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


Calculation method used for the reference solution
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The field of movement along the :math:`y` axis at the end of the plate (segment :math:`\mathit{BC}`) is given in the hypothesis of beam theory by:

:math:`{u}_{y}^{\mathit{BC}}=\frac{{\mathit{PL}}^{3}}{{\mathrm{3EI}}_{z}}(1+0.98\frac{{l}^{2}}{{L}^{2}})` (solution taking into account the shear force in a Timoshenko beam)

Hence :math:`{u}_{y}^{\mathit{BC}}=0.00121m`

The normal stress field :math:`{\sigma }_{\mathit{xx}}` due to bending is given by:

:math:`{\sigma }_{\mathit{xx}}=\frac{\mathit{Pl}}{{\mathrm{2I}}_{z}}(L-x)` on the :math:`\mathit{AB}` ridge

Be :math:`{\sigma }_{\mathit{xx}}=37.8\times {10}^{6}(L-x)`


Benchmark results
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* :math:`{u}_{y}` movements of nodes :math:`B` and :math:`C`


* :math:`{\sigma }_{\mathit{xx}}` constraints of nodes :math:`A`, :math:`B`, :math:`E`


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


* Analytical solution.


Bibliographical references
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*S. Tymoshenko.*Material resistance, part 1*. Librairie Polytechnique Ch. Béranger, Paris, 1947, pp 163-168.