Stability of carbon nanotube-reinforced composite plates with surface-bonded piezoelectric layers and under bi-axial compression

Based on Reissner's mixed variational theorem (RMVT), we develop a unified formulation of finite layer methods (FLMs) for the three-dimensional (3D) buckling analysis of simply-supported, functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) plates with surface-bonded piezoelectric actuator and sensor layers and under bi-axial compressive loads. In this work, a set of membrane stresses is assumed to exist just before instability occurs, and determined using the predefined 3D deformations for the prebuckling state. The carbon nanotubes (CNTs) are considered to be uniformly distributed (UD), and FG rhombus- and X-type variations through the thickness coordinate, and the effective material properties of the FG CNTRC layer are evaluated using the rule of mixtures, and two different surface conditions, open- and closed-circuit, are considered. In the formulation, the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations for the field variables of each individual layer, respectively. The accuracy and convergence of the FLMs with various orders used for the expansion of each field variable in the thickness are assessed by comparing their solutions with the exact 3D ones available in the literature.