N modeling
==============


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

COQUE_SOLIDE elements with hexahedra (quarter plate modeling)


.. image:: images/100000000000056E000002461C5991134288E91A.png
    :width: 6.3374in
    :height: 2.6528in


.. _RefImage_100000000000056E000002461C5991134288E91A.png:

Boundary conditions:


* On the face corresponding to the plane X=0, symmetry condition :math:`\mathit{DX}=0`


* On the face corresponding to the plane Y=0, symmetry condition :math:`\mathit{DY}=0`


* On the face corresponding to the outer quarter circle: embedding condition :math:`\mathit{DX}=\mathit{DY}=\mathit{DZ}=0`

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* On the upper side: distributed pressure :math:`p=0.01172\mathit{MPa}`


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

Number of knots: 182

Number of meshes and types: 75 HEXA9


Tested sizes and results
------------------------------

Coordinates of Gauss points (COOR_ELGA): test of the mesh at the center of the disk (GROUP_MA ='CellMiddle'). Lobatto diagram with five integration points in the thickness, in the middle of the mesh.

For :math:`\mathit{Pg}=1`, the face below, coordinates of the Gauss point:

.. csv-table::

    "**Identification**", "**Reference type**", "**Reference values**
    **(mm)**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`X` ", "'ANALYTIQUE'", "4, 9", "0"
    ":math:`Y` ", "'ANALYTIQUE'", "4.9", "0"
    ":math:`Z` ", "'ANALYTIQUE'", "0", "0"


For :math:`\mathit{Pg}=3`, at half the thickness, coordinates of the Gauss point:

.. csv-table::

    "**Identification**", "**Reference type**", "**Reference values**
    **(mm)**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`X` ", "'ANALYTIQUE'", "4, 9", "0"
    ":math:`Y` ", "'ANALYTIQUE'", "4.9", "0"
    ":math:`Z` ", "'ANALYTIQUE'", "0.5", "0"


For :math:`\mathit{Pg}=5`, the top face, coordinates of the Gauss point:

.. csv-table::

    "**Identification**", "**Reference type**", "**Reference values**
    **(mm)**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`X` ", "'ANALYTIQUE'", "4, 9", "0,"
    ":math:`Y` ", "'ANALYTIQUE'", "4.9", "0"
    ":math:`Z` ", "'ANALYTIQUE'", "1.0", "0"


Vertical movement in the center of the plate:

.. csv-table::

    "**Identification**", "**Reference type**", "**Reference values**", "**Tolerance** :math:`(\text{\%})`"
    "DZ", "'ANALYTIQUE'", ":math:`-\mathrm{2.09114}\mathit{mm}` "," :math:`<1.E-6`"


Constraint :math:`{\sigma }_{\mathit{zz}}` at the middle node of the quarter circle (SIEF_NOEU):

.. csv-table::

    "**Identification**", "**Reference type**", "**Reference values**", "**Tolerance** :math:`(\text{\%})`"
    "Top side", "'ANALYTIQUE'", ":math:`-0.01172\mathit{MPa}` ", "0, 5"
    "Underside", "'ANALYTIQUE'", "0", "0""