3. Modeling A#

3.1. Characteristics of modeling#

Modeling: C_ PLAN.

The structure is a healthy rectangle, in which an interface is introduced directly into the command file using the DEFI_FISS_XFEM [U4.82.08] operator. The interface is present at a distance \({L}_{Y}\mathrm{=}\mathrm{1,8}m\) from the top edge of the plate.

3.2. Characteristics of the mesh#

Number of knots: 661

Number of meshes and types: 200 QUAD8 for the plate and 50 SEG3 for the edges.

_images/100002010000020F0000031193B4B0EF5C4FCF2B.png

Figure 3.2‑a: 2D quadrangle mesh and interface position

3.3. Tested sizes and results#

The movements resulting from the operator STAT_NON_LINE are post-processed in order to recover the values at the nodes of the crack from the new mesh.

Identification

Reference

Aster

tolerance

\(\mathrm{DX}\) at point \(A\)

1.10-5

Analytical

1.10-12

\(\mathrm{DX}\) at point \(B\)

-1.10-5

Analytical

1.10-12

\(\mathrm{DY}\) at point \(A\)

5,52.10-6

Analytical

1.10-12

\(\mathrm{DY}\) at point \(B\)

5,52.10-6

Analytical

1.10-12

\(\mathrm{DY}\) at point \(O\)

8,02.10-6

Analytical

1.10-12

3.4. Comments#

This test validates:

  • the calculation of the stiffness matrix and the second member vectors (taking into account the pressure distributed over elements with quadratic edges),

  • X- FEM post-processing of \(\mathrm{P2}\) elements.