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Recent Developments in Stochastic Finite Elements
Several recent developments in the stochastic finite element method are reviewed. Topics addressed include: the modeling and discretization of random fields, the weighted integral approach, computation of response gradients, and reliability analysis of components and systems by the first and second-order reliability methods (FORM and SORM).
A. Der Kiureghian, C.-C. Li, Y. Zhang
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Choice of input fields in stochastic finite elements
The problem of the arbitrary choice of variables for random field modelling in structural mechanics or in soil mechanics is treated. For example, it is relevant to ask the question of whether it is best to choose a stiffness field along a beam element or
Ove Ditlevsen
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Stochastic perturbation finite elements
Computers & Structures, 1996This paper extends the stochastic perturbation method to vector-valued and matrix-valued functions. The numerical method for the response and reliability of uncertain structures is formulated using matrix calculus, Kronecker algebra and perturbation theory.
Zhang, Yimin +3 more
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Practical Application of the Stochastic Finite Element Method
Archives of Computational Methods in Engineering, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arregui-Mena, José David +2 more
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Behavior of a single element in a finite stochastic array
Physical Review E, 2012We describe statistical properties of a single element in a nonlinear stochastic array with a finite number of elements with mean-field-like (global) coupling. Desai and Zwanzig [J. Stat. Phys. 19, 1 (1978)] made use of a self-consistent dynamic mean-field ansatz to derive, in the infinite-size limit, a nonlinear Fokker-Planck equation (NLFPE) for the ...
José, Gómez-Ordóñez +2 more
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Stochastic Finite Elements: A Spectral Approach
Roger G. Ghanem, Pol D. Spanos
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The stochastic finite-element method
Computers & Structures, 1980Abstract A generic stochastic finite-element method for modeling structures is proposed as a means to analyze and design structures in a probabilistic framework. Stochastic differential and difference equation theory is applied in structures discretized with the finite-element methodology.Transient structural loads, idealized as stochastic processes,
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Spectral techniques for stochastic finite elements
Archives of Computational Methods in Engineering, 1997A formulation for the stochastic finite element method is presented which is a natural extension of the deterministic finite element method. Discretization of the random dimension is achieved via two spectral expansions. One of them is used to represent the coefficients of the differential, equation which model the random material properties, the other
R. G. Ghanem, P. D. Spanos
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Polynomial Chaos in Stochastic Finite Elements
Journal of Applied Mechanics, 1990A new method for the solution of problems involving material variability is proposed. The material property is modeled as a stochastic process. The method makes use of a convergent orthogonal expansion of the process. The solution process is viewed as an element in the Hilbert space of random functions, in which a sequence of projection operators is ...
Roger Ghanem, P. D. Spanos
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