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

Geometry
---------


.. image:: images/10000CD80000284F000012EABCD9F9D362A9C8AE.svg
    :width: 519
    :height: 244


.. _RefImage_10000CD80000284F000012EABCD9F9D362A9C8AE.svg:

Flat structure symmetric with respect to the line :math:`y=4.`


.. csv-table::

    "Section beams", "circular", "outside diameter", ":math:`\mathrm{de}=0.04m`"
    "", "inner diameter", ":math:`\mathrm{di}=0.01m`"
    "Elbow", "center", "(:math:`y=4` :math:`z=0`)", "and radius = :math:`2\sqrt{2}m`"
    "Node-node link", "", ":math:`\mathrm{Kx}=\mathrm{Kz}={10}^{5}N/m` ", "in the local coordinate system"


**Point coordinates (in** :math:`m` **) :**

.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C` "," "," :math:`D` "," "," :math:`E` "," :math:`F` ", "G"
    ":math:`x` ", "0. ", "0. ", "0. ", "0. ", "0. ", "0. ", "0."
    ":math:`y` ", "—2. ", "0. ", "2. ", "4. ", "6. ", "8. ", "10."
    ":math:`z` ", "—2. ", "0. ", "2. "," :math:`2\sqrt{2}` ", "2. ", "0. ", "—2."



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

Young's module: :math:`E=2.1{10}^{11}\mathrm{Pa}`

Poisson's ratio: :math:`\nu =0.3`

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

Coefficient of thermal expansion: :math:`\alpha ={10}^{-6}m/°C`


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

.. csv-table::

    "Points :math:`A` and :math:`G` embedded", "(:math:`v=w=0`)", "(except for load case 2)"



.. csv-table::

    "Loading:", ""
    "1) load concentrated in :math:`C` and :math:`E` "," :math:`F=1000N`"
    "2) displacement imposed in :math:`A` and :math:`G` "," :math:`\mathrm{Dx}=\sqrt{2}` as a local coordinate system for links :math:`\mathrm{AB}` and :math:`\mathrm{GF}`"
    "3) thermal expansion at :math:`t=100°C` ", ""
    "4) own weight", ""
    "5) material dependent on T", ""