High order solutions for the magneto-electro-elastic plate with non-uniform materials

In the frame of the scaled boundary finite element method (SBFEM), deformations of the magneto-electro-elastic plate with non-uniform materials are solved in this paper. There are no limitations of shapes and kinds of materials of the plate. At the same time, three different types of external loadings are prescribed at the top plane. Starting with the governing equations of equilibrium and the constitutive equations of magneto-electro-elastic materials, and based on the scaled boundary coordinates, the 3D key partial differential equations are converted into the ordinary differential equations without enforcing the kinematics of plate theory. Only the in-plane dimensions of the plate are divided into 2D finite element, which contributes to reducing the space dimension by one. Moreover, making use of the high order spectral element can produce lumped coefficient matrices, which is helpful to acquire high accuracy and efficiency. The elastic displacements, electric potential and magnetic potential in the vertical direction are solved analytically. The analytical solutions are expressed as a matrix exponent in terms of the thickness which is calculated by the Padé expansion. Finally, several numerical examples are provided to demonstrate the accuracy of the proposed solutions and to display the influence of material partition and loading types on the response of the magneto-electro-elastic plate.