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


Geometry
---------

Because of the geometric and physical symmetry of the problem, only a quarter of the plate is modelled. By taking into account symmetry conditions, only symmetric buckling modes can be captured.


.. image:: images/10003486000069BB000066BC48DB072974BC2319.svg
    :width: 606
    :height: 588


.. _RefImage_10003486000069BB000066BC48DB072974BC2319.svg:


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

:math:`E=2.1E5\mathrm{Mpa}`.

:math:`\nu =0.3`

The transverse shear coefficient for the plate is :math:`{A}_{\mathrm{CIS}}=5/6`.


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


.. csv-table::

    "Boundary conditions:", ":math:`\mathrm{P2P3}`:", "", "", ":math:`\mathrm{DZ}=0.` ", ""
    "", ":math:`\mathrm{P3P4}`:", "", ":math:`\mathrm{DZ}=0.` ", "", ""
    "Symmetry", ":math:`\mathrm{P1P2}`:", ":math:`\mathrm{DY}=0.` "," ", "", ":math:`\mathrm{DRX}=\mathrm{0 }\mathrm{.}` "," :math:`\mathrm{DRZ}=0.`"
    "", ":math:`\mathrm{P4P1}`:", ":math:`\mathrm{DX}=0.` ", "", ":math:`\mathrm{DRY}=\mathrm{0 }\mathrm{.}` "," :math:`\mathrm{DRZ}=0.`"


Charging:

Linear compression force :math:`q` on :math:`\mathrm{P2P3}`


notes
---------

It is not possible to solve the problem of compression deformation without introducing symmetry conditions. In fact, imposing symmetry boundary conditions for a quarter of a plate is the same as eliminating rigid body modes for the complete plate.