7. E modeling#

7.1. Characteristics of modeling#

A D_ PLAN modeling is used with the element type QUAD4 and the contact processing method LAC.

7.2. 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 0:6 SEG2, 4 QUAD4

  • mesh 1:12 SEG2, 10 QUAD4

  • mesh 2:24 SEG2, 28 QUAD4

  • mesh 3:48 SEG2, 88 QUAD4

  • mesh 4:96 SEG2, 304 QUAD4

  • mesh 5:192 SEG2, 1120 QUAD4

The curved \(\text{MAITRE}\) surface is represented by a single SEG3.

7.3. 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 \({\parallel {\underline{U}}^{\text{calc}}-{\underline{U}}^{\text{ref}}\parallel }_{\mathrm{0,}\Omega }<{C}_{U}\times {h}^{{\alpha }_{U}}\) where \({C}_{U}\) is independent of \(h\) for displacement;

  • the largest real \({\alpha }_{p}>0\) such as \({\parallel {p}^{\text{calc}}-{p}^{\text{ref}}\parallel }_{\mathrm{0,}{\Gamma }_{C}}<{C}_{p}\times {h}^{{\alpha }_{p}}\) where \({C}_{p}\) is independent of \(h\) for contact pressure.

Identification

Reference type

Reference value

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

“ANALYTIQUE”

2.0

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

“ANALYTIQUE”

0.5