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


Geometry
---------

It is a hollow cylinder, similar to the one treated in SSNA106.


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


.. csv-table::

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



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


Umat data
~~~~~~~~~~~~

For the Umat behavior present as an example in the Code_Aster sources, elasticity is expressed by:

:math:`\mathrm{C1}=\lambda =\frac{E\nu }{(1+\nu )(1-2\nu )}`

:math:`\mathrm{C2}=\mu =\frac{E}{2(1+\nu )}`

:math:`\mathrm{C3}=\mathrm{C4}=\mathrm{C5}=0`


Aster data
~~~~~~~~~~~~~

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

Poisson's ratio: :math:`\nu =0.3`

Expansion coefficient: :math:`\alpha =0.7`


Boundary conditions and loads
-------------------------------------

**Boundary conditions:**

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

Charging:

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