6. D modeling#

6.1. Characteristics of modeling#

3D modeling and the DISCRETE method of the projected conjugate gradient (GCP) of contact treatment are used.

6.2. 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 0:2 elements of type TRIA6, 6 elements of type QUAD9 and 1 element of type HEXA27

  • mesh 1:2 elements of type TRIA6, 24 elements of type QUAD9 and 8 elements of type HEXA27

  • mesh 2:2 elements of type TRIA6, 96 elements of type QUAD9 and 64 elements of type HEXA27

  • mesh 3:2 elements of type TRIA6, 384 elements of type QUAD9 and 512 elements of type HEXA27

Note that, compared to models A and B, the base is meshed with 2 TRIA6 instead of QUAD8. Indeed, discrete methods are not adapted to the use of these elements (see [R5.03.50]).

6.3. Tested sizes and results#

The sum of the absolute values of the difference between the calculated solution and the analytical solution for the displacement is tested. We do not test the convergence rate because element HEXA27 provides the exact solution with a single element.

Identification

Reference type

Reference value

\(\sum ^{\text{noeuds}n}\mid {\underline{U}}_{\text{n}}^{\text{calc}}-{\underline{U}}_{\text{n}}^{\text{ref}}\mid\)

“NON_REGRESSION”

0