ABSTRACT
One of the essential features of piezoelectric materials is the capability of converting the energy between mechanical energy and electric energy. Due to this attractive feature, piezoelectric materials are currently widely used in various applications such as sensors, actuators, transducers, and active damping devices for various engineering systems [1-4]. These materials are also used to design “smart” structures in industrial, medical, military, and communication areas (e.g., [2,5]). Because of the outstanding adaptation to complicated geometry, the FEM is currently the most popular numerical tool for analyzing and designing piezoelectric structures [512]. Since the work of Ref. [7] for piezoelectric analysis using the FEM, most of the finite element models use displacement and electric potential as primary functions of field variable, and both the functions and their derivatives satisfy fully the compatibility conditions. These elements are, however, often found to be less accurate and sensitive to mesh distortion due to the overestimation or over stiffness of the stiffness matrix. Many techniques have been proposed to improve the standard finite elements such as the bubble/incompatible displacement method, mixed and hybrid formulations [13-18], and formulation of the piezoelectric finite element with drilling DOFs [19-21]. Special types of elements have also been proposed for the analysis of piezoelectric plates [22,23]. Several mesh-free methods [24] have also been used to analyze piezoelectric structures such as the point collocation method (PCM) [25], the PIM [26], and the radial point interpolation method (RPIM) [27,28].
