A Multiscale Design Methodology for Hierarchical Systems With Random Field Uncertainty

A multiscale design methodology is proposed for hierarchical material and product systems with random field uncertainty that propagates across multiple length scales. Using the generalized hierarchical multiscale decomposition pattern in multiscale modeling, a set of computational techniques is developed to manage the system complexity. Design of experiments and metamodeling strategies are proposed to manage the complexity of propagating random field uncertainty through three generalized levels of transformation: the material microstructure random field, the material property random field, and the probabilistic product performance. Multilevel optimization techniques are employed to find optimal design solutions at individual scales. A hierarchical multiscale design problem that involves a two-scale (submicro- and microscales) material design and a macroscale product (bracket) design is used to demonstrate the applicability and benefits of the proposed methodology.