Potential problems with random parameters by the generalized perturbation-based stochastic finite element method

The main aim of this paper is to present the new version and the application of the generalized nth order stochastic perturbation technique to the solution of the field problems with random coefficients. The variational stochastic nth order principles are proposed here using Taylor expansions with random parameters together with the additional stochastic finite element method discretization of the problem; a derivation of up to the fourth probabilistic moments and the coefficients of the potential function are also provided. The formulation is dual in the sense that both Direct Differentiation Method and the Response Function Method in its local version are proposed and implemented using the symbolic computer system MAPLE to determine numerically the random system response and to make the additional visualization. This methodology is illustrated with two examples – 1D viscous irrotational and incompressible fluid flow and 2D torsion of the prismatic rectangular beam with random transverse modulus.