Iterative Simulation for Stochastically Nonlinear Large Variability

Abstract

Monte Carlo simulation can be accelerated for material stochasticity when the samples are ordered according to their closeness in the constitutive moduli. Iteration on the previous solution is proposed with the samples organized in descending order according to a stiffness norm. A proof of unconditional convergence is established here. A formal definition of stochastic nonlinearity is derived to characterize large variability. Iterations will diverge for a such case when the computation for the ensemble is initiated with average parameters. In reliability analysis this stochastic nonlinearity is independent of the familiar constitutive and kinematic nonlinearities. The present methodology makes large scale Monte Carlo simulations economically feasible for practical design-analysis.