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

Geometry
---------

Piping bent in plane :math:`\mathrm{XY}`. The straight sections are :math:`L=1m` in length.

The radius of curvature of the elbow is: :math:`{R}_{c}=1.25m`

The tubular section has an average radius :math:`{r}_{\mathit{moy}}=395.5\mathit{mm}` and a thickness :math:`e=\mathrm{77mm}`.


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

The material is elastoplastic with isotropic linear work hardening.

:math:`E=2.E11\mathrm{Pa}`

:math:`\nu =0.3`

Elasticity limit :math:`\mathrm{SIGY}={200.10}^{6}\mathrm{Pa}`

Work hardening module :math:`\text{D\_SIGM\_EPSI}={2.10}^{10}\mathrm{Pa}`


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

Embedding in :math:`A` (blocked beam degrees of freedom, but free ovalization degrees of freedom).

Moment :math:`\mathrm{MZ}` imposed in growing :math:`D`:

.. csv-table::

    "Increment 1"," :math:`\mathrm{Mz}=3086702.1520853\mathrm{Nm}`"


10 equal increments up to:

.. csv-table::

    "11" increment," :math:`\mathrm{Mz}=7091146.5935484\mathrm{Nm}`"



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

Not applicable.