Piezolaminated plates – Highly accurate solutions based on the extended Kantorovich method

Piezoelectric materials become more and more common in various industrial applications, which can be simulated as a piezoelectric plate. An exact mathematical solution solving flexural behavior of a rectangular plate can be achieved, based on the Levy method, only when two parallel edges of the plate are simply supported. For any other combinations of boundary conditions, it becomes necessary to turn to one of the available approximate solutions, such as energy methods, and finite elements. In this paper, we present an original model that can be used to predict the flexural behavior of piezoelectric plates on various boundary conditions. The analytical solution is based on the extended Kantorovich iterative procedure. The differential equations for the iterative procedure are derived using the Galerkin method. The solution was developed based on the classical plate’s theory (CLPT), and for this reason, it is limited only for the solution of extension type piezoelectric mechanism. This iterative procedure yields highly accurate solutions, which were compared against other available analytical results.