Asymptotic Construction of a Generalized Reissner-Mindlin Model for Multilayer Piezoelectric Plates

The variational asymptotic method is used to construct a generalized Reissner-Mindlin model for multilayer piezoelectric plates with faces surfaces or other surfaces parallel to the reference surface coated with electrodes. Without invoking a priori kinematic assumptions, we asymptotically split the original three-dimensional electromechanical problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The through-the-thickness analysis is implemented using the finite element method into the computer program VAPAS (Variational Asymptotic Plate and Shell Analysis). The resulting model is as simple as an equivalent single-layer, first-order shear deformation theory with accuracy comparable to higher-order layerwise theories. Numerical results of cylindrical bending problems for piezoelectric plates have been compared with 3D exact solutions to validate the present model.