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


Calculation method
------------------

The critical load value is given in [:ref:`bib1 <bib1>`] by the following expression:

:math:`{F}_{\mathrm{cr}}=\frac{14.68D}{{R}^{2}}`

with: :math:`D` the flexural stiffness of the plate (in :math:`\mathrm{N.m}`) defined by the following expression:

:math:`D=\frac{E{h}^{3}}{12(1-{\nu }^{2})}`

This critical load is associated with a circumferential mode equal to 0.


.. _Ref64186338:


Reference quantities and results
-----------------------------------

For the given characteristics, the critical load is equal to:

:math:`{F}_{\mathrm{cr}}=2668.315N/m`


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

Analytical solution


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


1. S.P. TIMOSHENKO, J.M. GERE: Elastic Stability Theory, Second Edition, DUNOD (1966)