An improved method for evolutionary structural optimisation against buckling

In this paper, an improved method for evolutionary structural optimisation against buckling is proposed for maximising the critical buckling load of a structure of constant weight. First, based on the formulations of derivatives for eigenvalues, the sensitivity numbers of the first eigenvalue or the first multiple eigenvalues (for closely spaced and repeated eigenvalues) are derived by performing a variation operation. In order to effectively increase the buckling load factor, a set of optimum criteria for closely-spaced eigenvalues and repeated eigenvalues are established, based on the sensitivity numbers of the first multiple eigenvalues. Several examples are provided to demonstrate the validity and effectiveness of the proposed method.