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


Geometry
---------


.. image:: images/100017D400002CDB000017FAC289F932EB18ED55.svg
    :width: 578
    :height: 309


.. _RefImage_100017D400002CDB000017FAC289F932EB18ED55.svg:


.. csv-table::

    "Length:", ":math:`L=4m`"
    "width:", ":math:`l=2m`"
    "height:", ":math:`h=2m`"
    "Shell thickness:", ":math:`e={10}^{-3}m`"
    "Radius of the spheres:", ":math:`R=0.5m`"



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

Structure: steel - elastic material

:math:`E={2.10}^{11}\mathrm{Pa}`

:math:`\nu =0.3`

:math:`{\rho }_{s}=7800\mathrm{kg}/{m}^{3}`

The springs have the following stiffness:


.. csv-table::

    ":math:`\mathrm{K1}={10}^{6}N/m` "," :math:`\mathrm{K2}={10}^{5}N/m` "," :math:`\mathrm{K3}={10}^{7}N/m`"


Fluid: water - equivalent thermal material

:math:`\lambda =1.`

the specific heat plays the role of the density of the fluid: :math:`{\rho }_{f}=1000\mathrm{kg}/{m}^{3}`


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

On the structure side: the degrees of freedom of rotation :math:`\mathrm{DRX}`, :math:`\mathrm{DRY}`, :math:`\mathrm{DRZ}` of sphere 1 are blocked:


.. code-block:: text
 DRX: 0.0 DRY: 0.0:0.0 DRZ: 0.0

On the fluid side: zero pressure (i.e. temperature) is imposed on a node of the fluid mesh.