Reliability Analysis of Random Structure under Static Load Using Non-orthogonal Polynomial Expansion

摘要

A new approach for the reliability analysis of random structure subjected to static load is presented based on non-orthogonal polynomial expansion, which polynomial bases constitute a complete Hilbert space. In the process of analysis, structural material parameters, geometrical parameters (e.g. the thickness of plate) as well as static loads supplied can be considered as random quantities. Furthermore, for continuous random fields, the Karhunen-Loeve expansions are employed to decompose the covariance functions describing the random fields into a series of independent random variables. With reference to the perturbation technique, the initial coefficients of the non-orthogonal polynomial terms of the random vector, which represents the unknown static response, are determined in terms of defined mathematical operators. Afterwards, the Galerkin projection scheme is adopted to improve the convergence speed of the non-orthogonal polynomial expansion. According to the definition of reliability, the failure probability of performance function can be conveniently calculated through the obtained explicit polynomial expansion of the random response. Numerical examples are investigated to demonstrate the effectiveness of the proposed approach.