Linear buckling topology optimization of reinforced thin-walled structures considering uncertain geometrical imperfections

Geometrical imperfections significantly affect the load-carrying capacity of thin-walled structures (TWSs). Herein, we develop a topology optimization method for the stiffeners of thin-walled structures considering the worst-case critical buckling load with spatially varying geometrical uncertainties. The thickness imperfections of the thin-walled structures are modeled using a non-probabilistic bounded field model because of a lack of sufficient probability information. The bounded field uncertainty is discretized using series expansion and represented as a set of uncorrelated uncertain coefficients. Then, as an inner loop of the topology optimization problem, the worst-case critical buckling load is assessed under the non-probabilistic field description. The outer loop optimization problem is expressed as determining the optimum stiffener topology that maximizes the worst-case critical buckling load under constrained material volume, and the nested optimization problem is solved via a gradient-based algorithm. Numerical examples demonstrate that the proposed method for stiffener optimization improves the stability of thin-walled structures with uncertain geometrical imperfections.