New formulations and methods for analyzing stochastic coupled boundary-value problems of electro-magnetic elasticity for composites with pieso-active structural elements are presented. Unique properties of pieso-composites with reciprocal polarization of oriented ellipsoidal inclusions and the matrix, layered structures with reciprocal polarization of the layers made of the PVF polymeric piezo-electric have been revealed. The magnetic-electrical effect of inducing an eclectic-motive force in the material under the action of a constant magnetic field for a composite containing piezo-electric and pieso-magnetic components has been investigated; if such a pieso-composite is placed in a magnetic field, the pieso-magnetic component will deform, and the pieso-electric component as well as the entire composite will deform too. Due to the deformation of the piezo-electric component, an electric field will be induced in the composite; on the macro-level, the electric field induction tensor will be coupled with the magnetic field stress vector through the tensor of effective magneto-electric constants. On the macro-level, the constitutive relations of the pieso-composite differ from those of the structural elements, in particular, by the presence of electro-magnetic coupling tensors. New solutions for coupled boundary-value problems of electro-magnetic elasticity in a generalized singular approximation of statistical mechanics of composites are presented, based on new solutions for singular components of the second derivatives of Green's function for a uniform transversal-isotropic piezo-electro-magnetic medium with an ellipsoid inclusion. New solutions for the tensors of effective magneto-electrical properties of a transversally-isotropic composite with a pieso-electric matrix and oriented pieso-magnetic ellipsoid inclusions are presented; in particular, magneto-electrical properties of a layered composite with alternating pieso-electric and pieso-magnetic layers have been determined. The results of the calculation of all the 20 independent constants of the effective transversally-isotropic elastic and pieso-magnetic properties of the PVF pieso-electric with pieso-magnetic ellipsoid inclusions are presented. In a particular case of a layered composite with alternating piezoelectric and piezo-magnetic layers the calculation results in the singular approximation of all the independent effective constants perfectly agree with the exact analytical solutions using the direct averaging of these constants.
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