Orthogonal Series Expansions of Random Fields in Reliability Analysis

A new approach for first‐order reliability analysis of structures with material parameters modeled as random fields is presented. The random field is represented by a series of orthogonal functions, and is incorporated directly in the finite‐element formulation and first‐order reliability analysis. This method avoids the difficulty of selecting a suitable mesh for discretizing the random field. A general continuous orthogonal series expansion of the random field is derived, and its relationship with the Karhunen‐Loeve expansion used in recent stochastic finite‐element studies is examined. The method is illustrated for a fixed‐end beam with bending rigidity modeled as a random field. A set of Legendre polynomials is used as the orthogonal base to represent the random field. Two types of correlation models are considered. The Karhunen‐Loeve expansion leads to a lower truncation error than does the Legendre expansion for a given number of terms, but one or two additional terms in the Legendre expansion yields almost the same results and avoids some of the computational difficulties associated with the use of the Karhunen‐Loeve expansion.