Reliability-based topology optimization with stochastic heterogeneous microstructure properties

With advanced manufacturing processes, many modern structural designs need to include microscale uncertainties of material properties and microstructures that can affect overall performances, such as microelectromechanical systems, micro–opto–electro–mechanical systems, and micro-optical electronics systems. Topology design optimization at this scale must consider uncertainties from material microstructures as the scale of the structure and material microstructure is comparable. Very few studies consider microstructure uncertainties in topology design due to their scales are much different in classical mechanical/civil engineering. A novel framework of reliability-based topology optimization is proposed to specifically address this gap for the design. The microscale uncertainties of heterogeneous materials are quantified by the explicit mixture random field model. Then, the material distribution is optimized by a heuristic updating scheme, and sensitivities of reliability constraints are calculated using the adjoint design-point-based importance sampling method. The proposed methodology simultaneously considers microscale hierarchical uncertainties in microstructures and material property variations for each phase. The feasibility of the framework is demonstrated by several numerical examples with different multi-phase materials. Compared with deterministic topology optimization and classical topology optimization with first-order reliability method approximations, the optimal design obtained from the proposed method can achieve accurate target reliability with minimized limit state function evaluations.