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


Geometry
---------

A rectangular parallelepiped modeling concrete, and a line included in this volume modeling the prestress cable:


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

All dimensions are in meters. The cross-sectional area of the cable is :math:`A=0.00015{m}^{2}` The cable is parallel to the :math:`x` axis. Its intersection with plane :math:`(\mathrm{Oyz})` is defined by point :math:`(1.,0.3)`.


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

:math:`E=2.1{10}^{11}\mathrm{Pa}` for cable, and :math:`E={3.10}^{10}\mathrm{Pa}` for concrete.

:math:`{\rho }_{c}=2{10}^{4}\mathrm{kg}/{m}^{3}` for cable, and for concrete, :math:`{\rho }_{b}=3\mathrm{kg}/{m}^{3}` (non-physical values intended to make the weight of the cable preponderant)


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

:math:`\mathrm{DY}=0` at point :math:`1001`, :math:`\mathrm{DZ}=0` for all nodes on face :math:`z=0`, and :math:`\mathrm{DX}=0` for all nodes on face :math:`x=0`.

A single load is applied: gravity, with :math:`g=10m/{s}^{2}`, successively in the direction :math:`–z` then :math:`–x`.

There is also an initial voltage in cable :math:`N=2.{10}^{5}N`.