3. Modeling A#

3.1. Characteristics of modeling#

A 3D modeling with the mesh crack is considered 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 \(5\times 30\times 50\) HEXA8, respectively along the axes \(x\) , \(y\) , \(z\) (see [Figure 3.2-a]). The two superimposed surfaces are the lips of the crack.

_images/10000000000001980000035C5C9BE1B34521ECEC.png

Figure 3.2-a: The mesh for modeling A

3.3. Tested sizes and results#

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

Identification

Reference

Code_Aster

% difference

Frequency mode 1

1.363

1.363

1.363

Frequency mode 2

3.220

3.220

3.220

Frequency mode 3

4.815

4.815

Frequency mode 4

7.195

7.195

7.195

Frequency mode 5

10.098

10.098

10.098

Frequency mode 6

11.789

11.789

11.789

Frequency mode 7

17.484

17.484

17.484

Frequency mode 8

18.281

18.281

18.281