Static Analysis of Timoshenko Beams with Interval Young's Modulus

An original procedure for the static analysis of Timoshenko beams with uncertain Young’s modulus is presented. Within a non-probabilistic framework, the uncertain material property is modeled as an interval field according to the definition recently introduced by the first two authors. The key idea is to account for the dependency between interval values of the Young’s modulus at various locations by means of a deterministic symmetric non-negative function playing the same role of the autocorrelation function in random field theory. After performing a finite difference discretization of the interval ordinary differential equations of equilibrium, approximate closed-form expressions of the bounds of beam response are obtained. For validation purposes, numerical results concerning a simply supported Timoshenko beam are presented.