Refined 2D Models for the Analysis of Functionally Graded Piezoelectric Plates

This article investigates the static analysis of a single-layered functionally graded piezoelectric plate, in both sensor and actuator configurations. Refined theories (order of expansion in the thickness direction from linear to fourth order) are compared with classical ones, such as the first order shear deformation theory, to demonstrate the effectiveness of these theories in the case of functionally graded piezoelectric materials (FGPMs). Both elastic and electrical properties in FGPMs are described via opportune thickness functions, which are a combination of Legendre polynomials, with an order of expansion in thickness direction equal to 10. Such types of functions permit any functional variation of the FGPM properties to be described efficiently in the thickness direction.