Problems of structural optimization for post-buckling behaviour

A proposal of a new approach to the optimal design of structures under stability constraints is presented. It is shown that the standard problem of maximization of the instability load may be modified so as to obtain a specified post-critical behaviour of the designed structure. The modified optimal structure represents stable post-buckling behaviour either locally, that is, in the vicinity of the critical point, or for a specified range of generalized displacements. First, some rigid-elastic finite-degree-of-freedom models are optimized, giving an insight into the modified design problems. Then a classification of the new optimization problems is presented. Various forms of instability are taken into account and a broad selection of objective as well as constraint functions is proposed. Based on the presented classification and following the proposed optimization concept, detailed formulations of nonlinear problems of design for post-buckling behaviour are given.