  This paper presents a new methodology for structural reliability analysis via
stochastic finite element method (SFEM). A novel sample-based SFEM is firstly
used to compute structural stochastic responses of all spatial points at the
same time, which decouples the stochastic response into a combination of a
series of deterministic responses with random variable coefficients, and solves
corresponding stochastic finite element equation through an iterative
algorithm. Based on the stochastic response obtained by the SFEM, the limit
state function described by the stochastic response and the multidimensional
integral encountered in reliability analysis can be computed without any
difficulties, and failure probabilities of all spatial points are calculated
once time. The proposed method can be applied to high-dimensional stochastic
problems, and one of the most challenging issues encountered in
high-dimensional reliability analysis, known as Curse of Dimensionality, can be
circumvented without expensive computational costs. Three practical examples,
including large-scale and high-dimensional reliability analysis, are given to
demonstrate the accuracy and efficiency of the proposed method in comparison to
the Monte Carlo simulation.
