Analyses of functionally graded plates with a magnetoelectroelastic layer

A meshless local Petrov–Galerkin (MLPG) method is presented for the analysis of functionally graded material (FGM) plates with a sensor/actuator magnetoelectroelastic layer localized on the top surface of the plate. The Reissner–Mindlin shear deformation theory is applied to describe the plate bending problem. The expressions for the bending moment, shear force and normal force are obtained by integration through the FGM plate and magnetoelectric layer for the corresponding constitutive equations. Then, the original three-dimensional (3D) thick-plate problem is reduced to a two-dimensional (2D) problem. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding the node. The weak-form on small subdomains with a Heaviside step function as the test function is applied to derive local integral equations. After performing the spatial MLS approximation, a system of ordinary differential equations of the second order for certain nodal unknowns is obtained. The derived ordinary differential equations are solved by the Houbolt finite-difference scheme. Pure mechanical loads or electromagnetic potentials are prescribed on the top of the layered plate. Both stationary and transient dynamic loads are analyzed. (paper)