Solutions for the magneto-electro-elastic plate using the scaled boundary finite element method

A semi-analytical technique based on the elastic theory is employed to study the deformation of a magneto-electro-elastic plate. Solutions are acquired by applying the scaled boundary finite element method (SBFEM), which requires the discretization of the boundary as in the boundary element method but does not need a fundamental solution. In the whole process, the detailed derivation is based on the three-dimensional governing equation. With the aid of the scaled boundary coordinates, the 3D key partial differential equation is converted into the ordinary differential equation. Only the in-plane dimensions are needed to be discretized, which contributes to reducing the computational effort. Furthermore, utilizing the high order spectral element can do good to obtain high accuracy and efficiency. The components of the magneto-electro-elastic field are solved numerically in the in-plane direction and analytically in the thickness direction. Solutions along the vertical direction are formulated as a matrix exponent which is solved by the Padé series expansion of order (2,2)(2,2). Comparisons with the numerical examples are provided to validate the proposed solutions. Meanwhile, other examples are carried out to demonstrate the versatility of the present method.