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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 538
    :height: 330


.. _RefImage_Object_1.svg:


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

The material constituting the cylinder is homogenous orthotropic. The orthotropy axes correspond to the curvilinear directions :math:`x` and :math:`y`.

:math:`\mathrm{[}{H}_{\mathit{membrane}}\mathrm{]}\mathrm{=}h\mathrm{[}H\mathrm{]}`; :math:`\mathrm{[}{H}_{\mathit{membrane}\mathrm{-}\mathit{flexion}}\mathrm{]}\mathrm{=}\mathrm{[}0\mathrm{]}`; :math:`\mathrm{[}{H}_{\mathit{flexion}}\mathrm{]}\mathrm{=}{h}^{3}\mathrm{[}H\mathrm{]}\mathrm{/}12`


.. csv-table::

    ":math:`{H}_{11}\mathrm{=}3.0644\mathrm{\times }{10}^{9}N\mathrm{/}{m}^{\mathrm{2 }}` ", ";", ":math:`{H}_{12}\mathrm{=}1.1048\mathrm{\times }{10}^{9}N\mathrm{/}{m}^{\mathrm{2 }}` ", "," ", ";", ":math:`{H}_{13}\mathrm{=}0`"
    ":math:`{H}_{22}\mathrm{=}18.597\mathrm{\times }{10}^{9}N\mathrm{/}{m}^{\mathrm{2 }}` ", ";", ":math:`{H}_{23}\mathrm{=}\mathrm{0 }` ", "," ", ";", ":math:`{H}_{33}\mathrm{=}1.250x{10}^{9}N\mathrm{/}{m}^{\mathrm{2 }}`"



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

- Boundary conditions: The ends of the cylinder rest on rigid diaphragms

- **A and B models**: Force per unit length: :math:`q\mathrm{=}\mathrm{-}2357.143N\mathrm{/}m`

- **C and D models**: Force per unit length: :math:`q\mathrm{=}\mathrm{-}\mathrm{896.552.}N\mathrm{/}m`


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

Not applicable