Semi-analytical analysis of static and dynamic responses for laminated magneto-electro-elastic plates

The scaled boundary finite element method (SBFEM) incorporated with the precise integration technique (PIT) is further extended to present the semi-analytical analysis of static bending and free vibration behaviors of laminated magneto-electro-elastic composite plates. It is applicable to thin and thick multilayered magneto-electro-elastic plates. The basic equations are formulated by only using the two dimensional model, which helps to make sure that the computation is efficient. The discretization is carried out in terms of spectral elements. Only three displacement components, electric and magnetic potentials are selected as the basic variables. Characterized by the important features of the SBFEM, the elastic displacements, electric and magnetic potentials along the thickness direction can be solved analytically. Differing from most plate models taking a priori assumptions on distributions of the mechanical, electric and magnetic variables, the derivation of governing SBFEM equations strictly follows the 3D theory of magneto-electro-elastic materials without introducing any assumptions on multiphysics fields. By virtue of the scaled boundary coordinates and the principle of virtual work, the key partial differential equations are simplified into the governing ordinary differential matrix equation. To increase the accuracy of the SBFEM governing equation, the PIT is utilized, which ensures that any desired accuracy of the results can be reached. Static and dynamic numerical examples show that variations of mechanical, electric, magnetic fields and natural frequencies predicted by the proposed approach are in excellent agreement with the elastic solutions of other methods. Therefore, the versatility and perfect accuracy of the present technique is fully validated. Furthermore, the influences of aspect ratios, boundary conditions and stacking sequences on the cross-thickness distributions of displacements, stresses, electric potential, electric displacements, magnetic potential, magnetic induction and vibration frequencies in the multilayered magneto-electro-elastic plate are discussed.