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Finite Element Analysis in Structural Mechanics

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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

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


Two-point support. Statically determinate.


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


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.

en/example/nlin/3/start.txt · Last modified: 2022-02-11 14:25 by Petr Pařík