1. Reference problem#

1.1. Geometry#

We study the buckling of a beam of length \(L\mathrm{=}1000\mathit{mm}\) and height \(h\mathrm{=}100\mathit{mm}\).

_images/Shape1.gif _images/100011CA000069D500004697973F4A11015B160D.svg

1.2. Material properties#

The material is assumed to be elastic. The material characteristics are as follows:

Young’s module \(E\mathrm{=}20000\mathit{MPa}\)

Poisson’s ratio \(\nu \mathrm{=}0.3\)

Density \(\rho \mathrm{=}{10}^{\mathrm{-}6}{\mathit{kg.mm}}^{\mathrm{-}3}\)

Large rotations are taken into account (DEFORMATION =” GREEN “).

1.3. Boundary conditions and loads#

The left side (\(\mathit{OC}\)) is recessed (\(\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}0\)).

Moreover, gravity applies (\({g}_{y}\mathrm{=}9810{\mathit{mm.s}}^{\mathrm{-}2}\)) and a compression force is imposed in the direction \(\mathrm{-}x\) on the right side \(\mathit{AB}\). The control is applied by controlling the movement of node \(A\):

  • a maximum displacement of \(–1\mathit{mm}\) according to \(y\) between each increment when applying gravity

  • a move of \(50\mathit{mm}\) following \(x\) and \(y\) between each increment when compression is imposed.