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


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

The reference solution [:ref:`1 <1>`] is a solution based on the theory of beams (non-deformation of the cross section), including or not including the effects of transverse shear.


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

Move point :math:`A` to :math:`Y`.

Move point :math:`A` to :math:`Z`.


.. csv-table::

    "Loading (:math:`N`)", "Reference (:math:`m`)"
    ":math:`{F}_{Y}=0`
    :math:`{F}_{Z}=1` "," :math:`\mathit{DY}=1.72\times {10}^{-3}`
    :math:`\mathit{DZ}=5.424\times {10}^{-3}`"
    ":math:`{F}_{Y}=1`
    :math:`{F}_{Z}=0` "," :math:`\mathit{DY}=1.754\times {10}^{-3}`
    :math:`\mathit{DZ}=1.72\times {10}^{-3}`"



Uncertainties about the solution
----------------------------

Semi-analytical solution.


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

[:ref:`1 <1>`] J. L. Batoz and G. Dhatt, "Modeling structures by finite elements Volume.3: Shells", editions HERMES. Paris, France, 1992.

[:ref:`2 <2>`] HAMMADI Fodil: 'Formulation and evaluation of finite elements with C° continuity of geometry for the linear and non-linear analysis of shells" PhD thesis, UTC, June 1998