On stochastic finite element method for linear elastostatics by the Taylor expansion

The main aim of the paper is to present an application of the Taylor expansion in formulation and computational implementation of the perturbation-based stochastic finite element method. Random-input parameters as well as all-state functions included in static equilibrium equations are expanded in this approach around their expectations via Taylor series up the order given a priori. It further enables a dual computational approach for determination of probabilistic moments of the state functions—a formation and the solution of increasing order equilibrium equations and, on the other hand, polynomial approximation of deterministic state functions with respect to a given input random parameter. Theoretical and technical details of such methodology are explained also; some elementary engineering application with analytical solution is available to derive explicitly fundamental probabilistic moments of the resulting state function.