4. B modeling#

4.1. Characteristics of modeling#

We use 3D modeling and the CONTINUE contact treatment method.

4.2. 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 0:1 element of type QUAD8, 12 elements of type TRIA6 and 6 elements of type TETRA10

  • mesh 1:1 element of type QUAD8, 48 elements of type TRIA6, and 48 elements of type TETRA10

  • mesh 2:1 element of type QUAD8, 192 elements of type TRIA6, and 384 elements of type TETRA10

  • mesh 3:1 element of type QUAD8, 768 elements of type TRIA6, and 3072 elements of type TETRA10

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

The sum of the absolute values of the difference between the calculated solution and the analytical solution for the displacement is also tested.

Identification

Reference type

Reference value
math:

sum ^ {text {nodes} n}} | {underline {U}} | {underline {U}}} _ {text {calc}} - {underline {U}}} _ {text {U}}} _ {text {U}}}} _ {text {n}}} |

“NON_REGRESSION”

4.13935026178E-05

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

“ANALYTIQUE”

3.0

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

“NON_REGRESSION”

2.534025066720

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

“ANALYTIQUE”

2.5