Optimization and Robustness of Deformable Systems with Randomness

Abstract

Synthetic Monte Carlo sampling and analytic Taylor series expansion offer two different techniques for the treatment of random input scatter. The paper expounds on the Taylor series approximation as applied to the stochastic analysis and design optimization of structures and deforming solids, including robustness against uncertainties. A unified approach is presented starting with linear elastic structures, extending to nonlinear and path dependent response, and progressing to deformation processes of inelastic solids. The methodology refers to finite element systems, and assumes that the response is a continuous function of the input; representation of the probability distribution is restricted to mean and variance. The approach is applicable to input scatter of practical relevance and is computationally efficient; its analytic nature allows utilization of optimization algorithms.