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Zbl 1156.74049
Proppe, C.
Reliability computation with local polynomial chaos approximations. (English)
[J] ZAMM, Z. Angew. Math. Mech. 89, No. 1, 28-37 (2009). ISSN 0044-2267; ISSN 1521-4001/e

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 2000:: *74S05 Finite element methods
74E35 Random structure
74K99 Thin bodies, structures
62N05 Reliability, etc. (statistics)

Keywords: local response surface; stochastic boundary value problem; stochastic finite element methods

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Zentralblatt MATH Berlin [Germany]