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

Geometry
---------

The geometry, as well as the modeling points are represented in the following figure:


.. image:: images/100018D600002A4500001A0C52F8BA0F02A87592.svg
    :width: 545
    :height: 336


.. _RefImage_100018D600002A4500001A0C52F8BA0F02A87592.svg:

Lengths in meters


* pipe outer diameter: :math:`0.185m`


* pipe thickness: :math:`6.12\mathrm{mm}`


* radius of curvature of the elbows: :math:`0.922m`


* pipes full of water


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

:math:`E=1.658E+11\mathrm{Pa}`

:math:`\nu =0.3`

:math:`\rho =13404.10\mathrm{kg}/{m}^{3}`

:math:`\alpha =0.1288E–4/C°`


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


* Points 1 (node group T1) and 15 (node group T15) embedded,


* Charging:


1. Gravity according to :math:`–z`,


2. Uniform temperature rise of :math:`472.22C°`,


3. Nodal forces.


.. csv-table::

    "Node groups", "T2", "T3", "T4, T3", "T4, T10", "T5, T9", "T6, T7, T8", "T11", "T11", "T12, T13", "T13", "T14"
    ":math:`\mathrm{Fz}` (:math:`N`)", "—624.897", "—624.897", "—788.724", "—327.654", "—214.839", "—102.5145", "—222.687", "—222.687", "—222.687", "—222.687", "—117.720", "—176.580"