Static response bounds of Timoshenko beams with spatially varying interval uncertainties

Response variability of Timoshenko beams with uncertain Young's modulus subjected to deterministic static loads is analyzed. The uncertain material property is idealized within a non-probabilistic context by using an interval field model recently proposed by the first two authors. Such a model is able to quantify the dependency between adjacent values of an interval uncertainty by means of a real, deterministic, symmetric, nonnegative, bounded function conceived as the non-probabilistic counterpart of the autocorrelation function characterizing random fields. In order to analyze the effects of Young's modulus uncertainty on the static response of the Timoshenko beam, a finite difference discretization of the coupled interval ordinary differential equations of equilibrium is performed. Then, approximate explicit expressions of the lower bound and upper bound of the interval response are derived. Numerical results showing the effects of interval material uncertainty on the static response of a simply supported beam under uniformly distributed load are presented.