Semi-analytical solutions for three-dimensional problems of multi-directional functionally graded magneto-electro-elastic circular plates

This chapter presents semi-analytical solutions for three-dimensional problems of multi-directional functionally graded magnetoelectroelastic circular plates under various boundary conditions. The semi-analytical approach combines the state space method, the differential quadrature method and the Fourier series expansion to give the solution. In the thickness direction of the plate the state space method which takes unknown displacement components, electric potential, magnetic potential and their first order derivatives as the state variables is employed to obtain the analytical solution. For the in-plane domain differential quadrature method is adopted in the radial direction to give the approximate solution while the Fourier series expansion is used in the circumferential direction of plates to separate variables. The proposed semi-analytical method is validated and the superiority of the method is also illustrated. Three-dimensional static and dynamic behavior of multi-directional functionally graded magnetoelectroelastic plates is investigated under various boundary conditions by using the semi-analytical method. And the influence of the graded variation of material constants is illuminated.