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چکیده
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This article aims to present a combination of stochastic finite element and spectral finite element methods as a new numerical tool for uncertainty quantification. One of the well-established numerical methods for reliability analysis of engineering systems is the stochastic finite element method. In this article, a commonly used version of the stochastic finite element method is combined with the spectral finite element method. Furthermore, the spectral finite element method is a numerical method employing special orthogonal polynomials (e.g., Lobatto) and quadrature schemes (e.g., Gauss-Lobatto-Legendre), leading to suitable accuracy, and much less domain discretization with excellent convergence as well. The proposed method of this article is a hybrid method utilizing efficiencies of bothmethods for analysis of stochastically linear elastostatic problems.Moreover, a spectral finite elementmethod is proposed for numerical solution of a Fredholm integral equation followed by the presentmethod, to provide further efficiencies to accelerate stochastic computations.Numerical examples indicate the efficiency and accuracy of the proposed method.
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