Reference problem
=====================


Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


.. csv-table::

    ":math:`{R}_{0}` "," :math:`1m`"
    ":math:`{R}_{1}` "," :math:`2m`"



Material properties
------------------------

Young's module: :math:`E=1\mathrm{MPa}`

Poisson's ratio: :math:`\nu \mathrm{=}0.3`

Expansion coefficient: :math:`\alpha \mathrm{=}0.7`

Law of LEMAITRE:

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


Boundary conditions and loading
------------------------------------

**Boundary conditions:**

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

**Charging:**

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