Spatial variability of interval material properties in Euler-Bernoulli beams

The effects of Young's modulus uncertainty on the response of Euler-Bernoulli beams are investigated within a non-probabilistic framework. To this aim, a novel definition of the interval field concept is introduced which allows to account for the dependency between interval values at various locations by means of a deterministic symmetric non-negative function playing the same role of the autocorrelation function in random field theory. Approximate closed-form expressions for the bounds of the interval displacement field of the beam are derived by performing a finite difference discretization of the governing interval ordinary differential equation and applying the so-called improved interval analysis, recently proposed by the authors. The effectiveness of the presented procedure is assessed through numerical results concerning a simply supported beam.