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International Journal for Multiscale Computational Engineering

Impact factor: 0.768

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v9.i3.20
pages 257-270

HOMOGENIZATION OF FIBER-REINFORCED COMPOSITES WITH RANDOM PROPERTIES USING THE LEAST-SQUARES RESPONSE FUNCTION APPROACH

Marcin Kaminski
Faculty of Civil Engineering, Architecture and Environmental Engineering, Technical University of Lodz, Poland

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.