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


Geometry
---------

We consider a hollow sphere with external radius :math:`30\mathit{mm}` and internal radius :math:`20\mathit{mm}`, included in a hollow sphere with external radius :math:`40\mathit{mm}` and internal radius equal to the external radius of the included sphere.


.. image:: images/Object_4.png
    :width: 3.4799in
    :height: 3.428in


.. _RefSchema_Object_4.png:


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

The material is isotropic elastic whose properties are:


* :math:`E=2000\mathit{MPa}`


* :math:`\nu =0.3`


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


.. _DdeLink__23919_998177675:

Symmetry conditions :math:`\mathit{DX}=0` on the surface :math:`\mathit{AD}` and :math:`\mathit{DY}=0` on the surface :math:`\mathit{BC}` are imposed in order to model only a quarter of the model.


.. image:: images/Object_13.png
    :width: 3.4791in
    :height: 3.4272in


.. _RefSchema_Object_13.png:

Pressure :math:`P=25\mathit{MPa}` is imposed on the surface :math:`\mathit{AB}`, inside the first sphere. The two spheres are kept in contact at the interface.