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

The objective of this test case is to validate the non-intrusive switch from a beam model to a mixed Beam-3D model in *Code_Aster*.

The results obtained are compared with those obtained from a complete 3D modeling in*Code_Aster*.


Geometry
---------

We consider a slender thin structure with a length :math:`\mathrm{0,25}m` along the Z axis and with a circular cross section. It is supported on its two ends located respectively in positions :math:`-\mathrm{0,1}m` (support 1) and :math:`\mathrm{0,15}m` (support 2). The radius of the section is equal to :math:`\mathrm{0,005}m`.


.. image:: images/100002000000043800000160B5065B2DDF76972C.png
    :width: 4.552in
    :height: 1.6571in


.. _RefImage_100002000000043800000160B5065B2DDF76972C.png:

Image 1.1-1: Rotor geometry


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

The double-supported beam has a density of :math:`\rho \mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}`.

The Young's modulus is :math:`E\mathrm{=}2.{10}^{11}N{m}^{\mathrm{-}2}` and the Poisson's ratio is :math:`\nu \mathrm{=}\mathrm{0,3}`.


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

The beam rests on two infinitely rigid supports:


* :math:`\mathit{DX}=\mathit{DY}=\mathit{DZ}=0` at support level 1


* :math:`\mathit{DX}=\mathit{DY}=\mathit{DZ}=0` at support level 2

Also, the movement of rigid bodies rotating along the axis of the beam is blocked (:math:`\mathit{DRZ}=0`) throughout the structure.