Exact solution for functionally graded and layered magneto-electro-elastic plates

Abstract

In this paper, an exact solution is presented for the multilayered rectangular plate made of functionally graded, anisotropic, and linear magneto-electro-elastic materials. While the edges of the plate are under simply supported conditions, general mechanical, electric and magnetic boundary conditions can be applied on both the top and bottom surfaces of the plate. The functionally graded material is assumed to be exponential in the thickness direction and the homogeneous solution in each layer is obtained based on the pseudo-Stroh formalism. For multilayered plate structure, the propagator matrix method is employed so that only a 5 × 5 system of linear algebraic equations needs to be solved. The exact solution is then applied to two functionally graded (exponential) sandwich plates made of piezoelectric BaTiO 3 and magnetostrictive CoFe 2O 4, under mechanical and electric loads on the top surface. While the numerical results clearly show the influence of the exponential factor, magneto-electro-elastic properties, and loading types on induced magneto-electric-elastic fields, they can also serve as benchmarks to numerical methods such as the finite and boundary element methods.