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.
Highlights
Available stochastic numerical methods for solving stochastic boundary-value problems include the Monte Carlo simulation, spectral stochastic finite element [1] and stochastic element-free Galerkin methods [2]
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
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
Summary
Available stochastic numerical methods for solving stochastic boundary-value problems include the Monte Carlo simulation, spectral stochastic finite element [1] and stochastic element-free Galerkin methods [2]. In a published study [5], a spectral stochastic meshless local Petrov-Galerkin method has been developed by coupling a meshless local Petrov-Galerkin formulation and radial basis functionbased meshfree shape functions with polynomial chaos expansions [6] of stochastic processes. Based on the published conclusion [8] that the MLPG5 scheme may substitute for the finite element method to solve boundary-value problems, the current study further derives a two-dimensional spectral stochastic meshless local Petrov-Galerkin formulation in elastostatics using the MLPG5 scheme.
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