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


Geometry
----------


.. image:: images/Object_1.svg
    :width: 626
    :height: 220


.. _RefImage_Object_1.svg:


.. image:: images/Object_2.svg
    :width: 626
    :height: 220


.. _RefImage_Object_2.svg:

The cylinder has an inner radius :math:`{R}_{1}=10m`, an outer radius :math:`{R}_{2}=20m`, a height :math:`h\mathrm{=}1m`. The circumferential frame has a cross section per unit length of :math:`e=1{m}^{2}/\mathrm{ml}`.


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

The material characteristics of concrete (hollow cylinder) are :math:`E=2E+10\mathrm{Pa}` and :math:`\nu =0.2`; those of steel (circumferential reinforcement) :math:`E=2E+11\mathrm{Pa}`, :math:`\nu =0`, :math:`{E}_{t}=2.E+09` (tangent module), :math:`{\sigma }_{y}=2.E+11\mathrm{Pa}` (very high plasticity constraint to remain in the elastic domain).

The reinforcing sheet has its main vertical direction and a cross section per linear meter of :math:`1m`.


.. _Ref473028113:


Boundary conditions and loading
------------------------------------

We are only interested in an angular section of the cylinder.

The following conditions are imposed:


1. a zero normal displacement on the lateral faces of the angular cylinder section (:math:`\mathrm{SG}` and :math:`\mathrm{SD}` in the schematic figure) (zero ortho-radial displacement)


2. zero vertical displacement on the bottom face of the cylinder section (simple support)


3. an imposed pressure of :math:`{10}^{6}\mathrm{Pa}` on the inner face of the cylinder section (:math:`\mathrm{SI}`) (in the schematic figure) (internal pressure)


.. image:: images/101B044C000069D5000038BE2E6CC650605CA831.svg
    :width: 626
    :height: 220


.. _RefImage_101B044C000069D5000038BE2E6CC650605CA831.svg:

**Schematic designation of cylinder surfaces**