Topology optimization for maximizing linear buckling load based on level set method

Stability and buckling have attracted extensive attention in the design of structural elements, especially in the design of thin-walled structures since they may naturally have poor stability and be prone to buckling failure. This paper proposes a level-set based topology optimization (TO) method that can maximize the lowest linear buckling load under a mean compliance constraint. First, we conduct the linearized buckling analysis and formulate the optimum design problem. Second, we derive the design sensitivity and revisit the reaction-diffusion equation-based level-set topology optimization. Finally, we solve several two-dimensional benchmark problems and the design results are presented to validate the proposed method.