Reference problem
=====================


Geometry
---------


.. image:: images/100000000000033C0000019433CA1CD7DE942051.png
    :width: 5.8626in
    :height: 2.8484in


.. _RefImage_100000000000033C0000019433CA1CD7DE942051.png:

It is a composite material made up of 16 superimposed layers of the same material and different fiber directions forming a :math:`4.48m` thick plate. The longitudinal direction or direction of the fibers of each layer is defined by the first direction of orthotropy.


Material property
---------------------

The properties of the material are:


* Longitudinal Young's modulus: :math:`\text{E\_L}=59000\mathrm{MPa}`


* transversal Young's module: :math:`\text{E\_T}=59000\mathrm{MPa}`


* shear modulus in plane :math:`\text{LT}`: :math:`\text{G\_LT}=3700\mathrm{MPa}`


* Poisson's ratio in plane :math:`\text{LT}`: :math:`\text{NU\_LT}=0.08`


* criterion for failure under traction in the longitudinal direction: :math:`\mathrm{XT}=560\mathrm{MPa}`


* criterion for failure under compression in the longitudinal direction: :math:`\mathrm{XC}=-475\mathrm{MPa}`


* Traction failure criterion in the transverse direction: :math:`\mathrm{YT}=560\mathrm{MPa}`


* compression failure criterion in the transverse direction: :math:`\mathrm{YC}=-475\mathrm{MPa}`


* shear failure criterion in plane :math:`\text{LT}`: :math:`\text{S\_LT}=48\mathrm{MPa}`

The orientation of the first layer is 0° with respect to the reference frame, for the second layer 45°, for the third 0° and so on.


Boundary conditions and loads
-------------------------------------


.. csv-table::

    "* :math:`\mathrm{N1}` "," :math:`\mathrm{DY}=0`, :math:`\mathrm{DZ}=0`, :math:`\mathrm{DRX}=0`,, :math:`\mathrm{DRY}=0`, :math:`\mathrm{DRZ}=0`"
    "* :math:`\mathrm{GAUCHE}` "," :math:`\mathrm{DX}=0`"
    "* :math:`\mathrm{DROITE}` "," :math:`\mathrm{FX}=-784N`"