考虑非局部剪切效应的碳纳米管弯曲特性研究

基于Hamilton(哈密顿)变分原理和非局部连续介质弹性理论，建立了新型非局部Timoshenko(铁木辛柯)梁模型（ANT），推导了碳纳米管（CNT）的ANT弯曲平衡方程以及两端简支梁、悬臂梁和简支 固定梁的边界条件表达式，分析了剪切变形效应和非局部微观尺度效应对碳纳米管弯曲特性的影响.数值计算结果显示，碳纳米管的弯曲刚度随着小尺度效应的增强而升高.其次，这种小尺度效应对自由端受集中力的悬臂梁碳纳米管有明显作用，其刚度变化规律和其它约束条件的碳纳米管一样，这一点是ANT模型区别于普通非局部纳米梁模型的主要特点.经分子动力学模拟验证，ANT模型是合理分析碳纳米管力学特性的有效方法.

Shear Deformable Bending of Carbon Nanotubes Based on a New Analytical Nonlocal Timoshenko Beam Model

According to Hamilton’s principle, a new mathematical model was established and the analytical solutions to the nonlocal Timoshenko beam model (ANT) were obtained based on the nonlocal elastic continuum theory in view of shear deformation and nonlocal effects. The new ANT equilibrium equations and boundary conditions were derived for bending analysis on carbon nanotubes (CNTs) of simply supported, clamped and cantilever types. The ANT deflection solutions demonstrate that the CNT stiffness is enhanced by the presence of nonlocal stress effects, as is predicted by the widely accepted but complicated molecular dynamics model and proved by tests. Furthermore, the new ANT model indicates verifiable bending behaviors of a cantilever CNT with point load at the free end, which depends on the magnitude of nonlocal stress. Therefore, this new model conveniently gives better prediction about the mechanical performances of nanostructures.