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

Calculation method used for the reference solution
--------------------------------------------------------

Analytics

The plate undergoes simple bending. The solution is of the "beam" type:

:math:`V=\mathrm{DZ}(C)=\mathrm{DZ}(D)=\frac{{\mathrm{PL}}^{3}}{{\mathrm{3E.I}}_{y}}` with :math:`{I}_{y}=\frac{{\mathrm{bh}}^{3}}{12}`

Arrow :math:`V` and load :math:`P` are unknown.

The two beams are in pure compression:

:math:`-P=2.\frac{\mathrm{ES}}{L}(V-U)` with :math:`U=\mathrm{DZ}(E)`

                         :math:`=\mathrm{DZ}(G)`

So we can find :math:`P` and :math:`V` from these two equations. We get:

:math:`\begin{array}{}P=\frac{6ESIU}{\mathrm{2SL³}+{\mathrm{3I}}_{y}l}\\ \\ V=\frac{\mathrm{2SL³}U}{\mathrm{2SL³}+{\mathrm{3I}}_{y}l}\end{array}`


Benchmark results
----------------------

:math:`\begin{array}{}V=-0.19005\mathrm{mm}\\ P=-9.5025{10}^{-3}N\end{array}`


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

Null. Analytical solution.