Static analysis of Euler–Bernoulli beams with interval Young’s modulus

A non-probabilistic approach for analyzing the effects of Young's modulus uncertainty on the response of Euler-Bernoulli beams under deterministic static loads is presented. The uncertain material property is described by applying an interval field model based on the so-called improved interval analysis. The bounds of the interval response are determined in approximate closed-form by performing a finite difference discretization of the governing interval ordinary differential equation and applying the so-called Interval Rational Series Expansion. The proposed procedure is applied to investigate the effects of Young's modulus uncertainty on the bending response of beams with different boundary conditions.