Journal ArticleDOI
Stochastic finite element analysis of simple beams
TLDR
In this paper, a stochastic finite element analysis method was developed for solving a variety of engineering mechanics problems in which physical properties exhibit one-dimensional spatial random variation, illustrated by evaluating the second-order statistics of the deflection of a beam whose rigidity varies randomly along its axis.Abstract:
A method of stochastic finite element analysis is developed for solving a variety of engineering mechanics problems in which physical properties exhibit one-dimensional spatial random variation. The method is illustrated by evaluating the second-order statistics of the deflection of a beam whose rigidity varies randomly along its axis. A key component of the approach is a new treatment of the correlation structure of the random material property in terms of the variance function and its principal parameter, the scale of fluctuation. The methodology permits efficient evaluation of the matrix of covariances between local spatial averages associated with pairs of finite elements. Numerical results are presented for a cantilever beam, with deformation controlled by shear, subjected to a concentrated force at its free end or to a uniformly distributed load.read more
Citations
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Journal ArticleDOI
The stochastic finite element method: Past, present and future
TL;DR: A state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future are provided.
Journal ArticleDOI
Optimal discretization of random fields
Chun-Ching Li,A. Der Kiureghian +1 more
TL;DR: The new method is found to be more efficient than other existing discretization methods, and more practical than a series expansion method employing the Karhunen‐Loeve theorem, and particularly useful for stochastic finite element studies involving random media.
Book ChapterDOI
The stochastic finite element method in structural reliability
Armen Der Kiureghian,Jyh-Bin Ke +1 more
TL;DR: In this article, first-order reliability and finite element methods are used to develop a methodology for reliability analysis of structures with stochastically varying properties and subjected to random loads, and the influence of the correlation length of random property or load fields on the reliability of example structures are investigated.
Journal ArticleDOI
A nonparametric model of random uncertainties for reduced matrix models in structural dynamics
TL;DR: In this paper, a nonparametric model of the generalized mass, damping and stiffness matrices is proposed, which does not require identifying the uncertain local parameters and obviates construction of functions that map the domains of uncertain local parameter vectors into the generalized matrix.
Journal ArticleDOI
Stochastic Finite Element Expansion for Random Media
Pol D. Spanos,Roger Ghanem +1 more
TL;DR: In this paper, a new method for the solution of problems involving material variability is proposed, which makes use of the Karhunen-Loeve expansion to represent the random material property.
References
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Journal ArticleDOI
Fractional Brownian Motions, Fractional Noises and Applications
Book
The Fourier Transform and Its Applications
TL;DR: In this paper, the authors provide a broad overview of Fourier Transform and its relation with the FFT and the Hartley Transform, as well as the Laplace Transform and the Laplacian Transform.
Journal ArticleDOI
The Fourier Transform and Its Applications
Journal ArticleDOI
On stationary processes in the plane
TL;DR: The sampling theory of stationary processes in space is not completely analogous to that of stationary time series, due to the fact that the variate of a time series is influenced only by past values, while for a spatial process dependence extends in all directions as mentioned in this paper.