Journal ArticleDOI
On Random Field Discretization in Stochastic Finite Elements
B. A. Zeldin,Pol D. Spanos +1 more
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TLDR
The Volterra series representation of nonlinear input/output relationships is utilized to assess the effect of the random field discretization methods on the response variability of stochastic mechanics problems.Abstract:
Several traditional methods for discretizing random fields in stochastic mechanics applications are considered; they are the midpoint method, the interpolation method, and the local averaging method. A simple and computationally convenient criterion for estimating the accuracy of these discretization methods is developed. Also, the Volterra series representation of nonlinear input/output relationships is utilized to assess the effect of the random field discretization methods on the response variability of stochastic mechanics problems. The theoretical developments are elucidated by a numerical example involving a beam problem.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
A multiscale Monte Carlo finite element method for determining mechanical properties of polymer nanocomposites
Pol D. Spanos,Antonios Kontsos +1 more
TL;DR: In this paper, a multiscale Monte Carlo finite element method (MCFEM) was proposed for determining mechanical properties of polymer nanocomposites (PNC) that consist of polymers reinforced with single-walled carbon nanotubes (SWCNT).
Journal ArticleDOI
Response and eigenvalue analysis of stochastic finite element systems with multiple correlated material and geometric properties
Lori Graham,George Deodatis +1 more
TL;DR: In this article, the variability of the random response displacements and eigenvalues of structures with multiple uncertain material and geometric properties are studied using variability response functions, and the variance of the displacement/eigenvalue is expressed as the sum of integrals that involve the auto-spectral density functions characterizing the structural properties, the cross-spectrals density functions between structural properties and the deterministic response functions.
Journal ArticleDOI
Faster computation of the Karhunen-Loeve expansion using its domain independence property
Srikara Pranesh,Debraj Ghosh +1 more
TL;DR: In this article, the authors proposed a numerical integration based method for discretizing second-order stochastic processes with a known covariance function, which is a homogeneous Fredholm equation of second type, and showed that the shape of the physical domain in a random field does not affect the realizations of the field estimated using KL expansion.
Journal ArticleDOI
Wave propagation in one-dimensional waveguides with slowly varying random spatially correlated variability
TL;DR: In this article, structural wave propagation in waveguides with randomly varying material and geometrical properties along the axis of propagation is investigated, where the properties vary slowly enough such that there is no or negligible backscattering due to any changes in the propagation medium.
References
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Book
Stochastic Finite Elements: A Spectral Approach
Roger Ghanem,Pol D. Spanos +1 more
TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.
Journal Article
Spectral Analysis and Time Series
TL;DR: In this article, the authors introduce the concept of Stationary Random Processes and Spectral Analysis in the Time Domain and Frequency Domain, and present an analysis of Processes with Mixed Spectra.
Journal ArticleDOI
Random field finite elements
TL;DR: In this article, the probabilistic finite element method (PFEM) is formulated for linear and non-linear continua with inhomogeneous random fields, and the random field is also discretized.
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.