Modeling A
==============


Characteristics of modeling
-----------------------------------


.. image:: images/10000000000004AE0000031090491E2344399B1A.png
    :width: 6.889in
    :height: 4.5075in


.. _RefImage_10000000000004AE0000031090491E2344399B1A.png:


1. The total mesh includes 8163 knots, i.e. approximately 125,000 degrees of freedom,


2. The point element :math:`Q` (modeling DIS_TR) makes it possible to simply represent an accelerometer present in the model in article [:ref:`bib1 <bib1>`],


3. The deformable plate is modelled by 5120 solid solid elements (3D modeling) pentahedral with 6 knots (10 layers in the thickness for a good approximation of the flexural behavior despite the linearity of the elements),


4. the free surface is modelled by 512 elements MEFP_FACE3 (2D_ FLUI_PESA modeling) triangles with 3 knots,


5. the fluid volume is modeled by 24576 fluid elements (3D modeling FLUIDE) tetrahedral fluid elements with 4 nodes.


Writing boundary conditions
-----------------------------------

The bottom of the tank can only move in direction :math:`x`:


.. code-block:: text
 CONDLIM = AFFE_CHAR_MECA (MODELE = MODELE,
DDL_IMPO =( _F (
GROUP_NO =( 'FONDS', 'FONDP',),
DY=0.0, DZ=0.0,),),);

In this direction :math:`x`, a sinusoidal displacement in time, with a frequency :math:`\mathrm{1,7704}\mathrm{Hz}` and an amplitude :math:`\mathrm{0,001}m`, is imposed on the bottom of the tank:


.. code-block:: text
 FREQ = 1,7704;
LFONC = DEFI_LIST_REEL (DEBUT =0.0, INTERVALLE =_F (JUSQU_A =10.0,
PAS =0.01,),);
FONC = FORMULE (REEL = "'(REEL: INST) =
(0.001) *SIN (2*PI*FREQ* INST) "');
DEPLX = CALC_FONC_INTERP (FONCTION = FONC,
NOM_PARA =' INST ',
LIST_PARA = LFONC,);
CHARG_SE = AFFE_CHAR_MECA_F (MODELE = MODELE,
DDL_IMPO =_F (
GROUP_NO =( 'FONDS', 'FONDP',), DX= DEPLX,),);

Volume gravity loading is defined as follows:


.. code-block:: text


    PESA = AFFE_CHAR_MECA (MODELE = MODELE,
PESANTEUR =_F (GRAVITE =9.81,
DIRECTION =( 0.,0., -1.,),),);


Characteristics of the mesh
----------------------------


.. csv-table::

    "The mesh contains:", "24575 TETRA4"
    "", "5120 PENTA6"
    "", "4096 TRIA3"



Tested values
---------------

The tests are carried out on the value of the following displacement :math:`x` (noted :math:`\mathit{DX}`) for various times and for the nodes :math:`\mathit{N145}` and :math:`\mathit{N3119}`.


.. csv-table::

    "**Identification**", "**Reference**"
    ":math:`\mathit{DX}(\mathit{N145},t=\mathrm{0,8}s)` ", "5.162416932321991e-04"
    ":math:`\mathrm{DX}(\mathrm{N145},t=\mathrm{1,4}s)` ", "1.4970110110314375e-04"
    ":math:`\mathrm{DX}(\mathrm{N145},t=\mathrm{2,0}s)` ", "-2.392741313131721e-04"
    ":math:`\mathrm{DX}(\mathrm{N3119},t=\mathrm{1,0}s)` ", "-9.973627272860105e-04"
    ":math:`\mathrm{DX}(\mathrm{N3119},t=\mathrm{1,6}s)` ", "-8.785505656121762e-04"
    ":math:`\mathrm{DX}(\mathrm{N3119},t=\mathrm{2,0}s)` ", "-2.392916161952584e-04"


We also test the critical eigenvalue calculated with CRIT_STAB.


.. csv-table::

    "**Identification**", "**Reference**"
    "CHAR_CRIT ", "-2.477264942149"