Journal of Theoretical
and Applied Mechanics

47, 4, pp. 957-975, Warsaw 2009

A generalized version of the perturbation-based stochastic finite difference method for elastic beams

Marcin Kamiński
The main idea of this paper is to demonstrate a stochastic computational technique consisting of the generalized stochastic perturbation method using the Taylor expansions of random variables and the classical Finite Difference Method based on regular grids. As it is documented by computational illustrations, it is possible to determine, using this approach, also higher probabilistic moments for any random dispersion of input variables unlike in the second order second moment technique worked out before. A numerical algorithm is implemented here using straightforward partial differentiation of hierarchical equations with respect to the random input quantity and further symbolic computations of probabilistic moments and characteristics by the system MAPLE.
Keywords: stochastic perturbation technique; finite difference method; response function method; elastic Euler-Bernoulli beam; Winkler foundation