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

• Published in: Computers & structures Vol. 156; pp. 72 - 82
• Main Authors: Sofi, A., Muscolino, G.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2015
• Subjects: Approximation; Differential equations; Euler-Bernoulli beams; Explicit solutions; Finite difference method; Improved interval analysis; Interval field; Interval Rational Series Expansion; Intervals; Mathematical analysis; Mathematical models; Modulus of elasticity; Uncertainty; Upper bound and lower bound; Interval Rational Series Expansion; Improved interval analysis; Explicit solutions; Upper bound and lower bound; Interval field; Finite difference method
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2015.04.002

•The response of Euler–Bernoulli beams with interval Young’s modulus is analyzed.•Spatial variability of uncertainty is handled by a novel interval field model.•A finite difference discretization of the interval equilibrium equation is performed.•The bounds of the interval displacement field are evaluated in explicit form.•Numerical results demonstrate both the accuracy and consistency of the proposed model. 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.