悬臂碳纳米管纯弯问题的非局部弹性解

摘要

Pure bending problem of cantilever carbon nanotubes( CNTs) is studied based on Eringen' s nonlocal elastic theory and cylinder shell semimoment theory, considering the influence of small scale effect, the stress-strain relationship of single-walled carbon nanotubes(SWCNTs) is given, and the theory solutions of internal force field and displacement field are obtained. It is shown that small scale effect will be prominent for CNTs with small radius.%基于Eringen非局部弹性理论和圆柱壳半无矩理论,研究了悬臂碳纳米管的纯弯曲问题.计及小尺度效应的影响,给出了单臂碳纳米管的应力-应变关系,得到了内力场和位移场的理论解.研究结果表明,对半径较小的碳纳米管,尺度效应较为明显.随着碳纳米管的半径增大,尺度效应逐渐减小.当碳纳米管的半径大于或等于8 nm时,可以忽略尺度效应的影响.