Owing to the variations in geometric dimensions, material properties and external loads in engineering applications, robust topology optimization (RTO) has garnered increasing attention in recent years to account for the uncertain behaviors during the preliminary concept design phases. This paper presents a hybrid RTO method to simultaneously resolve the epistemic and aleatory uncertainties. First, based on the probabilistic and fuzzy methodologies, the hybrid RTO model is formulated with nested double optimization loops using Monte Carlo simulations. Second, an efficient iterative method is proposed based on the perturbation method to accelerate the rate of convergence of the proposed hybrid RTO model. The derivatives of the hybrid robust compliance objective function with respect to the deterministic design variables, random parameters, and fuzzy parameters are then derived using the adjoint variable method. Finally, a T‐shaped beam design, an L‐shaped beam design, and a three‐dimensional cantilever beam design are tested to validate the proposed hybrid RTO method.

中文翻译：

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概率和模糊不确定性下连续结构的鲁棒拓扑优化方法

由于工程应用中几何尺寸，材料特性和外部载荷的变化，稳健的拓扑优化（RTO）近年来引起了越来越多的关注，以解决初步概念设计阶段中的不确定行为。本文提出了一种混合RTO方法，以同时解决认知和偶然的不确定性。首先，基于概率和模糊方法，使用蒙特卡洛模拟方法，使用嵌套的双重优化循环来制定混合RTO模型。其次，基于扰动方法，提出了一种有效的迭代方法，以加快所提出的混合RTO模型的收敛速度。关于确定性设计变量，随机参数，然后使用伴随变量法导出模糊参数。最后，测试了T形梁设计，L形梁设计和三维悬臂梁设计，以验证所提出的混合RTO方法。