SUMMARYThin-walled structures, when compressed, are prone to buckling. To fully utilize the capabilities of such structures, the post-buckling response should be considered and optimized in the design process. This work presents a novel method for gradient based design optimization of the post-buckling performance of structures. The post-buckling analysis is based on Koiter's asymptotic method. To perform gradient based optimization, the design sensitivities of the Koiter factors are derived and new design optimization formulations based on the Koiter factors are presented. The proposed optimization formulations are demonstrated on a composite square plate and a curved panel where the post-buckling stability is optimized. Copyright c 0000 John Wiley & Sons, Ltd. Thin-walled structures are often designed such that buckling does not occur during service. To ensure a structure does not buckle, the specified buckling load is often much greater than the design load. If a structure can be allowed to buckle during operation, thus operating in the post-buckling regime, it enables the possibility to design lighter and more efficient structures. To enable such an approach, the engineer must optimize the post-buckling response of the structure. Fiber reinforced polymers are ideally suited for such design tasks, as these materials allow a high degree of tailoring of the considered structure, and thus applied here for the post-buckling design optimization of structures. When optimizing structures, robustness of the resulting structure is of major importance, as the imperfection sensitivity can increase during the optimization process [1]. One method is to collect these into an equivalent geometric imperfection and use that to evaluate the knockdown in performance. Refs. [2,3] demonstrate robust design optimization by combining "worst" shape imperfection optimization and laminate optimization, thereby efficiently decreasing the imperfection sensitivity of laminated composite structures. A different approach is to handle all imperfections simultaneously by modeling the uncertainties using statistics, therefore quantifying * Correspondence to: Department of Mechanical and Manufacturing Engineering, Aalborg University (AAU), the imperfections arising from material, geometry, load etc., and perform robust buckling optimization based on the uncertainties, see e.g., [4] for a review of different approaches. Many textbooks describe the coupling between imperfections, buckling load factor, and post-buckling stability, see e.g., [5]. Focusing on simple i.e., distinct buckling load factors, the sensitivity towards imperfections relates to the stability of the post-buckling response. Generally speaking, a stable post-buckled structure is less sensitive towards imperfections than an unstable post-buckled structure. Because of these considerations, the post-buckling stability can be utilized to design robust structures.Post-buckling analysis of plates and shells has been subject to much research. Driven by the aerospace industry, large re...
