Journal ArticleDOI
Stochastic Finite-Element Analysis of Soil Layers with Random Interface
Roger Ghanem,W. Brzakala +1 more
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TLDR
In this paper, the problem of a medium with two layers separated by an interface randomly fluctuating in space was formulated using the second-moments characteristics of the interface spatial fluctuations, and the Karhunen-Loeve and polynomial chaos expansions were used to transform the problem into a computationally tractable form.Abstract:
This paper addresses the problem of a medium with two layers separated by an interface randomly fluctuating in space. The medium is subjected to an in-plane strain field simulating the effect of a surface foundation. The second-moments characteristics of the interface spatial fluctuations are used to formulate the problem. The Karhunen-Loeve and the polynomial chaos expansions are utilized to transform the problem into a computationally tractable form, thus resulting in a system of linear algebraic equations to solve. The difficulty in this problem stems from the geometric nature of the randomness, resulting in a stiffness matrix that is nonlinear in the randomness. This leads to a nonlinear stochastic problem, the solution of which is accomplished by relying on the polynomial chaos representation of stochastic processes.read more
Citations
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Ingredients for a general purpose stochastic finite elements implementation
TL;DR: This paper presents the main ingredients for developing a general purpose version of the Spectral Stochastic Finite Element Method.
Journal ArticleDOI
Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements
TL;DR: In this paper, the main sources of uncertainties involved in the analysis of structures and solids are discussed and the tools available to deal with them, as well as the techniques and methods involved in stochastic modeling.
Journal ArticleDOI
Comparison of finite element reliability methods
TL;DR: In this article, the spectral stochastic finite element method (SSFEM) is considered in conjunction with the first-order reliability method (FORM) and with importance sampling for finite element reliability analysis.
Journal ArticleDOI
Stochastic Finite Elements with Multiple Random Non-Gaussian Properties
TL;DR: In this paper, the spectral stochastic finite element method is applied to the problem of heat conduction in a random medium, where the conductivity of the medium and its heat capacity are treated as uncorrelated random processes with spatial random fluctuations.
Journal ArticleDOI
Probabilistic characterization of transport in heterogeneous media
TL;DR: In this article, the hydraulic properties of a random porous medium are modeled as spatial random processes and the concentrations over the whole domain are also random processes, with unknown probabilistic structure.
References
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Journal ArticleDOI
Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations
TL;DR: The first part of the memoir is devoted to the definition of various terms employed, and to the re-statement of the consequences which follow from Hilbert's theorem as discussed by the authors, with a discussion of the properties of functions belonging to the wider classes.
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The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals
R. H. Cameron,W. T. Martin +1 more
TL;DR: In this paper, Kaczmarz and Steinhaus [I, pp. 143-144] showed that the equality W 1~~~~~~~~~~~~ |G a, ot(t) dx(t), *,Iap(t)-dx(t)] dwx (2.5) c 00 -p/2 L G(ui, *, up)euhu du,... du.
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Simulation of Stochastic Processes by Spectral Representation
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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.
Journal ArticleDOI
Polynomial Chaos in Stochastic Finite Elements
Roger Ghanem,Pol D. Spanos +1 more
TL;DR: In this article, a new method for the solution of problems involving material variability is proposed, where the material property is modeled as a stochastic process and the solution process is represented by its projections onto the spaces spanned by these polynomials.