Optimum design of cantilever columns in the post buckling region with constraint on axial load-an optimality criterion approach

Abstract

An optimality criterion and resizing formula for design variables are developed for obtaining minimum weight (volume if density is constant) of cantilever columns subjected to axial load constraints in the post-buckling region. A variational formulation is developed which forms the basis for the finite element analysis for the postbuckling analysis of cantilever columns. A method is presented to obtain absolute design variables from the converged design vector obtained through the resizing formula. Linear buckling constraints can be treated in the present study as special cases. Optimum configurations of cantilever columns of circular cross-section are obtained for three different axial load cases. Comparison of the present solution (linear buckling constraint) in the case of a cantilever column subjected to a concentrated tip load with a continuum solution shows the effectiveness of the present optimality criterion approach.