2. Reference solution

2.1. Calculation method used for the reference solution

2.1.1. A and B models

Arrow \(\mathrm{fl}\) is given by the formula: \(\mathrm{fl}={\mathrm{FlL}}^{3}/\mathrm{3EI}\)

where \(l\) is the width, \(L\) is the length of the plate, and \(I={\mathrm{lh}}^{3}/12\), \(h\) is the thickness.

2.2. Benchmark results

2.2.1. A and B models

They consist of the values of the displacement field \(\mathrm{DZ}\) at point \(\mathrm{A3}\) and the efforts at point \(\mathrm{A1}\). On the other hand, the 4 lowest frequencies of the structure are calculated.

2.2.2. C to N modeling

In this case, only one eccentric plate is represented (eccentricity \(e=\mathrm{0,4}m\), thickness \(h/2=\mathrm{0,4}m\)). The arrow \(w\) at the free end is given by the expression: \(w=\left(2{F}_{z}L-3{F}_{x}e\right)\ell {L}^{2}/6\mathit{EI}+{F}_{z}L/(6\mathit{Gh5}/6)\). The overall stresses on the recessed edge \(\mathrm{A1A4}\), of length \(\ell =5m\), are: \({N}_{x}={F}_{x}\) and \({V}_{z}=-{F}_{z}\).

2.3. Uncertainty about the solution

For models \(A\) and \(B\), the reference solution is analytical. So there is no uncertainty.

For the other models, another solution coming from a non-eccentric calculation is used as a reference solution for the natural frequency.

For O modeling, two calculations are carried out, the first in monolayer serving as a reference and the second in multi-layer.