轴向冲击载荷作用下双壁碳纳米管的动力屈曲

应用改进的有限元方法,建立考虑层间范德华力作用的壳-弹簧非线性有限元模型,基于B-R运动准则,系统地研究了双壁碳纳米管的动力屈曲问题,得到了轴向冲击载荷作用下双壁碳纳米管的临界动力屈曲载荷和临界动力失效载荷. 研究结果表明,在动力屈曲过程中,双壁碳纳米管层间距的变化非常小,各管的变形相互协调;碳纳米管中应力波的传播导致碳纳米管出现非对称屈曲模态,可明显观测到四个环向波瓣,沿着碳纳米管的轴线方向,四个波瓣的波峰和波谷交替变化. 对碳纳米管动力屈曲问题的研究表明,冲击载荷的大小和持续时间对碳纳米管的动力屈曲有 关键词： 碳纳米管 动力屈曲 冲击载荷     

轴压和扭转复合载荷作用下氮化硼纳米管屈曲行为的分子动力学模拟

采用分子动力学方法模拟了氮化硼纳米管在轴压和扭转复合荷载作用下的屈曲和后屈曲行为.在各加载比例下,给出了初始线性变形阶段和后屈曲阶段原子间相互作用力的变化,确定了屈曲临界荷载关系.通过对屈曲模态的细致研究,从微观变形机理上分析了纳米管对不同外荷载力学响应的差异.研究结果表明,扶手型和锯齿型纳米管均呈现出非线性的屈曲临界荷载关系,复合加载下的屈曲行为具有强烈的尺寸依赖性.温度升高将导致屈曲临界荷载的下降,且温度的影响随加载比例的变化而变化.无论在简单加载或复合加载中,同尺寸的碳纳米管均比氮化硼纳米管具有更强地抵抗屈曲荷载的能力.     

单壁碳纳米管非线性力学行为的数值模拟

单壁碳纳米管的力学行为是纳米复合材料和纳米器械的基本问题之一.使用有限元方法系统地研究了单壁碳纳米管的轴压和纯弯变形，并将有限元模拟结果和分子动力学模拟结果进行了比较.研究结果表明单壁碳纳米管的轴压屈曲载荷受直径变化的影响；单壁碳纳米管在弯曲载荷作用下的屈曲和后屈曲行为强烈地依赖于管长和管径的变化，合理地选择碳纳米管的弹性模量和壁厚，有限元方法能够很好地解释碳纳米管的屈曲机理.研究大尺度的纳米力学问题时，有限元方法将会成为更加准确、快捷的数值模拟方法.     

单壁碳纳米管非线性力学行为的数值模拟

单壁碳纳米管的力学行为是纳米复合材料和纳米器械的基本问题之一.使用有限元方法系统地研究了单壁碳纳米管的轴压和纯弯变形,并将有限元模拟结果和分子动力学模拟结果进行了比较.研究结果表明单壁碳纳米管的轴压屈曲载荷受直径变化的影响;单壁碳纳米管在弯曲载荷作用下的屈曲和后屈曲行为强烈地依赖于管长和管径的变化,合理地选择碳纳米管的弹性模量和壁厚,有限元方法能够很好地解释碳纳米管的屈曲机理.研究大尺度的纳米力学问题时,有限元方法将会成为更加准确、快捷的数值模拟方法. 关键词： 单壁碳纳米管 非线性力学行为 有限元     

单壁碳纳米管受压屈曲行为的数值模拟

采用以Tersoff Brenner势函数来描述碳纳米管中碳原子间的相互作用的分子动力学方法,模拟了单壁 碳纳米管(SWCNTs)的受压屈曲行为.计算结果表明,单壁碳纳米管的杨氏模量随着管径的增大而减小;碳纳米 管屈曲的临界应力和临界应变与碳纳米管细长比有关,不同的细长比决定了碳纳米管结构不同的屈曲模态;碳纳 米管的受压屈曲机理和连续介质力学中柱体壳的受压屈曲理论随细长比的不同而存在一些异同.     

轴向载荷下功能梯度材料Timoshenko梁动力屈曲分析

假设功能梯度材料Timoshenko梁各项物性参数只沿厚度方向按幂函数进行连续变化,研究了功能梯度材料Timoshenko梁的动力屈曲。基于一阶剪切理论,采用Hamilton原理推导出轴向载荷作用下,功能梯度材料Timoshenko梁动力屈曲的控制方程。利用里兹法与棣莫弗公式相结合,获得了功能梯度材料Timoshenko梁在夹支-固支边界条件下动力屈曲临界载荷的解析表达式和屈曲解。应用MATLAB编程计算,讨论了功能梯度材料Timoshenko梁的几何尺寸、梯度指数、模态数、材料构成、泊松比以及弹性模量对临界载荷的影响。结果表明:功能梯度材料Timoshenko梁动力屈曲临界载荷随梁长度的增大而减小,随着梯度指数的增大而减小,随模态数的增大而增大,说明冲击载荷越大,高阶模态越容易被激发;随着泊松比和弹性模量的增大而增大,且泊松比的影响较小,而弹性模量的影响较大。由于剪切项的影响,临界载荷-临界长度的关系曲线在加载端变化趋势平缓。随着模态数的增大,梁的屈曲模态越为复杂。     

碳纳米管-聚乙烯复合材料界面力学特性分析

本文采用分子动力学模拟办法对碳纳米管-聚乙烯复合材料的界面力学特性进行了模拟和分析. 通过对单壁碳纳米管从无定形聚乙烯中抽出过程进行模拟, 研究了界面剪切应力随碳管滑移速度、聚乙烯分子链长和碳纳米管管径之间的变化关系, 并对界面的滑移机理进行了讨论. 模拟结果发现, 随着聚合物分子链长的增加, 界面临界剪切应力有显著增大, 而滑移剪切应力略显增加; 界面临界剪切应力和滑移剪切应力随着碳纳米管管径的增大而明显增加. 本文同时对界面应力的变化机理进行了模拟和讨论.     

碳纳米锥力学特性的分子动力学研究

结合原子间短程作用势(Brenner势)和长程作用势(Lennard-Jones势),利用分子动力学方法对各种锥角的碳纳米锥进行拉伸和压缩实验,获得其载荷-应变关系曲线、受拉/压载荷极限、应变极限和构形演变等力学特性,并与等量原子组成的碳纳米管进行比较研究.研究结果表明,等量碳原子组成的碳纳米锥的受拉/压载荷极限随着锥角的增大先是增大后减小,受拉/压应变极限则随着锥角的增大而增大.与碳纳米锥相比,等量碳原子组成的碳纳米管的受拉/压载荷极限和应变极限显得既不突出也不逊色.在受压构形演化方面,与碳纳米管丰富的径向屈曲/扭转/侧向屈曲组合形变不同,112.88°和83.62°锥角的碳纳米锥受压沿轴向完美内陷,而60.0°和38.94°锥角的碳纳米锥受压发生侧向屈曲.     

范德华力对双壁碳纳米管轴向压缩屈曲行为的影响

使用分子动力学方法研究几种不同半径尺寸的单壁碳纳米管组成的双壁碳管，预测了其初始稳定构型；分析了其自由弛豫阶段的特征；并模拟了它们在轴向压缩载荷作用下的屈曲行为；研究了不同层间距导致的范德华力变化对屈曲行为的影响.采用Tersoff-Brenner势描述单壁碳纳米管内原子间作用，Lennard-Jones势描述内外层间的范德华相互作用.计算结果表明：在通常意义下的双壁管间距(约0.34 nm)外还可以存在稳定的双壁碳管构型，并且这些新的稳定构型表现出了不同的力学性质. 关键词： 双壁碳纳米管 分子动力学 屈曲     

轴向荷载下功能梯度材料圆柱壳的动力屈曲

基于Donnell壳体理论和经典板壳理论,利用Hamilton变分原理得到轴向荷载作用下材料属性呈幂律分布的功能梯度材料圆柱壳的动力屈曲控制方程。根据圆柱壳周向连续性设出径向位移的函数表达,利用分离变量法求解得到功能梯度材料圆柱壳在轴向荷载作用下的动力屈曲临界荷载的解析表达式和屈曲解。利用MATLAB软件编程计算,讨论了径厚比、梯度指数、环向模态数、轴向模态数等对功能梯度材料圆柱壳动力屈曲临界荷载的影响。结果表明:圆柱壳的临界荷载随临界长度的增加而减小;冲击端为夹支的临界荷载比冲击端为简支的临界荷载大,说明约束条件对临界荷载有较大影响;圆柱壳的临界荷载随着模态数的增加而增大,说明临界荷载越大,高阶模态越易被激发;屈曲模态图随着模态数的增加而复杂化。     

Combined torsional buckling of double-walled carbon nanotubes with axial load in the multi-field coupled condition

The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable s...     

Influence of temperature change on column buckling of multiwalled carbon nanotubes

Based on theory of thermal elasticity mechanics, an elastic multiple column model is developed for column buckling of MWNTs with large aspect ratios under axial compression coupling with temperature change. In this model, each of the nested concentric tubes is regarded as an individual column and the deflection of all the columns is coupled together through the van der Waals interactions between adjacent tubes. The thermal effect is incorporated in the formulation. Following this model, an explicit expression is derived for the critical buckling strain for a double-walled carbon nanotube. The influence of temperature change on the buckling strain is investigated. It is concluded that the effect of temperature change on the buckling strain is dependent on the temperature changes, the aspect ratios, and the buckling modes of carbon nanotubes.     

Nonlocal shear deformable shell model for thermal postbuckling of axially compressed double-walled carbon nanotubes

An investigation is reported of the thermal buckling and postbuckling of axially compressed double-walled carbon nanotubes (CNTs) subjected to a uniform temperature rise. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell, which contains small-scale effects and van der Waals interaction forces. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and include thermal effects. Temperature-dependent material properties, which come from molecular dynamics (MD) simulations, and an initial point defect, which is simulated as a dimple on the tube wall, are both taken into account. The small-scale parameter, e ₀ a, is estimated by matching the buckling temperature of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. The numerical illustrations concern the thermal postbuckling response of perfect and imperfect, single- and double-walled CNTs with different values of compressive load ratio. The results show that buckling temperature and postbuckling behavior of nanotubes are very sensitive to the small-scale parameter. The results reveal that temperature-dependent material properties have a significant effect on the thermal postbuckling behavior of both single- and double-walled CNTs.     

Double-walled carbon nanotube with surrounding elastic medium under axial pressure

In this paper, the buckling behavior and critical axial pressure of double-walled carbon nanotubes (DWCNTs) with surrounding elastic medium are investigated. A double-shell (circular cylindrical shell) model is presented and the effects of surrounding elastic medium on the outer tube and the van der Waals forces between two adjacent tubes are taken into account. The analysis and the numerical solution method are based on the classical theory of plates and shells and the Galerkin method. Equations are derived for the critical axial forces and pressures of DWCNTs; the critical axial forces and pressures are calculated for different axial half sine wavenumbers and circumferential sine wavenumbers and compared with those for single-walled carbon nanotubes (SWCNTs).Results indicate that the critical axial force of a DWCNT is higher than that of an SWCNT, but the critical axial pressure of a DWCNT is lower than the critical axial pressure of a SWCNT. Although the critical axial force of a DWCNT decreases as the axial half sine wavenumbers increase, it rises as the circumferential sine wavenumbers increase.     

Sound wave propagation in zigzag double-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory

In the present work, nonlocal Euler–Bernoulli beam theory is used to investigate the wave propagation in zigzag double-walled carbon nanotube (DWCNT) embedded in an elastic medium. Winkler-type foundation model is employed to simulate the interaction of the DWCNT with the surrounding elastic medium. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. It is noticed in the presented study that the equivalent Young’s modulus for zigzag DWCNT is derived using an energy-equivalent model. Influences of nonlocal effects, the chirality of zigzag DWCNT, Winkler modulus parameter, and aspect ratio on the frequency of DWCNT are analyzed and discussed. The new features of the vibration behavior of zigzag DWCNTs embedded in an elastic medium and some meaningful results in this paper are helpful for the application and the design of nanostructures in which zigzag DWCNTs act as basic elements.     

Effect of temperature and geometrical nonlinearity on wave propagation characteristics of carbon nanotubes

Considering the effect of temperature and geometrical nonlinearity in the constitutive relation, the equation of motion for a carbon nanotube is obtained based on the Euler–Bernouli beam model. Also, the effect of van der Waals forces is taken into account in the formulation. The carbon nanotube is assumed to be under the application of a constant distributed external load. At any temperature, the equilibrium solutions of the governing equations for a single-walled carbon nanotube (SWCNT) and a double-walled carbon nanotube (DWCNT) are obtained. A small perturbation is assumed around the equilibrium solution. Using this perturbation, the nonlinear equations of motion are linearized. Using the linearized form of the equations of motion, the characteristic equations and dispersion relations are obtained. It is shown that in the linear case and for the case of high temperature there exists a temperature beyond which the phase velocity does not exist. It is shown that in the case of room or low temperature there is no critical value for temperature. Based on the dispersion equation, a relation for the critical value of temperature is obtained. It is found that when the large deformation effect is taken into account, the critical value for temperature does not exist. Also, the effect of large deformations on phase velocities and lateral deformations of single-walled and double-walled carbon nanotube beams are studied. It is found that unlike the linear theory, the nonlinear theory predicts a non-zero phase velocity at the temperature corresponding to linear critical temperature.     

Buckling analysis of carbon nanotube bundles under axial compressive,bending and torsional loadings via a structural mechanics model

A structural mechanics model is employed for the investigation of the buckling behavior of carbon nanotube bundles of three single-walled carbon nanotubes (SWCNTs) under axial compressive, bending and torsional loadings. The effects of van der Waals (vdW) forces are further modeled using a nonlinear spring element.The effects of different types of boundary conditions are studied for nanotubes with various aspect ratios. The results reveal that bundles comprising longer SWCNTs exhibit lower critical buckling load. Moreover, for the fixed-free boundary condition the rate of critical buckling load reduction is highest, while the lowest critical buckling load occurs. Simulations show good agreement between our model and molecular dynamics results.     

Molecular dynamic investigation of mechanical properties of armchair and zigzag double-walled carbon nanotubes under various loading conditions

Using molecular dynamic simulation (MDS), effects of chirality and Van der Waals interaction on Young's modulus, elastic compressive modulus, bending, tensile, and compressive stiffness, and critical axial force of double-walled carbon nanotube (DWCNT) and its inner and outer tubes are considered. Achieving the highest safety factor, mechanical properties have been investigated under applied load on both inner and outer tubes simultaneously and on each one of them separately. Results indicate that as a compressive element, DWCNT is more beneficial than single-walled carbon nanotube (SWCNT) since it carries two times higher compression before buckling. Except critical axial pressure and tensile stiffness, in other parameters zigzag DWCNT shows higher amounts than armchair type. Outer tube has lower strength than inner tube; therefore, most reliable design of nanostructures can be attained if the mechanical properties of outer tube taken as the properties of DWCNT.     

Dynamic column buckling of multi-walled carbon nanotubes under axial impact load

This paper studies the dynamic column buckling of multi-walled carbon nanotubes (MWNTs) under axial impact load. The analysis is based on the continuum mechanics model and a simplified model for the van der Waals forces between adjacent layers. By introducing initial imperfections for MWNTs and applying the method of preferred mode, a buckling condition is derived for the buckling load and associated buckling mode. In particular, explicit expressions are obtained for double-walled carbon nanotubes (DWNTs). Finally, numerical calculations are worked out for a DWNT and a five-layer MWNT with different length-to-radius ratios.