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

Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

Dimension in :math:`(m)`


* Average radius of curvature :math:`R=\mathrm{0.1m}`


* Thickness: :math:`h=0.005m`


* Width: :math:`b=0.010m` (perpendicular plane)


* Area: :math:`A=5\times {10}^{-5}{m}^{2}`


* Moment of inertia: :math:`{I}_{z}=1.042\times {10}^{-10}{m}^{4}` :math:`{I}_{y}=4.167\times {10}^{-10}{m}^{4}`


* Torsional moment: :math:`J=2.859\times {10}^{-10}{m}^{4}`


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


*
    *
        * Elastic


            * :math:`E=7.2\times {10}^{10}\mathrm{Pa}` Young's module


            * :math:`\nu =0.3` Poisson's ratio


            * :math:`\rho =2700\mathrm{kg}/{m}^{3}` Density


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


* Moves: all points in the ring are free


* Charging: none