Optimum design of Beck's column

Abstract

The present paper treats a problem of determining the mass distribution of a cantilever column subject to a compressive follower force, i.e. Beck's column, which maximizes its critical load of dynamic stability under the constraint of a specified total mass. A considerable increase of the critical load can be achieved by taking two characteristic loads into account and maximizing them simultaneously. The present optimum design is found to be a point in the space of design variable at which the critical load varies in a discontinuous fashion. The finite element method is used as a technique for discretizing the basic equations, while the gradient projection method is used as an optimization technique. The computational algorithm is developed and some numerical examples are shown.