RT Journal Article ID 5f7551423658d1cc A1 Tashkinov, M. A. A1 Vil'deman, V. E. A1 Mikhailova, N. V. T1 METHOD OF SUCCESSIVE APPROXIMATIONS IN A STOCHASTIC BOUNDARY-VALUE PROBLEM IN THE ELASTICITY THEORY OF STRUCTURALLY HETEROGENEOUS MEDIA JF Composites: Mechanics, Computations, Applications: An International Journal JO CMCA YR 2011 FD 2011-05-06 VO 2 IS 1 SP 21 OP 37 K1 composite materials K1 boundary-value problem K1 stochastic structure K1 moment functions K1 stress and deformation fields K1 Green function K1 successive approximations AB This work deals with a problem of calculation of micro stress and micro deformation in matrix composites with random inclusions over the volume. A stochastic structure of composites is described by a set of multipoint moment functions that are used for searching the statistical characteristics of deformation fields. The boundary-value problem is reduced to the integral differential equation relative to pulsations of displacements. The problem solution is searched in second approximation. Analytical expressions are obtained for calculation of statistical characteristics of stress and deformation fields, and numerical results of calculation of average quantities for a partial case of a macroheterogeneous stressed-strained state − pure shear − are presented. PB Begell House LK https://www.dl.begellhouse.com/journals/36ff4a142dec9609,1c07ee685480b68d,5f7551423658d1cc.html