Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates by the element-free kp-Ritz method

A nonlinear analysis is presented for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates using the element-free kp-Ritz method. The nonlinear governing equations are developed to investigate problems related to small strains and moderate rotations, based on the first-order shear deformation plate theory and von Kármán strains. Two-dimensional displacement fields of the plates are approximated by a set of mesh-free kernel particle functions. Single-walled carbon nanotubes (SWCNTs) are selected as reinforcement and effective material properties of FG-CNTRC plates are assumed to be graded through the thickness direction and are estimated through an equivalent continuum model based on the Eshelby–Mori–Tanaka approach. For eliminating shear locking for a very thin plate, a stabilized conforming nodal integration scheme is employed to evaluate the system bending stiffness, and the membrane as well as shear terms are calculated by the direct nodal integration method. Numerical simulations are carried out to investigate effects of various parameters on nonlinear behaviors of FG-CNTRC plates and results for uniformly distributed (UD) CNTRC plates are provided for comparison. Numerical results indicate that carbon nanotube content by volume, plate width-to-thickness ratio, plate aspect ratio and boundary condition have pronounced effects on the nonlinear response of CNTRC plates.