Static analysis of Euler-Bernoulli beams with interval Young's modulus

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.

[1]  Manolis Papadrakakis,et al.  Flexibility-based upper bounds on the response variability of simple beams , 2005 .

[2]  Giuseppe Muscolino,et al.  RESPONSE STATISTICS OF LINEAR STRUCTURES WITH UNCERTAIN-BUT-BOUNDED PARAMETERS UNDER GAUSSIAN STOCHASTIC INPUT , 2011 .

[3]  Roberta Santoro,et al.  Explicit frequency response functions of discretized structures with uncertain parameters , 2014 .

[4]  Wim Desmet,et al.  Numerical dynamic analysis of uncertain mechanical structures based on interval fields , 2011 .

[5]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[6]  Jiří Rohn.  Interval solutions of linear interval equations , 1990 .

[7]  A. Sofi,et al.  Stochastic analysis of structures with uncertain-but-bounded parameters via improved interval analysis , 2012 .

[8]  Giuseppe Muscolino,et al.  One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis , 2013 .

[9]  R. Baker Kearfott,et al.  Introduction to Interval Analysis , 2009 .

[10]  David Moens,et al.  A survey of non-probabilistic uncertainty treatment in finite element analysis , 2005 .

[11]  Masanobu Shinozuka,et al.  Response Variability of Stochastic Finite Element Systems , 1988 .

[12]  Vladik Kreinovich,et al.  Interval Arithmetic, Affine Arithmetic, Taylor Series Methods: Why, What Next? , 2004, Numerical Algorithms.

[13]  Masanobu Shinozuka,et al.  Neumann Expansion for Stochastic Finite Element Analysis , 1988 .

[14]  E. R. Hansen,et al.  A Generalized Interval Arithmetic , 1975, Interval Mathematics.

[15]  M. Hanss,et al.  Review: Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances , 2011 .

[16]  I. Elishakoff,et al.  Large variation finite element method for beams with stochastic stiffness , 2003 .

[17]  I. Elishakoff,et al.  Convex models of uncertainty in applied mechanics , 1990 .

[18]  W. Desmet,et al.  Interval fields to represent uncertainty on the output side of a static FE analysis , 2013 .

[19]  Sanjay R. Arwade,et al.  Variability response functions for effective material properties , 2011 .

[20]  M. Shinozuka,et al.  Some exact solutions for the bending of beams with spatially stochastic stiffness , 1995 .

[21]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[22]  E. Vanmarcke,et al.  Random Fields: Analysis and Synthesis (Revised and Expanded New Edition) , 2010 .

[23]  A. Sofi,et al.  Bounds for the stationary stochastic response of truss structures with uncertain-but-bounded parameters , 2013 .

[24]  I. Elishakoff,et al.  Novel parameterized intervals may lead to sharp bounds , 2012 .