In addition to the hexagonal crystals of class 6 mm, many piezoelectric materials （e.g., BaTiO3）, piezomagnetic materials （e.g., CoFe2O4）, and multiferroic com-posite materials （e.g., BaTiO3-CoFe2O4 composites） also exhibit symmetry of transverse isotropy after poling, with the isotropic plane perpendicular to the poling direction. In this paper, simple and elegant line-integral expressions are derived for extended displace-ments, extended stresses, self-energy, and interaction energy of arbitrarily shaped, three-dimensional （3D） dislocation loops with a constant extended Burgers vector in trans-versely isotropic magneto-electro-elastic （MEE） bimaterials （i.e., joined half-spaces）. The derived solutions can also be simply reduced to those expressions for piezoelectric, piezo-magnetic, or purely elastic materials. Several numerical examples are given to show both the multi-field coupling effect and the interface/surface effect in transversely isotropic MEE materials.
A three-dimensional size-dependent layered model for simply-supported and func- tionally graded magnetoelectroelastic plates is presented based on the modified couple-stress theory. The functionally graded material is assumed to be exponential in the thickness direc- tion of the plate. The final governing equations are reduced to an eigensystem by expressing the extended displacements in terms of two-dimensional Fourier series. Using the propagator matrix method, the exact solutions of the magnetic, electric and mechanical fields of sandwich nanoplates with couple-stress effect and under the surface loads are derived. Numerical examples for two functionally graded sandwich plates made of piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials are presented to demonstrate the effect of the functional gradient factor and material length-scale parameter on the induced fields. The exact solutions presented in this work can also serve as benchmarks to various numerical methods for analyzing the size-dependent features in layered systems.
