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


Geometry
---------

Cylinder with :math:`X` axis, length :math:`L`, average radius :math:`R`, thickness :math:`e`.


.. image:: images/Object_1.svg
    :width: 432
    :height: 72


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Here, :math:`L\mathrm{=}\mathrm{1m}`, :math:`R\mathrm{=}\mathrm{0.1m}`, :math:`e\mathrm{=}\mathrm{0.01m}`.


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

Linear elasticity:

Young's module:

.. image:: images/Object_2.svg
    :width: 432
    :height: 72


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Poisson's ratio

.. image:: images/Object_3.svg
    :width: 432
    :height: 72


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

The shell mesh is connected to beam elements in :math:`A` and :math:`B`. This makes it possible to give boundary conditions compatible with beam kinematics. However, here we are only interested in the shell solution subjected to internal pressure.

Point :math:`D` is embedded.

The pressure is read on a "plexus" mesh of segment :math:`\mathit{AB}`, comprising 20 beam elements.

It varies as follows:


.. image:: images/Object_4.svg
    :width: 432
    :height: 72


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