Published 6 issues per year
ISSN Print: 1543-1649
ISSN Online: 1940-4352
Indexed in
HOMOGENIZATION OF FIBER-REINFORCED COMPOSITES WITH RANDOM PROPERTIES USING THE LEAST-SQUARES RESPONSE FUNCTION APPROACH
ABSTRACT
The main issue in this elaboration is computational study of the homogenized elasticity tensor for the periodic random composite using the improved stochastic generalized perturbation technique. The uncertainty of the composite appears at the component's material properties, treated here as the Gaussian random variables, while its micro- and macrogeometry remains perfectly periodic. The effective modules method consisting in the cell problem solution is enriched with the generalized stochastic perturbation method. This method is implemented without the necessity of a large number of increasing order equations. The response function between the homogenized tensor and the input random parameter is determined numerically using several deterministic solutions and the least-squares approximation technique. Since classical polynomial approximation techniques may result in some errors for the lower and upper bound of the input parameter variability set, the least-squares approximation is used, where the degree of an approximant is the additional input variable. This approach has hybrid computational implementation{partially in the homogenization-oriented finite element method code MCCEFF and in the symbolic environment of the MAPLE 13 system, giving a wide range of approximation techniques that can also be modified in a graphical mode.
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References, in The Stochastic Perturbation Method for Computational Mechanics, 2013. Crossref
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Pivovarov Dmytro, Zabihyan Reza, Mergheim Julia, Willner Kai, Steinmann Paul, On periodic boundary conditions and ergodicity in computational homogenization of heterogeneous materials with random microstructure, Computer Methods in Applied Mechanics and Engineering, 357, 2019. Crossref