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D. Xiu and G. E. Karniadakis, “Modeling Uncertainty in Flow Simulations via Generalized Polynomial Chaos,” Journal of Computational Physics, Vol. 187, No. 1, 2003, pp. 137-167. doi:10.1016/S0021-9991(03)00092-5

has been cited by the following article:

• TITLE: Structural Reliability Assessment by a Modified Spectral Stochastic Meshless Local Petrov-Galerkin Method

  AUTHORS: Guang Yih Sheu

  KEYWORDS: Spectral Stochastic Meshless Local Petrov-Galerkin Method; Generalized Polynomial Chaos Expansion; First-Order Reliability Method; Structural Failure Probability; Reliability Index

  JOURNAL NAME: World Journal of Mechanics, Vol.3 No.2, April 30, 2013

  ABSTRACT: This study presents a new tool for solving stochastic boundary-value problems. This tool is created by modify the previous spectral stochastic meshless local Petrov-Galerkin method using the MLPG5 scheme. This modified spectral stochastic meshless local Petrov-Galerkin method is selectively applied to predict the structural failure probability with the uncertainty in the spatial variability of mechanical properties. Except for the MLPG5 scheme, deriving the proposed spectral stochastic meshless local Petrov-Galerkin formulation adopts generalized polynomial chaos expansions of random mechanical properties. Predicting the structural failure probability is based on the first-order reliability method. Further comparing the spectral stochastic finite element-based and meshless local Petrov-Galerkin-based predicted structural failure probabilities indicates that the proposed spectral stochastic meshless local Petrov-Galerkin method predicts the more accurate structural failure probability than the spectral stochastic finite element method does. In addition, generating spectral stochastic meshless local Petrov-Galerkin results are considerably time-saving than generating Monte-Carlo simulation results does. In conclusion, the spectral stochastic meshless local Petrov-Galerkin method serves as a time-saving tool for solving stochastic boundary-value problems sufficiently accurately.