Bounds on Response Variability of Stochastic Finite Element Systems

Abstract

A methodology is developed to evaluate the spectral‐distribution‐free upper bounds of the response variability of stochastic systems. The structural systems examined consist of linearly elastic trusses and frames subjected to static loads. The computation of these bounds is achieved by extending the notion of the “variability‐response function” of a stochastic system to trusses and frames analyzed by the finite element method. The variability‐response function presents many similarities to the frequency‐response function used in random‐vibration analysis. Specifically, the variance of a specific response quantity is calculated as the integral of the product of the power‐spectral‐density function describing the stochastic properties of the system multiplied by the variability‐response function of the response quantity. Of equal importance is that this work provides insight into the underlying mechanisms controlling the response variability of stochastic truss and frame structures and an analytical basis on which the analysis can be extended to two‐dimensional structures such as plates and shells.