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


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

The value of the displacement field :math:`v`, at the free end of the plate (edge :math:`\mathit{BC}`) is given by:

:math:`{v}_{L}\mathrm{=}\frac{{\mathit{PL}}^{3}}{{\mathrm{3EI}}_{y}}` (neglected shear)

Hence :math:`{v}_{L}\mathrm{=}0.129m`

The flexural stress field :math:`{\sigma }_{\mathit{xx}}` is given by:

:math:`{\sigma }_{\mathit{xx}}\mathrm{=}\frac{\mathit{Ph}}{{\mathrm{2l}}_{y}}(L\mathrm{-}x)` on the :math:`\mathit{AB}` ridge

Be :math:`{\sigma }_{\mathit{xx}}\mathrm{=}2.04\mathrm{\times }{10}^{8}(L\mathrm{-}x)(\mathit{Pa})`


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


* Move :math:`{v}_{L}` of nodes :math:`B` and :math:`C`


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


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

Analytical solution.


Bibliographical references
---------------------------


1. S. TIMOSHENKO, Material Strength, Part 1. Librairie Polytechnique Ch.Béranger, Paris, 1947. p. 169 to 168