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


Geometry
---------

Slender beam oriented carried in space by the direction vector axis :math:`(\mathrm{1,}\mathrm{1,}1)`.


.. image:: images/10002210000069D500003CE0DE35EC54BD6A5F6F.svg
    :width: 562
    :height: 323


.. _RefImage_10002210000069D500003CE0DE35EC54BD6A5F6F.svg:

Square area section: :math:`4.0{10}^{-4}{m}^{2}`

Beam length: :math:`0.5m`


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

:math:`E=2.{10}^{11}\mathrm{Pa}`

:math:`\nu =0`

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

:math:`\text{A\_CIS}=0.8333` (transverse shear correction factor equal to :math:`5/6` for a Reissner thin shell theory)


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

Embedded beam free to rotate around an axis perpendicular to its largest dimension and passing through the center of the embedded face.

Rotation vector component: :math:`(\mathrm{1,}\mathrm{0,}–1)`.

Rotation speed: :math:`\omega =3000\mathrm{rd}/s`

There is nothing physical about the important value of the speed of rotation.