Abstract
To accurately simulate the continuous property change of functionally graded piezoelectric materials (FGPMs) and overcome the overstiffness of the finite element method (FEM), we present an electromechanical inhomogeneous cell-based smoothed FEM (ISFEM) of FGPMs. Firstly, ISFEM formulations were derived to calculate the transient response of FGPMs, and then, a modified Wilson-θ method was deduced to solve the integration of the FGPM system. The true parameters at the Gaussian integration point in FGPMs were adopted directly to replace the homogenization parameters in an element. ISFEM provides a close-to-exact stiffness of the continuous system, which could automatically and more easily generate for complicated domains and thus significantly decrease numerical errors. The accuracy and trustworthiness of ISFEM were verified as higher than the standard FEM by several numerical examples.
Highlights
Because of their outstanding electromechanical properties, easy fabricability, and preparation flexibility, piezoelectric materials are extensively applied as sensors and actuators to monitor and modulate the response of structures [1, 2]
Exact 3D analysis of functionally graded piezoelectric materials (FGPMs) rectangular plates was conducted by using a state-space approach [13] and to investigate the natural frequencies and mode shapes after being poled perpendicular to the middle plane [14]. e above method was applied to explore the free vibration of rectangular FGPM plates [15]. e semianalytical finite element method (FEM) was used to investigate the static response of anisotropic and linear functionally graded magneto-electro-elastic plates [16]
Given the continuous change of the gradient of material properties along the thickness x3 direction and with cellbased gradient smoothing, we deduced the basic formula of inhomogeneous cell-based smoothed FEM (ISFEM) and a modified Wilson-θ method to solve the integral solution of the FGPM system. e displacements and potentials of FGPM cantilever beams under sine wave load, cosine wave load, step wave load, and triangular wave load were analyzed in comparison with FEM
Summary
Because of their outstanding electromechanical properties, easy fabricability, and preparation flexibility, piezoelectric materials are extensively applied as sensors and actuators to monitor and modulate the response of structures [1, 2]. Piezoelectric layers with uniform material properties are limited by large bending displacement, stress concentration, creeping at high temperature, and failure from interfacial unbounding All these phenomena are induced by mechanical or electric loading at layer interfaces [8]. E Timoshenko beam theory was used to analyze the static and dynamic responses of FGPM actuators to thermo-electro-mechanical loading [22]. E first-order shear deformation theory was used to study the static bending, free vibration, and dynamic responses of FGPM plates under electromechanical loading [23]. Zhou et al [65, 66] deduced the linear and nonlinear cell-based smoothed finite element method of functionally graded magneto-electro-elastic (MEE) structures and further examined the transient responses of MEE sensors or energy harvest structures considering the damping factors. Given the continuous change of the gradient of material properties along the thickness x3 direction and with cellbased gradient smoothing, we deduced the basic formula of ISFEM and a modified Wilson-θ method to solve the integral solution of the FGPM system. e displacements and potentials of FGPM cantilever beams under sine wave load, cosine wave load, step wave load, and triangular wave load were analyzed in comparison with FEM
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