The Research, Based On The Complete Nonlocal Nonlinear Elasticity Model The Mechanical Properties Of Carbon Nanotubes

Nonlocal contimuum elastic theory is a nonlinear elastic theory about the mechanic behaviors of micro structure. Since the nonlocal constitutive equation is appropriate to descripe the small scale effects of carbon nanotubes in micro structure, more and more elastic beam and shell models based on nonlocal theory are applied in the study on mechanics propertities of carbon nanotubes recently. However, for most of these models, the nonlocal quantities such as bending moment and shear force are directly substituted into classical governing equations and boundary conditions. In this case, the classical equations and boundary conditions are considered to be tenable in the micro environment. Some contradictory predictions and surprising conclusions are obtained when these nonlocal models are applied. For example, the stiffness of carbon nanotubes predicted by such nonlocal models are contradict with the results by molecular dynamic simulation. Furthermore, the bending behaviors of nano cantilevers with point loading at the free end are not influent by nonlocal effect, which is not reasonable obviously. Therefore, the directly applying of classical models with nonlocal quantities is not a denpendable method. The nonlocal models established by this method are called as partial nonlocal models (PN) in this thesis. In order to modify these nonlocal models, the analytical nonlocal models (AN) are established according to variation principle. The nonlocal governing equations and boundary conditions are derived rigorously from constitutive equations. Some high order nonlocal terms are contained in these new AN models, which descript the nonlocal effect on carbon nanotubes. The reliability of AN models is confirmed by different means.In this thesis, the physical propertities and industy application of carbon nanotubes are investigated firstly. The study methods about mechanics behaviors of carbon nanotubes are also indicated. According to the comparasion of AN and PN models, AN models is derived from the nonlinear constitutive equation with variation principle. The integration form of strain energy density for AN models is applied to instead tranditional linear strain energy density. Thus the governing equations and boundary conditions with nonlocal high order terms is obtained, which are fail to consider by PN models. Since the contribution of high order terms, AN models could accurately simulate the influence by nonlocal effect on mechanics behaviors.When considering the shear effect on the mechanics behaviors of carbon nanotubes, the AN-Timoshenko beam models (ANT) are established in this thesis according to the principle of AN models at first time. Based on ANT models, the mechanical behaviors about bending, buckling, wave propagation and free vibration of single-walled carbon nanotubes and the wave propagation of double-walled carbon nanotubes are analyzed in this thesis. All the results confirm the stiffness enhancement of carbon nanotubes contributed by nonlocal effect. The buckling analysis shows carbon nanotubes with less freedom of boundary conditions are more sensitive to nonlocal effect. The wave propagation analysis of carbon nanotubes shows the nonlocal effect damp the high frequency wave propagation. The outer layers of double-walled carbon nanotubes are more sensitive to nonlocal effect than inner layers.Beside ANT models, the AN-Euler-Bernoulli beam models (ANE) without shear effect are also applied to the analysis of wave propagation of single-walled carbon nanotubes. Similar results as ANT models are obtained when the high frequency behaviors of wave propagation by ANE models are not accurate than ANT ones since the shear strain is negelected by ANE models. Moreover, AN shell models (ANS) are applied to study the axisymmetry wave propagation behaviors in carbon nanotubes in this thesis, which is the first time to employ two dimension AN models. The stiffness enhancement and high frequency wave decaying are also simulated by ANS models. It is verified by molecular dynamic simulation that the ANS models is more appropriate for the carbon nanotubes with small diameter/length ratio.Finally, when considering the application of carbon nanotubes, ANE models are employed on the analysis about wave propagation behaviors of fluid-filled carbon nanotubes in first time. Similar with common carbon nanotubes, the nonlocal effect leads to strong influence on the wave propagation behaviors, and the fluid velocity also make change for the phase velocity of elastic wave in nanotubes when comparing with PNE models. The calculate results show the wave frequency increase first and then decreas with fluid velocity. All of these results is guideful to industry application of carbon nanotubes.In conclusion, the ANT and ANS models are established according to variation principle when considering the nonlocal effect and shear strain in carbon nanotubes. The mechanics characteristics of carbon nanotubes are analyzed based on ANT models firstly. Then the axisymmetry wave propagation behaviors are investigated by ANS models. Furthermore, the wave propagation behaviors of fluid filled carbon nanotubes are studied by ANE models. By comparing and analysis for all the calculated results, the properties of ANE, ANT, and ANS models are obtained. The influence by shear strain and nonlocal effect on the mechanics behaviors of carbon nanotubes are discussed in details. Finally, the rationality of AN models are confirmed by molecular dynamic simulation approach.