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The stochastic perturbation - based finite volume method for 1 & 2D fluid and heat flow problems

Kamiński M., Ossowski R. L.

Mechanics and Mechanical Engineering

2010

Vol. 14, nr 1

151-173

This article is devoted to the mathematical formulation and computational implementation of the Stochastic Finite Volume Method for 1 and 2D fluid and heat flow problems. It is based on the stochastic generalized perturbation technique, which allows for a determination of the probabilistic moments of the state variables or functions for the general stationary transport equations with random parameters. Both numerical case studies contain a comparison of the stochastic perturbation approach of different orders, their relations to the Monte-Carlo simulation results as well as the effect of the perturbation parameter and input coefficient of variation on the output state functions.

Eigenvalue analysis for high telecommunication towers with lognormal stiffness by the response function method and SFEM

Kamiński M. M., Szafran J.

Computer Assisted Mechanics and Engineering Sciences

2009

Vol. 16, No. 3/4

279-290

The main aim of this paper is to demonstrate the application of the generalized stochastic perturbation techniąue to model the lognormal random variables in structural mechanics. This is done to study probabilistic characteristics of the eigenvibrations for the high telecommunication towers with random stiffness, which are modeled as the linear elastic 3D trusses. The generalized perturbation technique based on the Taylor expansion is implemented using the Stochastic Finite Element Method in its Response Function version. The main difficulty here, in a comparison to this techniąue previous applications, is a necessity of both odd and even order terms inclusion in all the Taylor expansions. The hybrid numerical approach combines the traditional FEM advantages with the symbolic computing and its visualization power and it enables for a verification of probabilistic convergence of the entire computational procedure.