1. Reference problem#

1.1. Geometry#

It is a rectangular plate with cracks:

_images/10000FF400001C5200001C6C0A2312F6CCECCA50.svg

Figure 1.1-a: Cracked rectangular plate

The dimensions of this plate are as follows:

Half plate height:

\(h=200.0\mathrm{mm}\)

Half-width of the plate:

\(I=100.0\mathrm{mm}\)

Half-length of crack:

\(a=50.0\mathrm{mm}\)

In modeling A

a quarter of the plate is modelled

as in FIG. 1.1-a.

In modeling B

the entire height of the plate is modelled.

1.2. Material properties#

Thermal properties:

\(\mathit{Cp}\mathrm{=}0.\)

\(\lambda =1.0W/m°C\)

Mechanical properties:

\(E=200000\mathrm{MPa}\)

\(\nu =0.3\)

\(\alpha ={5.10}^{-6}/°C\)

We are under the hypothesis of plane deformations.

1.3. Boundary conditions and loads#

1.3.1. Modeling A#

  • Temperature imposed in \(X=0.\): \(T=-100.0°C\)

  • Temperature imposed in \(X=100\): \(T=+100.0°C\)

  • Travel to \(a<X<I\), \(Y=0.\): \(v=0.\)

  • Travel to \(0<X<I\), \(Y=H\): \(v=0.\)

  • Travel to \(X=0.\), \(Y=H\): \(u=0.\)

1.3.2. B modeling#

  • Rigid body rotation at a 45° angle

  • Then pressure imposed in \(X=100\) and \(X=-100\): \(P=-10\mathit{MPa}\)