A Set-Based Method for Multilevel Design of Materials and Structures With Manufacturing Uncertainty

Recent research has indicated that embedding small volume fractions of negative stiffness (NS) inclusions within a host material can create composites with macroscopic mechanical stiffness and loss properties that exceed conventional composites. To design these composites, a multi-level, set-based approach that employs Bayesian network classifiers was developed to identify sets of satisfactory designs at each level of the multilevel design space. In this paper, manufacturing uncertainties are incorporated to further refine the design space mappings created by the set-based approach. Manufacturing uncertainty refers to the random deviations in dimensions and other properties that often arise when fabricating a specimen. Joint probability distributions are used to model this manufacturing uncertainty. The joint probability distributions are formulated as kernel density estimates that can be based on manufacturing data. The joint probability distributions are incorporated within the set-based approach to identify sets of designs that not only yield satisfactory performance but also offer robustness to manufacturing uncertainty. The approach is demonstrated in the context of hierarchical composite materials, but it can be applied to other multi-level design problems to efficiently yield sets of robustly manufacturable, high performance designs.