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We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of inclusions, when the concentration of the inclusions is a function of the coordinates (so-called functionally graded materials). The composite medium is subjected to essentially inhomogeneous loading by the fields of the stresses, temperature, and body forces (e.g. for a centrifugal load). The general integral equations connecting the stress and strain fields in the point being considered and the surrounding points are obtained for the random fields of inclusions. The method is based on a centering procedure of subtraction from both sides of a known initial integral equation their statistical averages obtained without any auxiliary assumptions, such as effective field hypothesis implicitly exploited in the known centering methods. In so doing the size of a region including the inclusions acting on a separate one is finite, i.e. the locality principle takes place.

On the thermo-elastostatics of heterogeneous materials: I. General integral equation