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Reliability computation with local polynomial chaos approximations. (English) Zbl 1156.74049
Summary: We discuss the reliability estimation for structural mechanics problems involving random fields. While in most of the literature on stochastic finite element methods to date only global approximations with Hermite polynomials are considered, the benefits of local approximations are investigated in this paper. Local polynomial approximations in the vicinity of the point of most probable failure are introduced. An adaptive algorithm is proposed, that allows for efficient and accurate computations of failure probabilities.
MSC:
74S05Finite element methods in solid mechanics
74E35Random structure
74K99Thin bodies, structures (solid mechanics)
62N05Reliability and life testing (survival analysis)