Reliability‐based topology optimization of continuum structure under buckling and compliance constraints

Buckling failure mainly occurs in slender rod structure under pressure, which incurs great concern and should be addressed in topology optimization (TO). However, due to the internal defects of material and the external environment interference of engineering system, the practical engineering structure inevitably produces many uncertain factors in the manufacturing and service stages. Therefore, a reliability-based topology optimization (RBTO) model under buckling and compliance constraints is established to operate the structural lightweight design considering reliability and stability requirements. To reduce the number of probabilistic constraints, the Kreisselmeier–Steinhauser aggregation function is adopted for combining the multiple constraints into a single smooth and differentiable constraint. Then, a single-loop approach combining modified chaos control strategy is applied to guarantee the robustness, effectiveness, and computational efficiency of RBTO. In addition, the sensitivities of the probabilistic constraint with respect to design and random variables are deduced, and the accuracy of sensitivities is verified by finite difference method. Finally, the validity of the RBTO method is verified by comparing with deterministic TO, in which three numerical examples are employed to demonstrate the robustness and computational accuracy.