On the treatment of uncertainties in structural mechanics and analysis
Computers and Structures
Generalized perturbation-based stochastic finite element method in elastostatics
Computers and Structures
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Generalized stochastic finite element method in elastic stability problems
Computers and Structures
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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.