Uncertainty analysis of elastostatic problems incorporating a new hybrid stochastic-spectral finite element method

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 both methods for analysis of stochastically linear elastostatic problems. Moreover, a spectral finite element method is proposed for numerical solution of a Fredholm integral equation followed by the present method, to provide further efficiencies to accelerate stochastic computations. Numerical examples indicate the efficiency and accuracy of the proposed method.