Laminated elastic plates with piezoelectric sensors and actuators

A meshless local Petrov-Galerkin (MLPG) method is applied to solve laminate piezoelectric plates described by the Reissner-Mindlin theory. The piezoelectric layer can be used as a sensor or actuator. A pure mechanical load or electric potential are prescribed on the top of the laminated plate. Both stationary and transient dynamic loads are analyzed here. The bending moment, the shear force and normal force expressions are obtained by integration through the laminated plate for the considered constitutive equations in each lamina. Then, the original threedimensional (3-D) thick plate problem is reduced to a two-dimensional (2-D) problem. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding this node. The weak-form on small subdomains with a Heaviside step function as the test functions 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 as a time-stepping method.