1. Reference problem#

1.1. Geometry#

_images/Shape1.gif

\({R}_{0}\)

\(1m\)

\({R}_{1}\)

\(2m\)

1.2. Material properties#

Young’s module: \(E=1\mathrm{MPa}\)

Poisson’s ratio: \(\nu \mathrm{=}0.3\)

Expansion coefficient: \(\alpha \mathrm{=}0.7\)

Law of LEMAITRE:

\(g(\sigma ,\lambda ,T)\mathrm{=}{(\frac{1}{K}\frac{\sigma }{{\lambda }^{\frac{1}{m}}})}^{n}\) with \(\frac{1}{K}\mathrm{=}1\), \(\frac{1}{m}\mathrm{=}0\), \(n\mathrm{=}1\)

1.3. Boundary conditions and loading#

Boundary conditions:

The cylinder is locked at \(\mathit{DY}\) on the \(\mathrm{[}\mathit{AB}\mathrm{]}\) and \(\mathrm{[}\mathit{CD}\mathrm{]}\) sides.

Charging:

The cylinder is subjected to a temperature field \(T(r,t)\mathrm{=}t{r}^{2}\)