Asymptotic Solutions for Multilayered Piezoelectric Cylinders under Electromechanical Loads

Based on the three-dimensional (3D) piezoelectricity, we presented asymptotic solutions for multilayered piezoelectric hollow cylinders using the method of perturbation. The material properties in the general formulation are firstly regarded to be heterogeneous through the thickness, and then specified as the layerwise step functions in the cases of multilayered cylinders. The transverse normal load and normal electric displacement are respectively applied on the lateral surfaces of the cylinders. The boundary conditions of cylinders are considered to be simply supported at the two edges. In the formulation the twenty-two basic equations of piezoelectricity are reduced to eight differential equations in terms of eight primary variables of elastic and electric fields. After performing nondimensionalization, asymptotic expansion and successive integration, we finally decompose the 3D problem into a series of 2D problems with the same governing equations for various orders except for the nonhomogeneous terms. In view of the recurrent property, it is illustrated that the present asymptotic solutions can be obtained in a hierarchic manner and asymptotically approach 3D piezoelectricity solutions.