15. L modeling#

15.1. Characteristics of modeling#

3D modeling is used with element type PENTA15 and the LAC contact processing method.

15.2. 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 PENTA15.

However, using the option DECOUPE_HEXA = “PYRA” in the CREA_MAILLAGE command, the slave meshes (PENTA15) are cut into TETRA10 and PYRAM13 for contact processing by the LAC method:

  • mesh 0:8 elements of type TRIA6, 4 elements of type QUAD8, 4 elements of type, 2 elements of type TETRA10, 6 elements of type PYRAM13 and 0 elements of type PENTA15

  • mesh 1:32 elements of type TRIA6, 16 elements of type QUAD8, 16 elements of type, 8 elements of type, 8 elements of type, 8 elements of type, 8 elements of type TETRA10 PYRAM13et PENTA15

  • mesh 2:128 elements of type TRIA6, 64 elements of type QUAD8, 64 elements of type, 32 elements of type TETRA10, 96 elements of type PYRAM13et, 96 elements of type PENTA15

  • mesh 3:512 elements of type TRIA6, 256 elements of type QUAD8, 256 elements of type, 128 elements of type TETRA10, 384 elements of type PYRAM13et 896 elements of type PENTA15

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.

15.3. 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