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


Geometry
---------

The structure is composed of a slender oriented beam carried in space by the direction vector axis :math:`(\mathrm{1,}\mathrm{1,}1)`.


.. image:: images/100000000000044B000003052782C1430B32DFFF.jpg
    :width: 3.6634in
    :height: 2.5772in


.. _RefImage_100000000000044B000003052782C1430B32DFFF.jpg:

Regarding the section of the beam, two cases are considered:


* Constant square section, with area :math:`4.0{10}^{-4}{m}^{2}` (A, B, C and D models),


* Circular section with homothetic variation, with initial radius :math:`2.0{10}^{-2}m` and final radius :math:`4.0{10}^{-2}m` (modeling E).

In all of the above cases, the length of the beam is :math:`0.5m`.


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

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

:math:`\nu =0`

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


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 coordinates: :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.