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We consider a linearly thermoelastic composite medium,which consists of ahomogeneous matrix containing a statistically inhomogeneous random set ofinclusions, when the concentration of the inclusions is a function of thecoordinates (so-called Functionally Graded Materials). The composite medium issubjected to essentially inhomogeneous loading by the fields of the stresses,temperature and body forces (e.g. for a centrifugal load). The general integralequations connecting the stress and strain fields in the point being consideredand the surrounding points are obtained for the random fields of inclusions.The method is based on a centering procedure of subtraction from both sides ofa known initial integral equation their statistical averages obtained withoutany auxiliary assumptions such as, e.g., effective field hypothesis implicitlyexploited in the known centering methods. In so doing the size of a regionincluding the inclusions acting on a separate one is finite, i.e. the localityprinciple takes place.

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