2. Benchmark solution#

2.1. Calculation method used for the reference solution#

Analytics

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

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

Arrow \(V\) and load \(P\) are unknown.

The two beams are in pure compression:

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

\(=\mathrm{DZ}(G)\)

So we can find \(P\) and \(V\) from these two equations. We get:

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

\(\begin{array}{}V=-0.19005\mathrm{mm}\\ P=-9.5025{10}^{-3}N\end{array}\)

Null. Analytical solution.