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


Geometry
---------


.. image:: images/10001DC600001F36000016BD37DE83119F0D6FF3.svg
    :width: 402
    :height: 293


.. _RefImage_10001DC600001F36000016BD37DE83119F0D6FF3.svg:

Coordinates of points (in meters):


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C` "," "," :math:`D` "," :math:`E` "," :math:`X`"
    ":math:`x` ", "0. ", "0. ", "0.5", "0.5", "0.5", "0. ", "0."
    ":math:`y` ", "0. ", "0. ", "0. ", "0. ", "0. ", "0.5"
    ":math:`z` ", "3. ", "0. ", "0. ", "3. ", "1.5", "3."



Material properties
-----------------------

Young's modules in directions :math:`x`, :math:`y`, and :math:`z`:

:math:`{E}_{L}=5.{10}^{11}\mathrm{Pa}`, :math:`{E}_{T}=5.{10}^{11}\mathrm{Pa}`, :math:`{E}_{N}=2.{10}^{11}\mathrm{Pa}`.

Coefficient of POISSON in the :math:`\mathrm{xy}`, :math:`\mathrm{xz}`, and :math:`\mathrm{yz}` planes:

:math:`{\nu }_{\text{LT}}=0.1`, :math:`{\nu }_{\text{LN}}=0.3`, :math:`{\nu }_{\text{TN}}=0.1`.

Shear modules in planes :math:`\mathit{xy}`, :math:`\mathit{xz}`, and :math:`\mathit{yz}`:

:math:`{G}_{\text{LT}}=7.69231{10}^{10}\mathrm{Pa}`, :math:`{G}_{\text{LN}}=7.69231{10}^{10}\mathrm{Pa}`,

:math:`{G}_{\text{TN}}=7.69231{10}^{10}\mathrm{Pa}`.

Density: :math:`\rho =7800\mathrm{kg}/{m}^{3}`.


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

Point :math:`A`: (:math:`u=v=w=0`, :math:`{\theta }_{x}={\theta }_{y}={\theta }_{z}=0`)

Own weight along axis :math:`z`: :math:`\rho gz`

Uniform tensile stress for the upper side:

:math:`{\sigma }_{z}=\rho gL=+229554.\mathrm{Pa}`