Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

The reference results were obtained with Europlexus.

The meshes used by Europlexus and Code_Aster are the same.


Benchmark results
----------------------

The reference results correspond to the following displacement :math:`Z` of the node :math:`\mathit{N9}` located in the center of the beam. They were obtained at moment :math:`t\mathrm{=}\mathrm{0.001s}`.


+---------------------------+----------------------+---------------------------------------------------------------------+-------------------------------------------------------------------+
|Grandeur                   |Location              |Europlexus elements                                                                                                                      |
+                           +                      +---------------------------------------------------------------------+-------------------------------------------------------------------+
|                           |                      |Q4GS                                                                 |T3GS                                                               |
+---------------------------+----------------------+---------------------------------------------------------------------+-------------------------------------------------------------------+
|Next move :math:`Z`        |:math:`X\mathrm{=}5.m`|:math:`\mathrm{-}1.79497\mathrm{\times }{10}^{\mathrm{-}5}\text{m}`  |:math:`\mathrm{-}1.79508\mathrm{\times }{10}^{\mathrm{-}5}\text{m}`|
+---------------------------+----------------------+---------------------------------------------------------------------+-------------------------------------------------------------------+
|Next speed :math:`Z`       |:math:`X\mathrm{=}5.m`|:math:`\mathrm{-}3.76207\mathrm{\times }{10}^{\mathrm{-}2}\text{m/s}`|:math:`-3.76309\times {10}^{-2}\text{m/s}`                         |
+---------------------------+----------------------+---------------------------------------------------------------------+-------------------------------------------------------------------+
|Next acceleration :math:`Z`|:math:`X\mathrm{=}5.m`|:math:`\mathrm{-}39.09299\text{m/s²}`                                |:math:`\mathrm{-}39.17340\text{m/s²}`                              |
+---------------------------+----------------------+---------------------------------------------------------------------+-------------------------------------------------------------------+


Uncertainty about the solution
---------------------------

Digital solution.


Bibliographical references
---------------------------

[:ref:`1 <1>`] MARKOVIC D., "Implantation of a new thick shell finite element (T3GS) in Europlexus", Note EDF /R &D/ AMA H-T-62-2008-00080-FR.