8. F modeling#

8.1. Characteristics of modeling#

3D modeling is used with element type TETRA10 and the LAC contact processing method.

8.2. 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 0:16 elements of type TRIA6 and 10 elements of type TETRA10

  • mesh 1:64 elements of type TRIA6 and 64 elements of type TETRA10

  • mesh 2:256 elements of type TRIA6 and 448 elements of type TETRA10

  • mesh 3:1024 elements of type TRIA6 and 3328 elements of type TETRA10

The curved \(\text{MAITRE}\) surface is meshed with a unique QUAD8.

8.3. 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 \({\alpha }_{U}>0\) such as \({\mathrm{\parallel }{\underline{U}}^{\text{calc}}\mathrm{-}{\underline{U}}^{\text{ref}}\mathrm{\parallel }}_{\mathrm{0,}\Omega }<{C}_{U}\mathrm{\times }{h}^{{\alpha }_{U}}\) 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.

Identification

Reference type

Reference value

\({\mathrm{\alpha }}_{U}\)

“ANALYTIQUE”

2.5

\({\mathrm{\alpha }}_{p}\)

“ANALYTIQUE”

1.0