Stability of Nonconservatively Elastic Systems Using Eigenvalue Sensitivity

The stability of a cantilever column, carrying a concentrated mass at the free end and resting on an elastic foundation of the Winkler-type, subjected to uniformly distributed in-plane follower forces is studied by “Timoshenko beam theory” finite elements. In order to more quickly and efficiently obtain the critical load for such a nonconservative system, a simple and cost-effective numerical technique which utilizes the eigenvalue sensitivity with respect to the follower force is introduced instead of the conventional trial-and-error technique. The high accuracy and rapid rate of convergence through the combination of the present finite element model and the solution technique are demonstrated with the numerical example given. The influence of some system parameters on the critical load is also discussed.