14. L modeling#

14.1. Characteristics of modeling#

3D modeling is used with element type PENTA6 and the LAC contact processing method.

14.2. 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 for element type PENTA6.

However, using the option DECOUPE_HEXA = “PYRA” in the CREA_MAILLAGE command, the slave meshes (PENTA6) are cut into TETRA4 and PYRAM5 for contact processing by the LAC method:

  • mesh 0:8 elements of type TRIA3, 4 elements of type QUAD4, 4 elements of type, 2 elements of type TETRA4, 6 elements of type PYRAM5 and 0 elements of type PENTA6

  • mesh 1:32 elements of type TRIA3, 16 elements of type QUAD4, 16 elements of type, 8 elements of type, 8 elements of type, 8 elements of type, 8 elements of type TETRA4 PYRAM5et PENTA6

  • mesh 2:128 elements of type TRIA3, 64 elements of type QUAD4, 64 elements of type, 32 elements of type TETRA4, 96 elements of type PYRAM5et, 96 elements of type PENTA6

  • mesh 3:512 elements of type TRIA3, 256 elements of type QUAD4, 256 elements of type, 128 elements of type TETRA4, 384 elements of type PYRAM5et 896 elements of type PENTA6

  • mesh 4:2048 elements of type TRIA3, 1024 elements of type QUAD4, 1024 elements of type, 512 elements of type TETRA4, 1536 elements of type PYRAM5et, 7680 element of type PENTA6

We note that, compared to the E and F models, the curved surface \(\text{MAITRE}\) is meshed with 2 TRIA6au instead of a single QUAD8.

14.3. 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”

2.0

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

“ANALYTIQUE”

0.5