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• W2101505636 startingPage "1804" @default.
• W2101505636 abstract "The stochastic finite element analysis of elliptic type partial differential equations with non-Gaussian random fields are considered. A novel approach by projecting the solution of the discretized equation into a reduced finite dimensional orthonormal vector basis is investigated. It is shown that the solution can be obtained using a finite series comprising functions of random variables and orthonormal vectors. These functions, called as the spectral functions, can be expressed in terms of the spectral properties of the deterministic coefficient matrices arising due to the discretization of the governing partial differential equation. Based on the projection in a reduced orthonormal vector basis, a Galerkin error minimization approach is proposed. The constants appearing in the Galerkin method are solved from a system of linear equations which has much smaller dimension compared to the original discretized equation. A hybrid analytical and simulation based computational approach is proposed to obtain the moments and probability density function of the solution. The method is illustrated using the stochastic nanomechanics of a zinc oxide (ZnO) nanowire deflected under the atomic force microscope (AFM) tip. The results are compared with the results obtained using direct Monte Carlo simulation, classical Neumann expansion and polynomial chaos approach for different correlation lengths and strengths of randomness." @default.
• W2101505636 created "2016-06-24" @default.
• W2101505636 creator A5007121098 @default.
• W2101505636 date "2011-05-01" @default.
• W2101505636 modified "2023-10-15" @default.
• W2101505636 title "A reduced spectral function approach for the stochastic finite element analysis" @default.
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• W2101505636 doi "https://doi.org/10.1016/j.cma.2011.01.015" @default.
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