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.