STOCHASTIC DESIGN AND CONTROL IN RANDOM HETEROGENEOUS MATERIALS

This paper discusses a sampling framework that enables optimization of complex systems characterized by high-dimensional uncertainties and design variables. We are especially concerned with problems relating to random heterogeneous materials where uncertainties arise from the stochastic variability of their properties. In particular, we reformulate topology optimization problems to account for the design of truly random composites. In addition, we address the optimal prescription of input loads/excitations in order to achieve a target response by the random material system. The methodological advances proposed in this paper consist of an adaptive sequential Monte Carlo scheme that economizes the number of runs of the forward solver and allows the analyst to identify several local maxima that provide important information with regard to the robustness of the design. We further propose a principled manner of introducing information from approximate models that can ultimately lead to further reductions in computational cost.