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


Geometry
---------

Consider a quarter of a 20 cm high pipe. The internal diameter is 4.118 cm and the external diameter is 4.746 cm (resulting in a thickness of 0.628 cm).

The geometry can be visualized in the figure, with the adjusted mesh that will be used.


.. image:: images/100002010000037700000221D6AD1C5B4B8A578B.png
    :width: 4.4839in
    :height: 2.7547in


.. _RefImage_100002010000037700000221D6AD1C5B4B8A578B.png:

**Figure** 1.1-a **:** **Geometry and mesh** of a quarter pipe


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

The quarter pipe consists of an orthotropic material whose properties are as follows:


* Young modules: :math:`{E}_{L}=10\mathit{GPa}`, :math:`{E}_{T}=10\mathit{GPa}`, and :math:`{E}_{N}=50\mathit{GPa}`


* Poisson coefficients: :math:`{\nu }_{\text{LT}}=\mathrm{0,1}`, :math:`{\nu }_{\text{LN}}=\mathrm{0,06}`, and :math:`{\nu }_{\text{TN}}=\mathrm{0,06}`


* shear modules: :math:`{G}_{\text{LT}}=5\mathit{GPa}`, :math:`{G}_{\text{LN}}=2\mathit{GPa}` and :math:`{G}_{\text{TN}}=2\mathit{GPa}`



It is an isotropic transverse material whose isotropy axis is axis :math:`N` (cylinder thickness axis).


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

 The underside of the quarter pipe is embedded.

A distributed force of components :math:`\mathit{FX}=\mathrm{0,5}\mathit{MPa}`, :math:`\mathit{FY}=\mathrm{0,5}\mathit{MPa}` and :math:`\mathit{FZ}=500\mathit{MPa}` is applied to the upper face.