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A Fourier–Karhunen–Loève discretization scheme for stationary random material properties in SFEM / Li C. F, Y. T Feng, D. R. J Owen, Li D. F, I. M Davis, Ian Davies, Yuntian Feng, Chenfeng Li, Roger Owen
International Journal for Numerical Methods in Engineering, Volume: 73, Issue: 13, Pages: 1942 - 1965
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In the numerical modelling of a physical system involving random media, the firstkey step is usually to represent, with a finite set of deterministic primary functions andrandom variables, the associated stochastic field (e.g. random Young’s modulus andrandom Poisson’s ratio) which is often defined...
|Published in:||International Journal for Numerical Methods in Engineering|
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In the numerical modelling of a physical system involving random media, the firstkey step is usually to represent, with a finite set of deterministic primary functions andrandom variables, the associated stochastic field (e.g. random Young’s modulus andrandom Poisson’s ratio) which is often defined by its statistical moments. In this paper,an efficient and accurate method is presented to represent a stochastic field given by itsexpectation and covariance functions. Based on the Karhunen-Loève expansion, thismethod represents stochastic fields in terms of multiple Fourier series and a vector ofmutually uncorrelated random variables. The result can be treated as a semi-analyticsolution of the Karhunen-Loève expansion, which is achieved by minimizing themean-squared error of the characteristic equation and solving a standard algebraiceigenvalue problem. To verify the proposed method, exponential covariance functionswith exact Karhunen-Loève expansion solutions are employed and good agreementsare observed on both eigenvalues and eigenfunctions. Representations of stochasticfields with Gaussian covariance functions are also performed to demonstrate theeffectiveness and robustness. As no meshing is required in this method, its efficiencyand accuracy are not sensitive to the dimensions or the correlation distance of thestochastic field under consideration.
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