| Owing to the effects of manufacturing and assembling, material properties > sizes and boundaries of engineering structures are usually stochastic, actually applied loads are also different with planned ones. In traditional determinate method these stochastic factors are neglected originally, which has been proved not to be scientific enough. Therefore, it is especially important to develop stochastic finite element method (SFEM). SFEM combines finite element method with random theories to analyze the random responses of complicated structures and judge the security of structures in terms of failure probability. In this paper stochastic finite element method and SFEM-based reliability evaluation are developed for linear, nonlinear, static and dynamic problems. The research work is mainly concerned with the following three aspects.1. SFEMAt first, Cholesky factorization method and Gram-Schmidt orthogonalization method is used to covert these correlated random variables into independent ones respectively; then, Monte Carlo sampling is applied to simulate them. The two methods are convenient to generate correlated random variables. Especially, Gram-Schmidt orthogonalization method can reduce the number of simulated random variables and hence cut down the computational amount.Trigonometric series is used to simulate stationary, non-stationary, Gaussian and non-Gaussin stochastic processes by spectral representation in which the non-stationary stochastic processes are expressed as the product of determinate functions and stationary stochastic processes.Combined with Monte Carlo sampling technique, local average discretization of random field and trigonometric series representation of stochastic processes are used to describe random variables, random fields, random processes. These random fields or random processes vary with spatial position and temporal course in aspects of means, variances, correlated lengths and power spectral densities.FEM governing equations analyzing linear elastic, elastoplastic, static, dynamic and geometric nonlinear problems are introduced. Then, based on the solving method of linear SFEM equations by Neumann series, the solving method of nonlinear SFEM equations by Neumann expansion combined with increment-solving technique step by step is presented. This method can be used to solve both linear and nonlinear static and dynamic problems. Astringency of Neumann series expansion to solve nonlinear problems is proved and a method to improve the convergence and enhance efficiency is presented. Examples show that the method has higher accuracy and application potential.2. Structural reliabilityIt is necessary to solve the integral equations with moment constraints of random variables in maximum entropy method of reliability analysis. These equations aresevere nonlinear and their solutions cannot be obtained by common solving methods of nonlinear equations. Cognate method is introduced effectively to solve them. The solutions obtained by maximum entropy method are consistent with corresponding theoretic distribution, which shows maximum entropy method is a sort of good method for reliability analysis.Based on the extreme transform method and first-cross reliability, dynamic reliability of structures is analyzed. Compared with Monte Carlo method, the two methods have good accuracy and efficiency.System reliability analysis methods are investigated for structures in series, parallel, and series-parallel. Among them, the extreme value transform method is presented to cut down the dimension of distribution function. Monte Carlo method is proposed to solve the integral of the multi-dimension probabilistic density function, and related example shows that the method leads to good accuracy and efficiency. Truncated enumeration method (TEM) is presented to identify primary failure modes, which seriously affect system reliability, and to reduce computational amount. Affects of correlated lengths of random fields are investigated. It is emphasized that reliability of general structu...
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