Techno Press
Techno Press

Structural Engineering and Mechanics   Volume 11, Number 4, April 2001, pages 373-392
Stochastic finite element method homogenization of heat conduction problem in fiber composites
Marcin Kaminski(Poland)

Abstract     [Full Text]
    The main idea behind the paper is to present two alternative methods of homogenization of
the heat conduction problem in composite materials, where the heat conductivity coefficients are assumed
to be random variables. These two methods are the Monte-Carlo simulation (MCS) technique and the second
order perturbation second probabilistic moment method, with its computational implementation known as
the Stochastic Finite Element Method (SFEM). From the mathematical point of view, the deterministic
homogenization method, being extended to probabilistic spaces, is based on the effective modules approach.
Numerical results obtained in the paper allow to compare MCS against the SFEM and, on the other hand,
to verify the sensitivity of effective heat conductivity probabilistic moments to the reinforcement ratio. These
computational studies are provided in the range of up to fourth order probabilistic moments of effective
conductivity coefficient and compared with probabilistic characteristics of the Voigt-Reuss bounds.
Key Words
    homogenization method; stochastic second order perturbation; stochastic finite element method; Monte-Carlo simulation; composites.
Marcin Kamioski, Division of Mechanics of Materials, Technical University of Lodo, Al. Politechniki 6, 93-590 Lodo, Poland

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