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

Geometry
---------


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The cylinder has an inner radius :math:`a=10m`, an outer radius :math:`b=20m`, a height of :math:`h=\mathrm{0.02m}`

The circumferential frame, positioned on the outside surface of the cylinder, has a cross section per unit length of :math:`s\mathrm{=}0.1{m}^{2}\mathrm{/}\mathit{ml}`. The main direction of the reinforcements is vertical.

Only a portion of the cylinder, corresponding to an angular section :math:`\theta ={0.1}^{°}`, is modelled.


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

The material characteristics of the concrete forming the hollow cylinder are:

• :math:`E=20000\mathrm{MPa}`, :math:`\nu =0.2`

The material characteristics of the frames are:

• :math:`E=200000\mathrm{MPa}`, :math:`\nu =0.0`, :math:`{\sigma }_{y}=200000\mathrm{MPa}`, :math:`{E}_{\mathrm{cr}}=20000\mathrm{MPa}`

To model reinforcement grids, we use RELATION =' GRILLE_ISOT_LINE 'in the stat_non_line command. To do this, the behavior assigned to reinforcement grids must define the plastic characteristics. In all models the behavior of steels must remain in the elastic domain, :math:`{\sigma }_{y}` is given large enough to meet this condition.


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

The following boundary conditions are imposed on the modelled angular section:

• zero displacement on the lower surface of the cylinder

• zero normal displacement on the lateral faces of the cylinder section

The load consists of an imposed pressure :math:`{10}^{6}\mathrm{Pa}` on the internal surface :math:`\mathit{SI}` of the cylinder section.


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

Initially, travel and constraints were zero everywhere.