Optimal Synthesis of Mesostructured Materials under Uncertainty

Uncertainties in material properties, geometry, manufacturing processes, and operational environments are clearly critical at all scales (nano-, micro-, meso-, and macro-scale). Specifically, the incorporation of reliability analysis is critical in designing mesostructured materials when material properties are uncertain. 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 mesostructured materials 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 is demonstrated with two examples including a ground truss structure and an automotive component which is composed of mesostructured material. Nomenclature Ai = area of cross section of each truss element di = distance from a sampling point f(b) = objective function gj(.) = limit state function K = stiffness matrix of the structure Li = length of each truss element P = Internal pressure of the tank ri = domain influence factor r = internal pressure of the tank u(.) = displacements of nodes V * = final volume of the structure W(.) = weight matrix βj = regression coefficient e = error of the model equation ξi = Gaussian random variable 1