Analysis of functionally graded piezoelectric structures by Hermite interpolation element-free Galerkin method

Abstract

Functionally graded piezoelectric structures (FGPSs) have excellent electromechanical properties and are promising for engineering applications. However, the inhomogeneous material properties and piezoelectric effects create great difficulties in the mechanical analysis of the FGPSs. In this paper, a Hermite interpolation element-free Galerkin method (HIEFGM) is proposed for the numerical analysis of the FGPSs. The HIEFGM utilizes a set of nodes to represent the problem domain, which can ideally reflect the inhomogeneous material properties of the FGPSs. Firstly, the governing equations of the FGPSs are derived through the constitutive equation, equilibrium equation, and boundary conditions. Secondly, the approximating function of the field quantities is obtained by the improved moving least-square method and Hermite interpolation. The HIEFGM formulation of the FGPSs is obtained using the variational principle. Furtherly, the influence of weight function, scaling parameter, and node densities on the HIEFGM of the FGPSs is discussed in detail through a parameter study. Finally, the availability of present method is estimated by several examples with different configurations and boundary conditions. The influence of gradation exponent on the electromechanical responses of the FGPSs is analyzed. The results show that the present method has excellent accuracy and stability in analyzing the FGPSs. As the gradation exponent increases, the distribution of the field quantities of the FGPSs exhibits nonlinear characteristics. This work may provide an effective methodology for the analysis of the FGPSs, and contribute to the theoretical research and engineering application of the FGPSs.