Generalized Variability Response Functions for Beam Structures with Stochastic Parameters

Abstract

A Monte Carlo–based methodology is introduced as a generalization of the variability response function (VRF) concept, applicable to both statically determinate and indeterminate beam structures with possibly large stochastic variations of parameters (bending stiffness or flexibility). This new methodology overcomes all limitations associated with the Taylor expansion-based VRFs used in the past. Two generalized VRFs (GVRFs) result from this methodology: a deflection GVRF and a bending moment GVRF. Numerical evidence indicates that these GVRFs are neither unique nor completely independent of the probabilistic characteristics of the random field modeling the variations of the bending flexibility. The GVRFs are found to be mildly sensitive to the non-Gaussian marginal distribution of this field, but are minimally dependent on its spectral density function. Taking advantage of this finding, a fast Monte Carlo–based methodology for estimating representative GVRFs is also introduced, significantly reducing the computational effort.