Theoretical analysis of in-plane problem in functionally graded nonhomogeneous magnetoelectroelastic bimaterials

By using the Fourier-transform technique, the two-dimensional full-field solutions of transversely isotropic functionally graded magnetoelectroelastic bimaterials subjected to generalized line forces and edge dislocations are presented in this study. For the nonhomogeneous problem, the mathematical derivation is much complicated than the homogeneous case since the material properties vary with coordinate. From the framework of the generalized stress function approach, only the generalized strain compatibility equations needed to be satisfied. A powerful analytical method is developed to solve the functionally graded magnetoelectroelastic planar problem. For the special case of the nonhomogeneous bimaterial with continuous material properties at the interface, it is shown in this study that all magnetoelectroelastic fields are continuous at the interface. Furthermore, this functionally graded bimaterial has the identical contour slopes for the generalized stresses (except for σxx(j)) across the interface. For the computational results, the full-field distributions of generalized stresses and strains in the nonhomogeneous bimaterial subjected to line forces or edge dislocations are presented with different functionally graded parameters.