Static Analysis of Carbon Nano-Tubes Based on Shell Model by Using Three-Dimensional Theory of Elasticity

摘要

This paper studies bending behavior of single-walled carbon nano-tubes (SWCNTs) based on three-dimensional theory of elasticity. To accounting the size effect of carbon nano-tubes, non-local theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. By using Fourier series expansion in axial and circumferential direction the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. The state equations obtained from constitutive relations and governing equations are solved analytically by making the use of state space method. A detailed parametric study is carried out to show the influences of the nonlocal parameter, thickness-to-radius ratio and radius-to-length ratio. Results reveal that excluding small scale effect caused missing in accuracy of stress and displacement fields.