Buckling Optimization of Beams and Plates on Elastic Foundation

Abstract

The structural optimization problem of minimizing the weight of beams and orthotropic plates on elastic foundation for a given critical buckling load is formulated and solved. The cross‐sectional area and thickness variations are sought for the beam and plate problems, respectively. Optimality conditions are first derived via variational calculus, and the semianalytical truncated Fourier series approach is used to obtain optimal designs that indicate up to 50% increase in buckling load for the beam and about 112% increase in buckling load for the plate.