Static response bounds of Timoshenko beams with spatially varying interval uncertainties

Response variability of Timoshenko beams with uncertain Young’s modulus subjected to deterministicstatic loads is analyzed. The uncertain material property is idealized within a non-probabilistic context byusing an interval field model recently proposed by the first two authors. Such a model is able to quantify thedependency 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 functioncharacterizing random fields. In order to analyze the effects of Young’s modulus uncertainty on the staticresponse of the Timoshenko beam, a finite difference discretization of the coupled interval ordinary differentialequations of equilibrium is performed. Then, approximate explicit expressions of the lower bound andupper bound of the interval response are derived. Numerical results showing the effects of interval materialuncertainty on the static response of a simply supported beam under uniformly distributed load are presented.