4. B modeling#

4.1. Characteristics of modeling#

Modeling: C_ PLAN. It is used to validate the “VERSION3” keyword used for ALGO_LAGR in DEFI_CONTACT. The structure is a healthy square, in which an arc-shaped interface is introduced.

Contact/friction is treated with elements X- FEMquadratiques \(\text{P2}\) (displacement) and \(\text{P1}\) (pressure), i.e. carrying the degrees of freedom of movement on all the nodes and the Lagranges of contact/friction on the vertex nodes.

4.2. Characteristics of the mesh#

Number of knots: 6561

Number of meshes and types: 3200 TRIA6 for the plate and 160 SEG3 for the edges.

_images/100000000000031C00000315549C5EFE4167F9B4.png

Figure 4.2‑a: 2D triangle mesh

4.3. Tested sizes and results#

The values only appear at the interface nodes from the new mesh.

Identification

Reference type

Reference value

Precision

\(\text{LAGS\_C}\) at points \(A\) and \(C\) (MIN)

“ANALYTIQUE”

-0.1

0.1%

\(\text{LAGS\_C}\) at point \(B\) (MAX)

“ANALYTIQUE”

-0.06110

0.1%

\(\text{LAGS\_F1}\) at point \(B\) (MIN)

“ANALYTIQUE”

0

0.1%

\(\text{LAGS\_F1}\) at point \(A\) (MAX)

“ANALYTIQUE”

0.39894

0.5%

4.4. Comments#

This test validates:

  • the calculation of the stiffness matrix (the right offset when filling the matrix because the nodes do not have the same number of degrees of freedom),

  • the calculation of contact matrices (integration on a SE3 at Gauss points),

  • subdivision (curved interface configurations and elements with straight edges),

  • the X- FEM post-processing of the \(\text{P2P1}\) elements,

  • the refinement of the mesh, makes it possible to obtain more accurate results (compared to modeling \(\text{A}\)),

  • the version 3 algorithm of equality relationships on cut edges, for quadratic elements in small slips, in order to satisfy LBB.