Three-dimensional solutions of multilayered piezoelectric hollow cylinders by an asymptotic approach

Three-dimensional (3D) solutions for the static analysis of multilayered piezoelectric hollow cylinders are presented by means of an asymptotic approach. Either applied load or applied electric potential on the lateral surfaces is considered. The edge conditions of the cylinders are considered as simple supports. In the present formulation, the 22 basic equations in a cylindrical coordinates system are firstly reduced to eight differential equations in terms of eight primary variables of elastic and electric fields. After the mathematical derivation of nondimensionalization, asymptotic expansion and successive integration, we obtained recurrent sets of governing equations for various order problems. In view of the recurrent property, the present asymptotic solutions can be obtained in a hierarchic manner and asymptotically approach the 3D piezoelectricity solutions. Several benchmark problems of single-layer and multilayered piezoelectric hollow cylinders are studied using the present asymptotic formulation.