13. K modeling#

13.1. Characteristics of modeling#

3D modeling is used with element type PYRAM13 and the LAC contact processing method.

13.2. 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 as in the G modeling for elements HEXA20.

However, by using the option DECOUPE_HEXA = “PYRA” in the CREA_MAILLAGE command, you can treat the slave meshes with the element type PYRAM13 for contact processing by the LAC method:

  • mesh 0:4 elements of type TRIA6, 5 elements of type QUAD8, 5 elements of type PYRAM13 and 0 elements of type HEXA20

  • mesh 1:16 elements of type TRIA6, 20 elements of type QUAD8, 20 elements of type PYRAM13et 4 element of type HEXA20

  • mesh 2:64 elements of type TRIA6, 80 elements of type QUAD8, 80 elements of type PYRAM13et, 48 elements of type HEXA20

  • mesh 3:256 elements of type TRIA6, 320 elements of type QUAD8, 320 elements of type PYRAM13et, 448 elements of type HEXA20

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.

13.3. 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