Optimal Design for Prescribed Buckling Loads

A gradient method is formulated for the least-weight design of structural systems, represented by finite element assemblages, that must sustain prescribed buckling loads. An approach applied previously to free vibration problems is extended to stability problems. Included are the effects of nonlinear weight-stiffness relationships and a lower-bound constraint on the design parameter. Results are compared with existing analytical solutions for single-span columns involving nonlinear weight-stiffness relations and the method is applied to cases of continuous columns and frameworks. A further practical use of the method incorporates an averaging technique whereby design parameters over prescribed segments are constrained to vary uniformly.