Large deflection geometrically nonlinear analysis of carbon nanotube-reinforced functionally graded cylindrical panels

Abstract

A large deflection geometrically nonlinear behavior of carbon nanotube-reinforced functionally graded (CNTR-FG) cylindrical panels under uniform point transverse mechanical loading is studied. The analysis is carried out using the kp-Ritz method with kernel particle function is employed to construct the shape functions for the two-dimensional displacement approximations. Based on the first-order shear deformation shell theory, nonlinear governing equations are developed with geometric nonlinearity taking the form of von Kármán strains. It is assumed that carbon nanotubes are uniaxially aligned in the axial direction and are functionally graded in thickness direction of the cylindrical panels. The effective material properties of resulting CNTR-FG panels are estimated by employing an equivalent continuum model based on the Eshelby–Mori–Tanaka approach. 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 to eliminate shear locking, for a very thin cylindrical panel. Several numerical example problems are examined to reveal the influences of volume fraction of carbon nanotubes, span angle, edge-to-radius ratio and thickness on nonlinear responses of the CNTR-FG panels. Moreover, effects of different boundary conditions and distribution type of carbon nanotubes are also investigated.