This study proposes a robust concurrent topology optimization method with considering dynamic load uncertainty for the design of structures composed of periodic microstructures based on the bi-directional evolutionary structural optimization (BESO) method. The objective function is formulated as the summation of the mean and standard deviation of the structural dynamic compliance modulus. The constraints are imposed on the macrostructure and material microstructure volumes, respectively. The hybrid dimension reduction method and Gauss integral (HDRG) method is proposed to quantify and propagate load uncertainty to estimate the objective function. By the HDRG method, robust topology optimization with uncertainty modeled by probabilistic methods can be handed uniformly. To reduce the computational burden, a decoupled sensitivity analysis method is proposed to calculate the sensitivities of objective function with respect to the microstructure design variables. Five numerical examples are used to validate the effectiveness of the proposed robust concurrent topology optimization method and demonstrate the influence of load uncertainty on the design results. Results illustrate that the proposed methods can obtain the clear topologies of macro and micro structures, and the dynamic load uncertainty has a significant impact on the design results.

本研究基于双向进化结构优化 (BESO) 方法，提出了一种考虑动态载荷不确定性的鲁棒并发拓扑优化方法，用于设计由周期性微结构组成的结构。目标函数被表述为结构动态顺应模量的平均值和标准偏差的总和。约束分别施加在宏观结构和材料微观结构体积上。提出了混合降维方法和高斯积分（HDRG）方法来量化和传播负载不确定性以估计目标函数。通过 HDRG 方法，可以统一处理具有不确定性的概率方法建模的鲁棒拓扑优化。为了减轻计算负担，提出了一种解耦灵敏度分析方法来计算目标函数对微观结构设计变量的灵敏度。五个数值例子被用来验证所提出的鲁棒并发拓扑优化方法的有效性，并论证负载不确定性对设计结果的影响。结果表明，所提出的方法可以获得清晰的宏观和微观结构拓扑结构，动态载荷不确定性对设计结果有显着影响。