Response Variability Bounds of Elastic Beams with Uncertain Parameters

This review paper describes probabilistic and non-probabilistic procedures for the analysis of response variability of elastic beams with uncertain flexibility under deterministic static loads. Within the probabilistic framework, the uncertain flexibility is modelled as a random field and the well established concept of response variability function is adopted. Spectral- and probability-distribution-free upper bounds on the response variability are thus obtained. Within the nonprobabilistic context, the uncertain flexibility is described by means of a novel interval field model, recently introduced by the authors as a natural extension of the random field concept. An efficient procedure for deriving the lower bound and upper bound of the interval deflection, useful for both statically determinate and indeterminate beams, is presented. Numerical results focus on the comparison between response variability under random and interval uncertainty.