D modeling
==============


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

The plate was cut into 200 TRIA3 meshes. a modeling for the plate is used: Q4G.

For the flexure problem, the boundary conditions are as follows:


* in all knots on the edge: :math:`\mathrm{DZ}=0`

For the membrane problem, the boundary conditions are:


* in all the nodes of the mesh: :math:`\mathrm{DZ}=0` :math:`\mathrm{DRX}=\mathrm{DRY}=\mathrm{DRZ}=0`,


* in all the nodes on sides :math:`\mathrm{AB}` and :math:`\mathrm{BC}`: :math:`\mathrm{DY}=0`


* At points :math:`A,B,C,D`, discrete stiffness elements are added (direction :math:`x`).


.. image:: images/10001A5E00001D8F0000110E1F11F87DCB2C3E07.svg
    :width: 381
    :height: 220


.. _RefImage_10001A5E00001D8F0000110E1F11F87DCB2C3E07.svg:


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

Number of knots: 121

Number of meshes and types: 200 TRIA3

The characteristic points of the mesh are as follows:


.. csv-table::

    "Point :math:`A` = :math:`\mathrm{N1}` ", "Point :math:`C` = :math:`\mathrm{N121}`"
    "Point :math:`B` = :math:`\mathrm{N111}` ", "Point :math:`D` = :math:`\mathrm{N11}`"



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

For flexure modes:


.. csv-table::

    "**Number**
    **of the mode**", "**Identification**", "**Reference Type**", "**Reference**", "**% tolerance**"
    "4", "Frequencies", "'ANALYTIQUE'", "35.63", "1.5"
    "5", "Frequencies", "'ANALYTIQUE'", "68.51", "3.5"
    "6", "Frequencies", "'ANALYTIQUE'", "109.62", "3.0"
    "7", "Frequencies", "'ANALYTIQUE'", "123.32", "7.0"
    "8", "Frequencies", "'ANALYTIQUE'", "142.51", "8.5"
    "9", "Frequencies", "'ANALYTIQUE'", "197.32", "10.0"