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

Geometry
---------

A cable of length :math:`2{l}_{0}` at rest, in the direction :math:`x`, is subjected to its own weight (gravity in direction :math:`-Z`). It is embedded at the :math:`O` and :math:`B` ends, which are themselves distant from :math:`\mathrm{2L}`.


.. image:: images/1000000000000192000000759F942EEEF5F0D230.png
    :width: 3.339in
    :height: 0.9689in


.. _RefImage_1000000000000192000000759F942EEEF5F0D230.png:

Initially, :math:`2{l}_{0}=2L=\mathrm{325m}`

The cable cross-sectional area is: :math:`2.2783E-04{m}^{2}`


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

:math:`E=5.70E+10\mathrm{Pa}`

:math:`\nu =0.3` (B modeling only)

:math:`\mathrm{ALPHA}:2.3E-5{K}^{-1}`

:math:`\mathrm{RHO}:2.844230E+03\mathrm{kg}/{m}^{3}`


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

Embedding in :math:`O` and :math:`B`

Gravity: :math:`(9.81\mathrm{,0}.0\mathrm{,0}.0,-1.0)`

The temperature in the cable varies over time, the reference temperature is :math:`0.°C`.

• Instant: 0. Temperature :math:`T=0.°C`

• Instant: 1.Temperature :math:`T=39.26°C`

We therefore treat:

• at instant 0, a cable subject to its own weight alone

• at instant 1, a heavy cable subjected to thermal expansion.