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

Geometry
---------


.. image:: images/1000000000000158000000CE7265D22D2D0C5543.png
    :width: 2.8571in
    :height: 1.7071in


.. _RefImage_1000000000000158000000CE7265D22D2D0C5543.png:

An AB beam of length :math:`l=100\mathrm{mm}` is located on the trisector of the trihedron :math:`(X,Y,Z)`: the coordinates of point B are: :math:`B=(\frac{100}{\sqrt{3}},\frac{100}{\sqrt{3}},\frac{100}{\sqrt{3}})`

A point C is also defined as the middle of A, B.

The local coordinate system :math:`(A,x,y,z)` is deduced from the global coordinate system :math:`(A,X,Y,Z)` by the nautical angles :math:`\{\begin{array}{}\alpha =45°\\ \beta =-35.26°\mathrm{solution}\mathrm{de}\mathrm{cos}\beta =\sqrt{\frac{2}{3}}\end{array}`


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

The material is linear elastic.

Young's module :math:`E=1.0\mathrm{MPa}` (without influence on the result).

Poisson's ratio: :math:`\nu =0`


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

Embedding in :math:`A`: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=\mathrm{DRZ}=0`.

**For modeling A:**

Loading: pre-deformation in the local coordinate system :math:`(A,x,y,z)`

• following elongation :math:`x`: :math:`{\epsilon }_{X}^{0}=0.001`

• curvature around :math:`y`: :math:`{\chi }_{y}^{0}=0.002`

• curvature around :math:`z`: :math:`{\chi }_{z}^{0}=0.003`


Characteristics of the beam section
----------------------------------------

All the characteristics (area, inertia,...) are taken to be equal to 1. They have no influence on the result.