ANALYTIQUE” |
3.0 |
\({\mathrm{\alpha }}_{p}\) |
“ANALYTIQUE” |
2.5 |
\({\mathrm{\alpha }}_{p}\) |
“NON_REGRESSION” |
2.8035 |