1. Reference problem#

1.1. Geometry#

The geometry, dimensions, and materials are taken to be identical to those of Mariani et al. [1].

Structure \(\mathrm{2D}\) is a rectangular plate (\(230\mathrm{mm}\times 75\mathrm{mm}\)), with a through crack []. The length of the initial crack is \(a=19\mathrm{mm}\).

The nodes noted \(\mathrm{P1}\), \(\mathrm{P2}\), and \(\mathrm{P3}\) are used to impose boundary conditions, which are explained in paragraph [§ 1.3].

_images/100000000000036C000001F4204637ECE470175F.jpg

Figure 1.1-a : geometry of the cracked plate

1.2. Material properties#

Young’s module: \(E=\mathrm{31,37}{10}^{9}\mathrm{Pa}\)

Poisson’s ratio: \(\nu =0.2\)

1.3. Boundary conditions and loads#

Charging consists of applying a unit nodal force in \(\mathrm{P3}\).

In order to block rigid modes, we block the movements of nodes \(\mathrm{P1}\) and \(\mathrm{P2}\) as follows:

  • \({\mathrm{DY}}^{\mathrm{P1}}={\mathrm{DY}}^{\mathrm{P2}}=0\);

  • \({\mathrm{DX}}^{\mathrm{P1}}=0\).