Study On Buckling Behaviors Of Carbon Nanotubes Based On Cylindrical Shell Theory

Carbon nanotubes are molecular-scale tubes of graphitic carbon with outstanding properties.They are among the stiffest and strongest fibers known,and have remarkable electronic properties and many other unique characteristics.For these reasons they have attracted huge academic interest,with thousands of papers on nanotubes being published every year.Commercial applications have been rather slow to develop,however,primarily because of the high production costs of the best quality nanotubes.The methods mostly used to investigate carbon nanotubes mainly contain Molecular-Dynamics Simulation(MDS) and Continuum Shell Method.MDS method is very time-consuming and requires a huge computer memory,and the size of carbon nanotubes that could be analyzed is very small.However,continuum shell theory becomes an effective and economic access to investigate the mechanical behaviors of carbon nanotubes.The article analysis the buckling behaviors of carbon nanotubes by using continuum shell theory considering Van der walls forces between any tubes.A lot of valuable conclusions are obtained.Recently,most researchers have only considered linear Van der walls forces between adjacent layers.This paper takes Van der walls forces between any tubes and nonlinear items into account.A serious of formulas is deduced.Double-walled, Triple-walled and four-walled carbon nanotubes are analyzed,in which different radius,length-radius ratio and other factors are considered.Finally,there is a comparison between the results I got and that without nonlinear Van der walls forces.The paper firstly introduces some general information about carbon nanotubes, and also brings in some buckling theory of continuum cylindrical shell.Secondly, some formulae are derived with nonlinear Van der walls forces.Thirdly,several examples are analyzed in order to compare the difference between the two results. During the calculation,a lot of simultaneous equations are solved by programming with the help of mathematic software Mathematic.Finally,several valuable conclusions are deduced.Nonlinear Van der waals forces has little effect on buckling of carbon nanotubes.While the length-radius ratio of carbon nanotubes considered is higher then 10,it is suggested to neglect the effect of nonlinear item, however,it is advised to take into account the effect when the length-radius ratio of carbon nanotubes is lower or equivalent to 10.The stability of carbon nanotubes is decreased with the raise of length-radius ratio.It also can be seen that,one can enhance the stability of carbon nanotubes by adding tubes.