SINGULAR APPROXIMATION OF THE METHOD OF PERIODIC COMPONENTS IN STATISTICAL-MECHANICS OF COMPOSITE-MATERIALS

A quasi-periodic model is developed for random structures of composite s, when the locations of inclusions are given in terms of random devia tions from nodes of an ideal periodic lattice. Solution of the stochas tic boundary problem of the theory of elasticity is examined for a qua si-periodic component by the method of periodic components, which if r educed to determination of the field of deviations from the known solu tion for ct corresponding periodic composite. The solution is presente d for the tensor elf effective elastic properties of a quasi-periodic composite in singular approximation of the method of periodic componen ts in terms of familiar solutions for tensors of the effective elastic properties of composites with periodic and chaotic structures and the parameters of the quasi-periodic structure: the coefficient of period icity and the tensor of the anisotropy of inclusion disorder. A numeri cal calculation is performed for the effective transversally isotropic elastic properties of unidirectional fibrous composites with differen t degrees of fiber disorder.