【作者】 李浩；

【导师】 卞立春；

【作者基本信息】 燕山大学 ， 力学， 2021， 硕士

【摘要】 碳纳米管具有非常良好的力学性能。本文研究不同尺寸的碳纳米管在热环境温度下的力学性能,补充并完善了相关内容,丰富了碳纳米管力学性能的研究理论。研究的课题第一个内容是碳纳米管杨氏模量的研究。采用分子结构力学方法结合连续介质力学理论,研究了与温度和尺寸相关的单壁碳纳米管的杨氏模量。在研究推导过程中完善了力学常数,考虑了壁厚的影响并建立了相应的理论公式。又采用有限元方法建立了与温度和尺寸相关的双壁碳纳米管有限元模型。考虑范德华力的影响,建立了一个非线性弹簧元件,利用数值模拟方法计算了与温度和尺寸相关的双壁碳纳米的等效杨氏模量。最后比较了单壁与双壁碳纳米管的杨氏模量特性。研究的课题第二个内容是碳纳米管体积模量在热温度环境下的研究。碳纳米管体积模量的研究文献不多,尤其是与热环境温度变化相关的研究更少。本文基于分子结构力学方法,考虑范德华力的影响,研究了与温度和尺寸相关的单壁和双壁碳纳米管的体积模量。丰富了温度影响下碳纳米管体积模量的研究。研究的课题第三个内容是弯曲碳纳米管(CCNT)热温度环境下屈曲分析的研究。近些年来,学者们一般对完美型碳纳米管进行研究。但是碳纳米管无论是在生产过程中还是在和弹性介质相结合时都有可能会产生弯曲,因此研究弯曲碳纳米管的力学性能则显得尤为重要。另外,基于本文研究的热环境温度对碳纳米管力学性能的影响参数,在研究弯曲碳纳米管的屈曲分析时,特意加入了环境温度变化参数,以此来更加全面的分析弯曲碳纳米管的热屈曲特性。采用Eringen非局部弹性理论,把弯曲碳纳米管等效为Euler-Bernoulli弯曲梁,推出了弯曲碳纳米管的热屈曲运动控制方程。最后利用微分求积方法得到了弯曲碳纳米管的热屈曲数值解。更多还原

【Abstract】 The carbon nanotubes(CNTs)have many good mechanical properties.In this study,the mechanical properties of carbon nanotubes of different type sizes under thermal environment temperature are studied,and some contents are improved and supplemented in order to enrich the theory of mechanical properties of carbon nanotubes.The first direction of research is the study of Young’s modulus of carbon nanotubes.The Young’s modulus of single-walled carbon nanotubes(SWCNTs)at different temperatures was studied by means of molecular structure mechanics and continuum mechanics.In the process of research and derivation,the mechanical constants are improved,the influence of wall thickness is considered,and the influence of wall thickness is expressed by theoretical formula.In this paper,the finite element method is used to establish the model for the double-walled carbon nanotubes.In order to consider the influence of van der Waals force,a nonlinear spring element is developed,and the equivalent Young’s modulus of double-walled carbon nanotubes under the influence of temperature is derived by numerical simulation method.Finally,the Young’s modulus of single-walled carbon nanotubes and double-walled carbon nanotubes are compared and validated with other data.The second direction of the research is the study of the volume modulus of carbon nanotubes under the change of ambient temperature.There are not many literatures for the study on the bulk modulus of carbon nanotubes,especially on the influence of ambient temperature change.In this paper,the volume modulus of single-walled and double-walled carbon nanotubes under ambient temperature change was studied,which enriched the study of the volume modulus of carbon nanotubes under the influence of temperature.The third direction of the research is the thermal buckling analysis of curved carbon nanotubes(CCNTs).In recent years,researchers generally focus on the study of perfect carbon nanotubes,but carbon nanotubes are likely to bend in the production process or when combined with elastic media,so it is particularly important to study the mechanical properties of curved carbon nanotubes.In addition,based on the influence analysis of ambient temperature on the mechanical properties of carbon nanotubes,in this paper,the parameters of ambient temperature change were specially added in the buckling analysis to more comprehensively analyze the thermal buckling characteristics of bending carbon nanotubes.Moreover,Eringen nonlocal elastic theory and stress gradient theory are used to simulate the bending CNTs as Euler-Bernoulli bending beams.The governing equations of the bending motion of CNTs are derived,and the analytical solution of thermal buckling of curved carbon nanotubes was obtained by differential quadrature method.更多还原