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


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


Geometry
---------

Node coordinates:


.. csv-table::

    "", ":math:`\mathit{N1}` "," :math:`\mathit{N2}` "," :math:`\mathit{N3}` "," "," :math:`\mathit{N5}` "," "," "," :math:`\mathit{N6}` "," :math:`\mathit{N7}` "," :math:`\mathit{N8}` "," :math:`\mathit{N9}` "," :math:`\mathit{N10}` "," :math:`\mathit{N11}` "," "," "", ""," "," "," "," "," "," "," :math:`\mathit{N12}`
    ":math:`x` ", "0. ", "1. ", "2. ", "1. ", "0. ", "0.5", "1. ", "0.5", "0. ", "1.5", "1.5"
    ":math:`y` ", "0. ", "0. ", "0. ", "1. ", "1. ", "0. ", "0.5", "1. ", "0.5", "0.5", "0.5", "0."
    ":math:`z` ", "0. ", "0. ", "0. ", "2. ", "2. ", "0. ", "1. ", "2. ", "1. ", "1. ", "0."


Thickness = 0.7


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


* Young's modulus


+---------+-----------------------+-------------+
|         |Temperature                          |
+         +-----------------------+-------------+
|         |:math:`\mathrm{-}1000°`|:math:`1000°`|
+---------+-----------------------+-------------+
|:math:`E`|:math:`\mathrm{-}1200` |:math:`1200` |
+---------+-----------------------+-------------+


* Poisson's ratio: :math:`\nu =0.3`


* Density :math:`\rho \mathrm{=}8.1`


* Coefficient of thermal expansion:


+--------------+-----------------------+-------------+
|              |Temperature                          |
+              +-----------------------+-------------+
|              |:math:`\mathrm{-}1000°`|:math:`1000°`|
+--------------+-----------------------+-------------+
|:math:`\alpha`|:math:`\mathrm{-}1200` |:math:`1200` |
+--------------+-----------------------+-------------+


* Temperature for defining the thermal expansion coefficient: :math:`1.5°`


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

Boundary conditions:


* Node :math:`\mathit{N1}`: :math:`\mathit{DX}\mathrm{=}1\text{;}\mathit{DY}\mathrm{=}2\text{;}\mathit{DZ}\mathrm{=}3\text{;}\mathit{DRX}\mathrm{=}1\text{;}\mathit{DRY}\mathrm{=}2\text{;}\mathit{DRZ}\mathrm{=}3`


* Node :math:`\mathit{N6}`: :math:`\mathit{DX}\mathrm{=}2\text{;}\mathit{DY}\mathrm{=}3\text{;}\mathit{DZ}\mathrm{=}4\text{;}\mathit{DRX}\mathrm{=}1\text{;}\mathit{DRY}\mathrm{=}2\text{;}\mathit{DRZ}\mathrm{=}5`

Loads


+-----------+---------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------+
|PESANTEUR  |:math:`g\mathrm{=}\mathrm{9,8}` Following the direction :math:`(0.3;0.1;\mathrm{-}0.4)`                                                                                                                                 |
+-----------+---------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------+
|FORCE_ARETE|Line force                                                                             |:math:`\mathit{FZ}\mathrm{=}8`                                                                                                  |
+-----------+---------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------+
|FORCE_COQUE|Distributed load                                                                       |:math:`\mathit{F1}\mathrm{=}5.` :math:`\mathit{F2}\mathrm{=}8.` :math:`\mathit{F3}\mathrm{=}9.` :math:`\mathit{MF1}\mathrm{=}5.`|
+-----------+---------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------+
|FORCE_COQUE|Uniform pressure                                                                       |:math:`\mathit{PRES}\mathrm{=}5.`                                                                                               |
+-----------+---------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------+

Temperature


* Temperature on the upper skin of the shell: :math:`\text{TEMP\_SUP}\mathrm{=}24°`


* Temperature on the average skin of the shell: :math:`\text{TEMP}\mathrm{=}18°`


* Temperature on the lower skin of the shell: :math:`\text{TEMP\_INF}\mathrm{=}12°`


* Reference temperature = :math:`1.5°`