Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs

This paper investigates the effects of both size-dependency and material-dependency on the nonlinear static behavior of carbon nanotubes (CNTs). The energy-equivalent model (EEM) derived on the basis of molecular mechanics is exploited to describe the size-dependence of mechanical properties of CNTs, such as, Young's modulus, shear modulus and Poisson's ratio. Carbon nanotube is modeled as modified nonlocal Euler-Bernoulli and Timoshenko nanobeams with mid-plane stretching. To include the size-dependency and length scale effect of nanostructure, a nonlocal differential form of Eringen's model is proposed. The governing equilibrium equations for proposed beam theories are derived using the principle of virtual displacements, wherein the modified nonlinear von Karman strains are considered. A finite element model is developed to solve the nonlinear equilibrium equations. Numerical results are presented to show the effects of chirality angle, nonlocal parameter, moderate rotation, and boundary conditions of CNTs. These findings are helpful in mechanical design of high-precision devices and structures manufactured from CNTs.