1. Reference problem#

1.1. YGéométrie#

C

D

X

A

B

L=20 cm

Thickness = \(\mathrm{0.25cm}\).

1.2. Material properties#

The material is isotropic elastic whose properties are:

  • \(E\mathrm{=}3.\mathrm{\times }{10}^{6}N\mathrm{/}{\mathit{cm}}^{2}\)

  • \(\nu \mathrm{=}0.3\)

  • \(\alpha \mathrm{=}6.5\mathrm{\times }{10}^{\mathrm{-}6}\mathrm{/}°C\)

1.3. Boundary conditions and loads#

Boundary conditions:

  • On edge \(\mathit{AB}\): \(\mathit{DY}\mathrm{=}\mathit{DRX}\mathrm{=}0\)

  • On edge \(\mathit{AD}\): \(\mathit{DX}\mathrm{=}\mathit{DRY}\mathrm{=}0\)

  • On edges \(\mathit{BC}\) and \(\mathit{CD}\): \(\mathit{DZ}\mathrm{=}0\)

Loading

  • The load applied is a loading temperature that varies as follows:

Upper skin: \(T(x,y)\mathrm{=}100\mathrm{-}5∣x∣\mathrm{-}5∣y∣+\frac{1}{2}∣\mathit{xy}∣\)

Lower skin: \(T(x,y)\mathrm{=}\mathrm{-}100+5∣x∣+5∣y∣\mathrm{-}\frac{1}{2}∣\mathit{xy}∣\)

_images/Shape16.gif

1.4. Initial conditions#

Néant