Sequential Semidefinite Programming for Optimization of Framed Structures Under Multimodal Buckling Constraints

An algorithm based on Semi-Definite Programming (SDP) formulation is proposed for optimum design of structures for specified linear buckling load factors. Optimal trusses and frames are computed by using the primal-dual interior-point method based on SDP scheme. It is well known that optimizing structures under buckling constraints is difficult because of the non-differentiability of buckling load factors for the case of multimodal solutions. The examples studied indicate that optimum designs with multiple buckling load factors can be found with no difficulty by successively solving the SDP problems.