The rapid development of additive manufacturing has made coated structures an innovative configuration with high design flexibility. However, poor forming accuracy and surface roughness during manufacturing will cause uncertainty in surface layer thickness, which results in structure performance deviation and failure to achieve the expected goals. This paper proposes a robust topology optimization method for coated structures considering the surface layer thickness uncertainty to obtain high-quality designs that can resist disturbance by uncertainties. First, an erosion-based approach is used to establish the model of the coated structure surface layer. Second, modeling the surface layer thickness uncertainty applies a random field whose dimensionality of the random fields is reduced by the Expansion Optimal Linear Estimation (EOLE) method. Then, minimizing the weighted sum of the mean and standard deviation of structural compliance is taken as the optimization objective, and robust topology optimization considering uncertainty is established. Finally, estimate the stochastic response by the perturbation technique, then the sensitivity of the objective function with respect to the design variables is derived. Numerical examples show that the structural design obtained with the proposed method has a stronger resistance to uncertainty than the deterministic topology optimization method, proving the method’s effectiveness in this paper.

增材制造的快速发展使涂层结构成为具有高度设计灵活性的创新配置。然而制造过程中不良的成形精度和表面粗糙度会造成表层厚度的不确定性，从而导致结构性能出现偏差而达不到预期目标。本文提出了一种考虑表面层厚度不确定性的涂层结构鲁棒拓扑优化方法，以获得能够抵抗不确定性干扰的高质量设计。首先，使用基于侵蚀的方法建立涂层结构表面层的模型。其次，对表面层厚度不确定性进行建模，应用随机场，其随机场的维数通过展开最优线性估计 (EOLE) 方法降低。然后，以结构柔度均值和标准差的加权和最小化为优化目标，建立考虑不确定性的鲁棒拓扑优化。最后，通过扰动技术估计随机响应，然后导出目标函数相对于设计变量的敏感性。数值算例表明，该方法获得的结构设计比确定性拓扑优化方法具有更强的抗不确定性，证明了本文方法的有效性。