Uncertainty inherently exists in quantity of a system’s parameters (e.g., loading or elastic modulus of a structure), and thus its effects have always been considered as an important issue for engineers. Meanwhile, numerical methods play significant role in stochastic computational mechanics, particularly for the problems without analytical solutions. In this article, spectral finite element method is utilized for stochastic spectral finite element analysis of 2D continua considering material uncertainties. Here, Lobatto family of higher order spectral elements is extended, and then influence of mesh configuration and order of interpolation functions are evaluated. Furthermore, Fredholm integral equation due to Karhunen Loève expansion is numerically solved through spectral finite element method such that different meshes and interpolation functions’ orders are also chosen for comparison and assessment of numerical solutions solved for this equation. This method needs fewer elements compared to the classic finite element method, and it is specifically useful in dynamic analysis as supplies desirable accuracy with having diagonal mass matrix. Also, these spectral elements accelerate the computation process along with Karhunen Loève and polynomial chaos expansions involving numerical solution of Fredholm integral equation. This research examines elastostatic and elastodynamic benchmark problems to demonstrate the effects of the undertaken parameters on accuracy of the stochastic analysis. Moreover, results demonstrate the effects of higher-order spectral elements on speed, accuracy and efficiency of static and dynamic analysis of continua.

Keywords: Spectral finite element, Stochastic mechanics, Polynomial chaos, Karhunen Loève expansion, Lobatto interpolation function

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