A stochastic-spectral finite element method applied to the analysis of stochastic structural mechanics problems

In this article, stochastic finite element and spectral finite element methods are combined as a new hybridized numerical method for uncertainty quantification. A popular version of stochastic finite element method is used for the combination. In the other hand, 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 desirable accuracy, and much less domain discretization with excellent convergence. The proposed method of this study is a hybrid method utilizing efficiencies of both methods for analysis of stochastically linear elastostatic problems. Additionally, spectral finite element is utilized fornumerical solution of Fredholm integral equation followed by the proposed numerical method, one which increases the efficiencies. Numerical examples demonstrate abilities of the proposed method

Keywords:

Karhunen–Loève expansion , Polynomial chaos expansion , Stochastic finite element method , Spectral finite element method , Stochastic structural analysis