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


Geometry
---------


.. image:: images/100002000000015D00000157F16083A09BAE7D4A.png
    :width: 2.8154in
    :height: 2.7563in


.. _RefImage_100002000000015D00000157F16083A09BAE7D4A.png:



Cube geometry :math:`(m)`: :math:`L=1`

Coordinates of points :math:`(m)`:

 :math:`\mathrm{NO1}:(0.0,1.0,0.0)` :math:`\mathrm{NO2}:(1.0,1.0,0.0)` :math:`\mathrm{NO3}:(0.0,0.0,0.0)` :math:`\mathrm{NO4}:(1.0,0.0,0.0)` :math:`\mathrm{NO5}:(0.0,1.0,1.0)` :math:`\mathrm{NO6}:(1.0,1.0,1.0)` :math:`\mathrm{NO7}:(0.0,0.0,1.0)` :math:`\mathrm{NO8}:(1.0,0.0,1.0)`



mesh:

 :math:`\mathrm{MA1}`: whole cube


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


*
    *
        *


        * Elastic


            * :math:`E={10}^{5}\mathrm{Pa}` Young's module


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


            * :math:`\alpha =0.\text{}/{}^{°}C` Expansion coefficient


*
    *
        * Lemaître


            * :math:`\frac{1}{K}={10}^{-6}`


            * :math:`\frac{1}{m}=0.207060772`


            * :math:`n=2.3364`


            * :math:`L=0.`


            * :math:`{\phi }_{0}=4.240281\times {10}^{21}`


            * :math:`\beta =1.2`


            * :math:`\mathrm{QSR}\text{\_}K=3321.093`


            * :math:`a=-1.51\times {10}^{-16}`


            * :math:`b=1.542\times {10}^{-13}`


            * :math:`S=0.396`


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


*
    * Imposed displacement :math:`(m)`:


*
    *
        *
            * :math:`\mathrm{N01}:\mathrm{DX}=\mathrm{DZ}=0`


            * :math:`\mathrm{N03}:\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=0`


            * :math:`\mathrm{N05}:\mathrm{DX}=0`


            * :math:`\mathrm{N07}:\mathrm{DX}=0`


*
    *
        * Charging

The load is imposed on the :math:`\mathrm{N02},\mathrm{N04},\mathrm{N06},\mathrm{N08},` nodes, varies progressively over the :math:`t\in [\mathrm{0,1}\mathrm{.}]` interval and remains constant over the :math:`t\in \text{]}1.,32.{10}^{6}\text{]}` interval as in the figure below.


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


* Fluence imposed on the nodes.


.. csv-table::

    "Instant
    :math:`(s)` ", "Fluence
    :math:`({\mathrm{n.m}}^{-2})`"
    ":math:`0.0` ", "0."
    ":math:`1.0` "," :math:`7.20000\times {10}^{21}`"
    ":math:`8.64990\times {10}^{2}` "," :math:`6.22793\times {10}^{24}`"
    ":math:`1.72898E+03` "," :math:`1.24487\times {10}^{25}`"
    ":math:`2.16097\times {10}^{3}` "," :math:`1.24487\times {10}^{25}`"
    ":math:`2.59297\times {10}^{3}` "," :math:`1.86694\times {10}^{25}`"
    ":math:`3.45696\times {10}^{3}` "," :math:`2.48901\times {10}^{25}`"



* Temperature imposed on the knots.

:math:`T=299.85°C` with a reference temperature of :math:`{T}_{\mathrm{ref}}=299.85°C`