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

Geometry
---------


.. image:: images/10000000000002950000015E5995D9654244415A.png
    :width: 5.5028in
    :height: 2.9102in


.. _RefImage_10000000000002950000015E5995D9654244415A.png:

Beam length: :math:`\mathrm{1.5m}`

Discreet stiffness: :math:`\mathrm{kax}`, :math:`\mathrm{kay}`,, :math:`\mathrm{kbx}`, :math:`\mathrm{kby}`


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

Material for the line element: :math:`E=2.0E+10`, :math:`\rho =1000.0`

Mechanical characteristics of the girder: :math:`\mathrm{section}=\text{'}\mathrm{CERCLE}\text{'}`, :math:`\mathrm{rayon}=0.1`, :math:`\mathrm{ep}=0.1`

The stiffness of the springs:

.. csv-table::

    ":math:`\mathrm{Kxa}` "," :math:`\mathrm{Kya}` "," :math:`\mathrm{Kxb}` "," :math:`\mathrm{Kyb}`"
    ":math:`10N/m` "," :math:`20N/m` "," :math:`25N/m` "," :math:`22N/m`"



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

At points :math:`A` and :math:`B`: blocking the degrees of freedom: :math:`\mathrm{DX},\mathrm{DY},\mathrm{DZ}`

At points :math:`\mathrm{A1}` and :math:`\mathrm{B1}`: blocking the degrees of freedom: :math:`\mathrm{DZ},\mathrm{DRX},\mathrm{DRY}`

The springs are modelled by dimensionless discretes. Nodes :math:`A` and :math:`\mathrm{A1}`, :math:`B` and :math:`\mathrm{B1}` are geometrically confused.

The characteristics of the wind speed field, along axis :math:`y`:

:math:`\mathit{Vy}\mathrm{=}\mathrm{20.sin}(\omega \mathrm{.}t)`, with :math:`\omega =2.\pi \mathrm{.}f` and :math:`f=0.2\mathrm{Hz}`


Initial conditions
--------------------

The beam has an angle of :math:`30°` (:math:`{\theta }_{0}=30°`) with respect to the :math:`x` axis.