Elastostatic solutions of a multilayered transversely isotropic piezoelectric system under axisymmetric loading

Abstract

The precise integration algorithm (PIA) and the technique of dual vector formulation are extended to explore the axisymmetric response of multilayered transversely isotropic piezoelectric materials under the action of external forces. The planes of cross-anisotropy are assumed to be parallel to the horizontal surface. The mechanical and electrical loads distributed over a circular area can be applied either on the surface of the layered system or at the interface between neighboring layers with dissimilar materials. By means of the Hankel integral transformation and the approach of dual vector form, the governing partial differential equations are reduced to the standard ordinary differential matrix equation. The PIA is exploited to evaluate the first-order ordinary differential matrix equation in the transformed domain. As the PIA is a highly accurate algorithm, any desired accuracy of axisymmetric piezoelectric solutions can be accomplished. The whole calculation is based on standard matrix algebra, and computational effort can be saved to a great extent. Furthermore, dual vector forms of key equations can facilitate the combination of adjacent strata. Finally, several numerical examples are given to validate the accuracy of the proposed technique and to investigate the influence of loading positions, types of external forces, stratified characters, and weak and thin interlayer on the response of the layered piezoelectric medium.