1. Reference problem#

1.1. Geometry#

_images/1000000000000158000000CE7265D22D2D0C5543.png

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

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

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

1.2. Material properties#

The material is linear elastic.

Young’s module \(E=1.0\mathrm{MPa}\) (without influence on the result).

Poisson’s ratio: \(\nu =0\)

1.3. Boundary conditions and loads#

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

For modeling A:

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

  • following elongation \(x\): \({\epsilon }_{X}^{0}=0.001\)

  • curvature around \(y\): \({\chi }_{y}^{0}=0.002\)

  • curvature around \(z\): \({\chi }_{z}^{0}=0.003\)

1.4. Characteristics of the beam section#

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