### Table of Contents

# Buckling

##### by Dr. Jiří Plešek

## Problem description

Trace out the complete load-displacement history of the column at the critical state determined in Stability of a column and compare these results with the linearized solution therein. The flexural stiffness $EI_y<EI_z.$

## Material properties

$E=2\times10^5\text{ MPa},$ $\nu=0.3.$

## Support

Two-point support. Statically determinate.

## Loading

The load history is given as $F_x(t)=\left\{\begin{align}-3280 \\ -3290 \\ -3490 \\ -3500 \end{align}\right.\text{ N},$ $F_y=0,$ $F_z=1\text{ N}.$

## Solution

Note that $F_x=-3290\text{ N}$ is the theoretical load limit whereas $F_x=-3490\text{ N}$ is the critical force estimated by the eigenvalue computation on the mesh considered here. A small perturbation $F_z=1\text{ N}$ is added in the direction of the minimum bending stiffness in order to invoke the collapse mode in the total Lagrangian formulation. The load-deflection curve shown in the picture below was computed with a refined substepping.