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


Geometry
---------


.. image:: images/100006C600002E82000018E8B5BDC14137EACC6C.svg
    :width: 473
    :height: 253


.. _RefImage_100006C600002E82000018E8B5BDC14137EACC6C.svg:

Steel piston connected to the solid by a spring and coupled to a column of incompressible fluid:


.. csv-table::

    "length:", ":math:`L=1.0m`"
    "width:", ":math:`d=0.25m`"
    "piston width :math:`\mathit{AB}`:", ":math:`0.05m`"


**X-points (in** :math:`m` **) :**


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`L`"
    ":math:`x` ", "—0.05", "0. ", "1."



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

**Fluid:**

Water **:** :math:`{\rho }_{0}=1000.0{\mathrm{Kg.m}}^{-3}`

**Solid:**

Steel: :math:`{\rho }_{S}=7800.0{\mathrm{Kg.m}}^{-3}`; :math:`E=2.E11\mathrm{Pa}`; :math:`\nu =0.3`

**Spring connecting the piston to the solid:**

Discrete element of the K_T_D_L type: :math:`K\mathrm{=}(1.E5,1.E5,1.E5)N\mathrm{/}m`


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

Pressure is imposed (i.e. by thermal analogy a zero temperature [:ref:`R4.07.03 <R4.07.03>`]) at all the nodes at the end of the fluid column.

The spring is forced to be embedded on the solid and a zero displacement of the piston is imposed according to :math:`\mathrm{Oy}`.