Decomposition methods for structural reliability analysis

• Published in: Probabilistic engineering mechanics Vol. 20; no. 3; pp. 239 - 250
• Main Authors: Xu, H., Rahman, S.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.2005; Elsevier Science
• Subjects: Bivariate method; Decomposition; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Physics; Reliability; Response surface; Solid mechanics; Static elasticity (thermoelasticity...); Stochastic finite-element and mesh-free methods; Structural and continuum mechanics; Univariate method; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Response surface; Decomposition; Reliability; Stochastic finite-element and mesh-free methods; Bivariate method; Univariate method; Monte Carlo method; Probabilistic approach; Rupture; Structural reliability; Modeling; Finite element method; Response function; Meshless method; Mechanical system; Random load; Random medium; Effective medium model; Structural analysis
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2005.05.005

A new class of computational methods, referred to as decomposition methods, has been developed for predicting failure probability of structural and mechanical systems subject to random loads, material properties, and geometry. The methods involve a novel function decomposition that facilitates univariate and bivariate approximations of a general multivariate function, response surface generation of univariate and bivariate functions, and Monte Carlo simulation. Due to a small number of original function evaluations, the proposed methods are very effective, particularly when a response evaluation entails costly finite-element, mesh-free, or other numerical analysis. Seven numerical examples involving elementary mathematical functions and solid-mechanics problems illustrate the methods developed. Results indicate that the proposed methods provide accurate and computationally efficient estimates of probability of failure.