Efficient structural reliability analysis via a weak-intrusive stochastic finite element method

authored by: Zhibao Zheng, Hongzhe Dai, Michael Beer
Abstract: This paper presents a novel methodology for structural reliability analysis by means of the stochastic finite element method (SFEM). The key issue of structural reliability analysis is to determine the limit state function and corresponding multidimensional integral that are usually related to the structural stochastic displacement and/or its derivative, e.g., the stress and strain. In this paper, a novel weak-intrusive SFEM is first used to calculate structural stochastic displacements of all spatial positions. In this method, the stochastic displacement is decoupled into a combination of a series of deterministic displacements with random variable coefficients. An iterative algorithm is then given to solve the deterministic displacements and the corresponding random variables. Based on the stochastic displacement obtained by the SFEM, the limit state function described by the stochastic displacement (and/or its derivative) and the corresponding multidimensional integral encountered in reliability analysis can be calculated in a straightforward way. Failure probabilities of all spatial positions can be obtained at once since the stochastic displacements of all spatial points have been known by using the proposed SFEM. Furthermore, the proposed method can be applied to high-dimensional stochastic problems without any modification. One of the most challenging problems encountered in high-dimensional reliability analysis, known as the curse of dimensionality, can be circumvented with great success. Three numerical examples, including low- and high-dimensional reliability analysis, are given to demonstrate the good accuracy and the high efficiency of the proposed method.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): Harbin Institute of Technology
University of Liverpool
Tongji University
Type: Article
Journal: Probabilistic Engineering Mechanics
Volume: 71
ISSN: 0266-8920
Publication date: 01.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Statistical and Nonlinear Physics, Civil and Structural Engineering, Nuclear Energy and Engineering, Condensed Matter Physics, Aerospace Engineering, Ocean Engineering, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.probengmech.2023.103414 (Access: Closed)