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


Geometry
---------


.. image:: images/10000000000004370000018F8844DED8D226C3AB.png
    :width: 6.889in
    :height: 2.4583in


.. _RefImage_10000000000004370000018F8844DED8D226C3AB.png:

coordinates of the points (in :math:`m`): :math:`\mathrm{A1}(\mathrm{0,0}\mathrm{,0})` :math:`\mathrm{A2}(\mathrm{10,0}\mathrm{,0})` :math:`\mathrm{A3}(\mathrm{10,5}\mathrm{,0})` :math:`\mathrm{A4}(\mathrm{0,5}\mathrm{,0})`


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

The material consists of 4 orthotropic layers with a thickness of 0.1.

The first layer is characterized by:

.. csv-table::

    ":math:`\mathrm{EL}={20000.10}^{6}\mathrm{Pa}` "," :math:`\mathrm{ET}={20000.10}^{6}\mathrm{Pa}` "," :math:`\mathrm{VLT}=0.3` "," :math:`\mathrm{GLT}={2000.10}^{6}\mathrm{Pa}`"


the second layer by:

.. csv-table::

    ":math:`\mathrm{EL}={15000.10}^{6}\mathrm{Pa}` "," :math:`\mathrm{ET}={15000.10}^{6}\mathrm{Pa}` "," :math:`\mathrm{VLT}=0.3` "," "," GLT = 1500.10^6Pa"


the third layer by:

.. csv-table::

    ":math:`\mathrm{EL}={20000.10}^{6}\mathrm{Pa}` "," :math:`\mathrm{ET}={20000.10}^{6}\mathrm{Pa}` "," :math:`\mathrm{VLT}=0.3` "," :math:`\mathrm{GLT}={2000.10}^{6}\mathrm{Pa}`"


and the fourth layer by:

.. csv-table::

    ":math:`\mathrm{EL}={15000.10}^{6}\mathrm{Pa}` "," :math:`\mathrm{ET}={15000.10}^{6}\mathrm{Pa}` "," :math:`\mathrm{VLT}=0.3` "," :math:`\mathrm{GLT}={1500.10}^{6}\mathrm{Pa}`"



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

Node :math:`\mathrm{A1}` is embedded:


.. csv-table::

    ":math:`\mathrm{dx}=0.` "," :math:`\mathrm{dy}=0.` "," :math:`\mathrm{dz}=0.`"
    "", "", ""
    ":math:`\mathrm{dRx}=0.` "," :math:`\mathrm{dRy}=0.` "," :math:`\mathrm{dRz}=0.`"


Node :math:`\mathrm{A2}` is blocked according to the following ddls:


.. csv-table::

    ":math:`\mathrm{dx}=0.` "," :math:`\mathrm{dy}=0.` ", ""


A modal force :math:`\mathrm{Fz}=-\mathrm{1000.N}` is applied to node :math:`\mathrm{A3}`.