3. Modeling A#

3.1. Characteristics of modeling#

In this modeling we consider the framework of plane deformations (D_ PLAN), the crack is meshed, and the classical finite element method is used to perform the calculation. This modeling will serve as a reference and will allow comparison with the X- FEM method.

3.2. Characteristics of the mesh#

The structure is modelled by a regular mesh composed of \(30\times 50\) QUAD4, respectively along the \(x,y\) axes (see [Figure 3.2‑a]). The lips of the crack are generated by the two superimposed edges halfway up the plate (thicker line in the figure).

_images/100000000000022E000003DEBE63EC1573ED0C45.png

Figure 3.2‑a: Meshing for modeling A. Illustration of boundary conditions and loading

3.3. Tested features#

The first 8 natural modes of the structure are calculated by considering the contribution of the geometric rigidity due to the prestress induced to equilibrium by the load in question.

Orders

CALC_MATR_ELEM

OPTION = “RIGI_MECA” OPTION = “MASS_MECA” OPTION = “RIGI_GEOM”

CALC_MODES

CALC_FREQ

SOLVEUR_MODAL

OPTION = “PLUS_PETITE”

NMAX_FREQ = 8 METHODE = “SORENSEN”

3.4. Tested sizes and results#

For this modeling, non-regression tests on the natural frequencies of the first 8 modes are considered.