Exact solution for the bending deformations of layered magneto-electro-elastic laminates based on thin-plate formulation

Mei-Feng Liu

In this paper, a rather compact differential equation governing the bending behavior of a magneto-electro-elastic (MEE) rectangular thin plate is introduced, in particular, the exact solutions for the deformation response of laminated BaTiO3-CoFe2O4 composites subjected to certain types of surface loads are analytically obtained. Due to the omission of the transverse shear deformation and rotatory inertia assumed in Kirchhoff thin-plate theory, the governing equation can accordingly be expressed in terms of the transverse displacement only. As a result, the structural characteristics such as elastic displacements, electric potential and magnetic induction for a magneto-electro-elastic (MEE) rectangular plate can be carried out in a theoretical approach. For a laminate MEE composite, the material constants can be uniquely determined by the volume-fraction (v.f.) of the piezoelectric constituent BaTiO3, and are tabulated with 25% offset of the volume-fraction. According to the specified boundary conditions imposed on the MEE thin plate, the deformation variations with closed-circuit electric restriction are evaluated analytically in the present study. The results obtained in this paper by using the proposed model can be shown to have good agreements with the other available research works, however, with the advantage that the present study indeed provides a much simpler way in seeking the analytic solutions for the interactively coupled quantities of a layered MEE medium.