Design sensitivity analysis and optimization for nonlinear buckling of finite-dimensional elastic conservative structures

The purpose of this review paper is to summarize the existing methods of design sensitivity analysis and optimization of elastic conservative finite-dimensional systems with respect to nonlinear buckling behavior. Difficulties related to geometrical nonlinear singular behaviors are discussed in detail. Characteristics of optimized structures are demonstrated in reference to snapthrough behavior, hill-top branching, and degenerate critical points. A new optimization result of a flexible truss that fully utilizes the snapthrough behavior is also presented.