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


Geometry
---------

The domain is a rectangle of size :math:`10\mathrm{\times }20`, divided into 4 slices of :math:`10\mathrm{\times }5`. 3 points are associated with this rectangle: :math:`M`, :math:`N` and :math:`O`.

OPPOSE

J

11

O

.. image:: images/Shape6.gif


.. _RefSchema_Shape6.gif:


.. image:: images/Shape7.gif


.. _RefSchema_Shape7.gif:

D

C

B

A

6

N

1

M

ORIGINE

I

22

17

12

7

2

0


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

Two materials are used:

Material :math:`1` has the following characteristics:

:math:`E\mathrm{=}180000{\mathit{N.m}}^{\mathrm{-}2}`

:math:`\nu \mathrm{=}\mathrm{0,3}`

:math:`\alpha \mathrm{=}\mathrm{1,5}{10}^{\mathrm{-}7}`

:math:`\rho \mathrm{=}7700{\mathit{kg.m}}^{\mathrm{-}3}`

It is applied in slices :math:`A` and :math:`B`.

The second material has the following characteristics:

:math:`E\mathrm{=}220000{\mathit{N.m}}^{\mathrm{-}2}`

:math:`\nu \mathrm{=}\mathrm{0,3}`

:math:`\alpha \mathrm{=}\mathrm{1,6}{10}^{\mathrm{-}7}`

:math:`\rho \mathrm{=}8300{\mathit{kg.m}}^{\mathrm{-}3}`

It is applied in slices :math:`C` and :math:`D`.


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

At point :math:`\mathit{ORIGINE}`, the displacement is zero according to :math:`y`.

On the entire left edge, i.e. between points :math:`\mathit{ORIGINE}` and :math:`J`, the normal movement is zero.

On the upper edge, i.e. between points :math:`J` and :math:`\mathit{OPPOSE}`, pressure is imposed on :math:`1000`.


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

Not applicable.