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.

几何缺陷会严重影响薄壁结构（TWS）的承载能力。在此，我们考虑了最坏情况下的临界屈曲载荷（具有空间变化的几何不确定性），为薄壁结构的加劲肋开发了一种拓扑优化方法。由于缺乏足够的概率信息，使用非概率有界场模型对薄壁结构的厚度缺陷进行建模。使用级数展开将有界场不确定性离散化，并表示为一组不相关的不确定性系数。然后，作为拓扑优化问题的内循环，在非概率字段描述下评估最坏情况的临界屈曲载荷。外循环优化问题表示为确定最佳加劲肋拓扑，该拓扑在受约束的材料体积下最大化最坏情况下的临界屈曲载荷，并通过基于梯度的算法解决嵌套的优化问题。数值算例表明，所提出的加强筋优化方法提高了具有不确定几何缺陷的薄壁结构的稳定性。