3. Modeling A#

3.1. Characteristics of modeling#

The modeling used is a C_ PLAN modeling.

3.2. Characteristics of the mesh#

The mesh is composed of 240 linear triangles. The mesh is transformed into a quadratic mesh in the command file. In addition, the elements at the bottom of the crack are transformed into Barsoum elements.

_images/10000000000001F70000039E5A39A3D90F345547.gif

Figure 3.2-a : Mesh for problem 1

3.3. Tested sizes and results#

We test the values of the stress intensity factors given by the command POST_K1_K2_K3 (analytical comparison and non-regression) and the value of the error estimators for the 3 methods implemented in Code_Aster (parameters ERREUR_ERRE, ERREUR_ERZ1, ERREUR_ERZ2, ERREUR_QIRE,,,,,,, ERREUR_QIZ1, ERREUR_QIZ2) for the primal problem and the dual problem (non- comparison regression).

Quantity tested

Reference value

Tolerance (relative)

K1 (analytics)

9.37

0.005

ERREUR_ERRE

2.6654055228458E-03

1.E-8

ERREUR_ERZ1

3.087758564444437E-03

1.E-8

ERREUR_ERZ2

7.476798989844696E-03

1.E-8

ERREUR_ERRE

5.2145715958031E+01

1.E-8

ERREUR_ERZ1

6.2002976336900E+01

1.E-8

ERREUR_ERZ2

1.4362442647950E+02

1.E-8

ERREUR_QIRE

9.3257156697600E+01

1.E-8

ERREUR_QIZ1

3.087758564444437E-03

1.E-8

ERREUR_QIZ2

7.476798989844696E-03

1.E-8

Table 3.3-1 : Results for the quantities tested