Reference solution
=====================


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


A and B models
~~~~~~~~~~~~~~~~~~~~~~

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

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


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


A and B models
~~~~~~~~~~~~~~~~~~~~~~

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


C to N modeling
~~~~~~~~~~~~~~~~~~~

In this case, only one eccentric plate is represented (eccentricity :math:`e=\mathrm{0,4}m`, thickness :math:`h/2=\mathrm{0,4}m`). The arrow :math:`w` at the free end is given by the expression: :math:`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 :math:`\mathrm{A1A4}`, of length :math:`\ell =5m`, are: :math:`{N}_{x}={F}_{x}` and :math:`{V}_{z}=-{F}_{z}`.


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

For models :math:`A` and :math:`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.