Robust Topology Optimization of Coated Structures with Surface Layer Thickness Uncertainty Considered

Abstract

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.