1. Reference problem#
1.1. Geometry#
Plate width: |
\(W=\mathrm{0,6}m\) |
Plate length: |
\(L=\mathrm{0,3}m\) |
Crack length: |
\(\mathrm{2a}=\mathrm{0,3}m\) |
1.2. Material properties#
Notation for thermoelastic properties:
We are limited to isotropic material, both from a thermal and mechanical point of view:
\({E}_{x}={E}_{y}={2.10}^{5}\mathrm{MPa}\)
\({\nu }_{x}={\nu }_{y}=\mathrm{0,3}\)
\({\alpha }_{x}={\alpha }_{y}=\mathrm{1,2}{10}^{-5}°{C}^{-1}\)
\({\lambda }_{x}={\lambda }_{y}=54W/m°C\)
1.3. Boundary conditions and loading#
Two models are considered:
the half-model \(x\ge 0\)
the complete model
Mechanical boundary conditions:
half-model
\(\mathrm{UX}=0\) along the axis of symmetry \(X=0\)
\(\mathrm{UY}=0\) at point \((W/\mathrm{2,0})\)
full model
\(\mathrm{UX}=0\) at point \((\mathrm{0,}L/2)\)
\(\mathrm{UY}=0\) at points \((–L/\mathrm{2,0})\) and \((L/\mathrm{2,0})\)
Thermal boundary conditions:
half-model
\(T=100°C\) on the top edge \(Y=L/2\)
\(T=–100°C\) on the bottom edge \(Y=–L/2\)
zero flow on the axis of symmetry, on the free edge \(X=W/2\) and on the edge of the crack
full model
\(T=100°C\) on the top edge \(Y=L/2\)
\(T=–100°C\) on the bottom edge \(Y=–L/2\)
zero flux on free edges \(X=\pm W/2\) and on the edge of the crack