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.
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