An isogeometric Bezier finite element analysis for piezoelectric FG porous plates reinforced by graphene platelets

In this study, we for the first time present an isogeometric Bezier finite element formulation for bending and transient analysis of functionally graded porous (FGP) plates reinforced by graphene platelets (GPLs) embedded in piezoelectric layers. We name it as PFGP-GPLs for short. The plates are constituted by a core layer, which contains the internal pores and GPLs dispersed in the metal matrix either uniformly or non-uniformly according to three different patterns, and two piezoelectric layers perfectly bonded on the top and bottom surfaces of host plate. The modified Halpin-Tsai micromechanical model is used to estimate the effective mechanical properties which vary continuously along thickness direction of the core layer. In addition, the electric potential is assumed to vary linearly through the thickness for each piezoelectric sublayer. A generalized C-0-type higher-order shear deformation theory (C-0-HSDT) in association with isogeometric analysis (IGA) based on Bezier extraction is investigated. Our approach allows performing all computations the same as in the conventional finite element method (FEM) yet the present formulation shows more advantages. The system of time-dependent equations is solved by the Newmark time integration scheme. The effects of weight fractions and dispersion patterns of GPLs, the coefficient and distribution types of porosity as well as external electrical voltages on structure's behaviors are investigated through several numerical examples. These results, which have not been published before, can be considered as reference solutions for future works.