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


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


* Opposite forces perpendicular to the plate [:ref:`bib1 <bib1>`], [:ref:`bib2 <bib2>`]

The reference solution is the one given in sheet SSLS27 /89 of guide VPCS:

Displacement of point :math:`C`: :math:`w=35.37{10}^{-7}m`

Resulting of integration efforts (:math:`\mathit{AD}`) following :math:`\mathit{DZ}`: :math:`{\mathit{RESULT}}_{Z}\mathrm{=}0`

Moment associated with the result of the efforts to embed in the middle of :math:`\mathit{AD}`:

:math:`{\mathit{MOMENT}}_{X}\mathrm{=}\mathrm{-}1`

:math:`{\mathit{MOMENT}}_{Y}\mathrm{=}0`


* Forces in the same direction perpendicular to the plate [:ref:`bib3 <bib3>`]

The Euler beam formulation gives an approximate solution for a different Poisson's ratio :math:`\nu`.

Move all the nodes to the :math:`\mathrm{BC}` side:

.. image:: images/Object_1.svg
    :width: 100
    :height: 45


.. _RefImage_Object_1.svg:

Resulting of integration efforts (:math:`\mathit{AD}`) following :math:`\mathit{DZ}`: :math:`{\mathit{RESULT}}_{Z}\mathrm{=}\mathrm{-}2`

Moment associated with the result of the efforts to embed in the middle of :math:`\mathit{AD}`:

:math:`{\mathit{MOMENT}}_{X}\mathrm{=}0`

:math:`{\mathit{MOMENT}}_{Y}\mathrm{=}24`


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

Move points :math:`B`, :math:`C`, and :math:`E`. Resulting from embedding along :math:`\mathit{AD}`, embedding moment with respect to axes :math:`X` and :math:`Y` in the middle of :math:`\mathit{AD}`.


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

Analytical solution.


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


1. J. ROBINSON "Evaluation element. A set of assessment parts and standard tests" Proceedings of Finite Element Methods in the Commercial Environment, Vol. 1, (October 1978).


2. J.L. BATOZ, M.B. TAHAR "Evaluation of new quadrilateral thin plate boundary element" International Journal for Numerical Methods in Engineering, Vol. 18, John Wiley & Sons (1982).


3. R.J. ROARK, W.C. YOUNG "Formulas for Stress and Strain" New York: McGraw-Hill, 5th edition, p 96.