Uncertainties in material properties, geometry, manufacturing processes, and operational environments are clearly critical at all scales (nano-, micro-, meso-, and macro-scale). Specifically, reliabilty analysis in mesostructured materials can be driven by these uncertainties. The concept of mesostructured materials is motivated by the desire to put material only where it is needed for a specific application. This research develops a reliability-based synthesis method to design mesostructures under uncertainty, which have superior structural compliant performance per weight than parts with bulk material or foams. The efficiency of the proposed framework is achieved with the combination of topology optimization and stochastic approximation which utilizes stochastic local regression and Latin Hypercube Sampling. The effectiveness of the proposed framework was demonstrated using a ground structure topology optimization approach.

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