A MECHANICS MODEL OF A MONOLAYER GRAPHENE BASED ON THE LENOSKY INTERATOMIC POTENTIAL ENERGY

基于对Lenosky 碳-碳共价键作用势连续化得到的单层石墨烯的势能和Hamilton 原理,导出了单层石墨烯的动力学方程. 使用该数学模型及Galerkin 方法,研究了矩形单层石墨烯片的静力挠曲问题. 结果显示,石墨烯片的几何尺寸较小时,弯曲刚度对结构的受力影响较大,可用板理论来描述;随着结构尺寸的增大,弯曲刚度的影响迅速降低;当矩形石墨烯片的短边尺寸大于10 nm 时,可以忽略弯曲刚度对结构的影响,使用薄膜理论来描述单层石墨烯的力学性质.     

基于Lenosky原子作用势单层石墨烯片的力学模型

基于对Lenosky 碳-碳共价键作用势连续化得到的单层石墨烯的势能和Hamilton 原理,导出了单层石墨烯的动力学方程. 使用该数学模型及Galerkin 方法,研究了矩形单层石墨烯片的静力挠曲问题. 结果显示,石墨烯片的几何尺寸较小时,弯曲刚度对结构的受力影响较大,可用板理论来描述;随着结构尺寸的增大,弯曲刚度的影响迅速降低;当矩形石墨烯片的短边尺寸大于10 nm 时,可以忽略弯曲刚度对结构的影响,使用薄膜理论来描述单层石墨烯的力学性质.      

Atomistic–continuum coupled model for nonlinear analysis of single layer graphene sheets

In this paper, atomistic–continuum coupled model for nonlinear flexural response of single layer graphene sheet is presented considering von-Karman geometric nonlinearity and material nonlinearity due to atomic interactions. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that of at atomic level through Cauchy–Born rule. Strain and curvature dependent tangent in-plane extensional, bending–extension coupling, bending stiffness matrices are derived from strain energy density function constructed through Tersoff–Brenner potential. The finite element method is used to discretize the graphene sheet at continuum level and nonlinear bending response with and without material nonlinearity is studied. The present results are also compared with Kirchhoff plate model and significant differences at higher load are observed. The effects of other parameters like number of atoms in the graphene sheet, boundary conditions on the central/maximum deflection of graphene sheet are investigated. It is also brought out that the occurrence of bond length exceeding cutoff distance initiates at corners for CFCC, CFCF, SFSS, SFSF graphene sheets and near center for SSSS and CCCC graphene sheets.     

磁场力及膜曲率对磁敏感薄膜-基底界面黏附性能的影响与调控

界面黏附和脱黏的可调控在攀爬装置、黏附开关、机械抓手等方面具有重要的应用需求. 针对磁敏感薄膜-基底界面, 开展了薄膜初始曲率及外加磁场对界面黏附性能影响机制的研究. 首先实验制备了具有初始曲率的磁敏感薄膜, 分别开展了具有初始曲率的磁敏感薄膜-基底界面撕脱实验及理论研究, 研究了薄膜初始曲率、弯曲刚度和外加磁场强度对界面黏附性能的影响规律. 实验和理论结果一致表明: 具有初始曲率的磁敏感薄膜-基底界面黏附力随薄膜初始曲率的增大而减小, 而外加磁场能够有效提高界面黏附力;相比于初始零曲率薄膜-基底界面稳态撕脱力与薄膜弯曲刚度无关, 薄膜弯曲刚度减弱了具有初始曲率薄膜-基底界面的稳态撕脱力. 进一步从能量角度分析了界面等效黏附性能, 揭示了薄膜弯曲能、磁场势能、界面黏附能的相互竞争机制. 最后, 基于本文的实验及理论结果, 提出了一种磁场和薄膜初始曲率协同调控的简易机械抓手, 可连续实现物体的拾取、搬运和释放功能. 本文结果不仅有助于理解多场调控的界面可逆黏附机制, 对界面黏附可控的功能器件设计亦提供了一种新方法.      

基于初弯曲单元的某弦支穹顶非线性稳定承载力分析

在单元的随动坐标系下,建立了初始弯曲对杆单元轴向刚度影响的计算公式,导出了考虑初始弯曲的非线性杆单元刚度矩阵;从经典的梁-柱理论出发,给出了考虑初始弯曲的非线性空间梁单元切线刚度矩阵推导过程。将建立的初始弯曲单元应用于弦支穹顶结构算例的非线性稳定承载力分析,研究了杆件初始弯曲对结构整体非线性稳定性能的影响,结果表明,杆件初始弯曲的存在会降低结构的整体刚度和极限承载力,而在不同的初始预应力状态下,极限荷载随初始弯曲增加都基本呈线性下降,并且其关系曲线基本平行。本文建立的基于初弯曲单元的非线性分析方法,可推广应用于各种类型空间网格结构的非线性分析,为结构设计方案的选择提供更为科学的依据。     

基于高斯曲率极值点的桥梁结构损伤识别方法

目前中小桥梁日常安全巡检存在对检查人员依赖性高、缺乏可量化的科学依据等不足.针对这些问题,本文提出了一种利用高斯曲率极值点对结构进行损伤识别的方法.将桥面视为受弯弹性薄板,根据弹性薄板的弯曲理论得到了在荷载作用下结构刚度变化与桥面弯曲程度(高斯曲率)的理论关系,并由此推导了高斯曲率对结构刚度损伤的敏感程度公式.通过有限...     

Morphing of curved corrugated shells

Thin sheet materials of low bending stiffness but high membrane stiffness are often corrugated in order to achieve improvements of several orders of magnitude in bending stiffness with only minimal increases in weight and cost. If these corrugated sheets are initially curved along the corrugations, much of this stiffness gain is lost. In return, the sheets are then capable of significant elastic changes in shape overall, including large changes in overall Gaussian curvature. These shape changes are described here by non-linear and coupled kinematical relationships, which are verified against experiment and finite-element simulations. It is found that gross simplifications can be made about the large displacement behaviour of such shells without a loss of accuracy.     

Bending-induced extension in two-dimensional crystals

We find by ab initio simulations that significant overall tensile strain can be induced by pure bending in a wide range of two-dimensional crystals perpendicular to the bending moment, just like an accordion being bent to open. This bending-induced tensile strain increases in a power law with bent curvature and can be over 20% in monolayered black phosphorus and transition metal dichalcogenides at a moderate curvature of 2 nm?1 but more than an order weaker in graphene and hexagon boron nitride. This accordion effect is found to be a quantum mechanical effect raised by the asymmetric response of chemical bonds and electron density to the bending curvature.     

Zigzag carbon nanotubes—Molecular/structural mechanics and the finite element method

This paper discusses in details the relation between the bond bending stiffness used in molecular mechanics and the bending stiffness used in structural mechanics for zigzag carbon nanotubes (CNTs).Recent publications assumed the structural bending stiffness EI/a to be a constant and set it equal to the molecular bond bending stiffness C. By developing a closed form expression for the deformation of zigzag CNTs under simple tension, we suggest that the relation between EI/a and C is more complex. It actually depends on the bond bending stiffness C, the torsional angle φ and the lattice translational index n. In the limit of an infinite tube radius, which represents a graphene sheet, EI/a tends to C/2. Numerical simulations are also presented that validate the results.     

薄板弯曲分析的高阶高效无网格法

与传统有限元法相比,无网格法具有节点形函数高度光滑、易于形成高阶近似等优势,更适合于以薄板弯曲问题为代表的高阶偏微分方程的数值求解。然而,高阶无网格法的形函数是非多项式的有理函数,导致弱形式的区域积分难以得到精确计算,通常采用的高阶高斯积分方法需使用大量积分点,计算效率低且精度不高。本文针对薄板弯曲问题的高阶（三阶）无网格法分析,首次发展了与该高阶近似相一致的曲率光顺方案,并基于背景三角形积分单元建立了相应的数值积分格式,大幅度减少了所需的积分点数目。所发展方法的关键在于计算刚度阵所需的形函数的二阶导数由形函数及其一阶导数通过散度定理确定,而非对形函数直接求导获得。数值结果表明,基于标准的高斯积分方案的高阶无网格法精度不高,不能精确再现纯弯曲和线性弯曲模式,且得到的弯矩场分布存在严重的虚假数值振荡。而本文所建议的基于曲率光顺方案的高阶无网格法能够方便高效地求解薄板弯曲问题,尤其是它能精确反映纯弯曲和线性弯曲模式。与标准的高斯积分方法和目前主流的常曲率光顺方法相比,本文方法在计算效率、精度、弯矩分布等方面均展现出显著优势,因而具有较好的应用价值。     

基于均匀荷载面曲率的简支裂纹梁损伤识别

为了采用模态参数对结构裂纹进行定位与定量,基于集中柔度模型,采用无质量的扭转弹簧模拟裂纹,建立简支裂纹梁的振动微分方程。针对现有柔度曲率指标仅能判断裂纹的大致范围,基于线性插值理论,建立裂纹位置与相邻测点均匀荷载面曲率差的关系,提出裂纹进一步定位公式,实现裂纹位置的精确定位。针对现有大多数损伤识别方法无法实现裂纹的损伤定量,基于位移曲率与结构刚度和弯矩的关系,理论推导了均匀荷载面曲率的结构刚度损伤程度识别方法,基于弹簧串联原理和线刚度思想,首次提出串联等效线刚度模型,建立裂纹深度与均匀荷载面曲率的关系,实现裂纹深度的定量。通过简支裂纹梁数值算例,考虑多裂纹的损伤情况,验证了新方法对裂纹定位与定量的有效性。     

Post-buckling behaviour of slender structures with a bi-linear bending moment-curvature relationship

Certain classes of slender structures of complex cross-section or fabricated from specialised materials can exhibit a bi-linear bending moment-curvature relationship that has a strong influence on their global structural behaviour. This condition may be encountered, for instance, in (a) non-linear elastic or inelastic post-buckling problems if the cross-section stiffness may be well approximated by a bi-linear model; (b) multi-layered structures such as stranded cables, power transmission lines, umbilical cables and flexible pipes where the drop in the bending stiffness is associated with an internal friction mechanism. This paper presents a mathematical formulation and an analytical solution for such slender structures with a bi-linear bending moment versus curvature constitutive behaviour and subjected to axial terminal forces. A set of five first-order non-linear ordinary differential equations are derived from considering geometrical compatibility, equilibrium of forces and moments and constitutive equations, with hinged boundary conditions prescribed at both ends, resulting a complex two-point boundary value problem. The variables are non-dimensionalised and solutions are developed for monotonic and unloading conditions. The results are presented in non-dimensional graphs for a range of critical curvatures and reductions in bending stiffness, and it is shown how these parameters affect the structure's post-buckling behaviour.     

冠脉支架纵向柔顺性优化模型

柔顺性是冠脉支架主要的力学性能之一,因此改进支架的柔顺性是一个重要的研究课题。本文利用有限元方法建立了MACTM支架的悬臂梁结构模型,经过非线性数值模拟,发现该支架在弯曲时只有LINK构件发生变形,而且局部模型和整体模型的弯曲结果十分接近。根据上述结论,本文建立了对支架柔顺性进行优化的数学模型,利用ANSYS的一阶优化...     

冠脉支架纵向柔顺性数值模拟

柔顺性是冠脉支架重要的力学性能之一。本文针对一种具有非对称结构的冠脉支架,利用有限元方法深入研究与弯曲方向有关的支架柔顺性,在柔顺性数值模拟中使该支架获得较大的弯曲曲率并且考虑了接触因素。在一个周期结构内的多个弯曲方向上分别进行模拟,详细研究了支架抗弯刚度的各向异性。计算结果显示：在支架自接触现象发生前,支架的柔顺性表...     

考虑中性层位置变化的微悬臂梁气体传感器静态模型的分析

微悬臂梁是一种高灵敏度的生化传感器。本文考虑吸附表面应力引起的中性层位置的变化,采用能量法建立了微悬臂梁在单层分子吸附稳定后的静态弯曲模型,并以表面吸附有水蒸汽分子的微悬臂梁为例,研究了微悬臂梁曲率半径随其厚度、杨氏模量及吸附分子间距的变化规律以及中性层位置变化对微悬臂梁传感器性能预测的影响,结果发现：1)微悬臂梁的曲率半径与其杨氏模量、厚度及吸附分子间距之间可以近似用一次、二次和八次函数关系表示;2）中性层变化导致的曲率半径计算误差,随着微悬臂梁厚度、杨氏模量的增加而减小,但影响较小,而吸附分子间距会对该相对误差产生明显影响;3）中性层位置变化会对微悬臂梁传感器灵敏度和表面应变预测产生明显的影响。     

Single beam analysis of damaged beams verified using a strain energy based damage measure

Analytical expression of a new damage measure which relates the strain energy, to the damage location and magnitude, is presented in this paper. The strain energy expression is calculated using modes and natural frequencies of damaged beams that are derived based on single beam analysis considering both decrease in mass and stiffness. Decrease in mass and stiffness are a fallout of geometric discontinuity and no assumptions regarding the physical behavior of damage are made. The method is applicable to beams, with notch like non-propagating cracks, with arbitrary boundary conditions. The analytical expressions derived for mode shapes, curvature shapes, natural frequencies and an improved strain energy based damage measure, are verified using experiments. The improvement in the damage measure is that it is not assumed that the bending stiffness of the damaged beam is constant, and, equal to that of undamaged beam when calculating the strain energy of the entire beam. It is also not assumed that the bending stiffness of the element in which the damage is located is constant.     

Buckling and post-buckling of long pressurized elastic thin-walled tubes under in-plane bending

The present paper focuses on the structural stability of long uniformly pressurized thin elastic tubular shells subjected to in-plane bending. Using a special-purpose non-linear finite element technique, bifurcation on the pre-buckling ovalization equilibrium path is detected, and the post-buckling path is traced. Furthermore, the influence of pressure (internal and/or external) as well as the effects of radius-to-thickness ratio, initial curvature and initial ovality on the bifurcation moment, curvature and the corresponding wavelength, are examined. The local character of buckling in the circumferential direction is also demonstrated, especially for thin-walled tubes. This observation motivates the development of a simplified analytical formulation for tube bifurcation, which considers the presence of pressure, initial curvature and ovality, and results in closed-form expressions of very good accuracy, for tubes with relatively small initial curvature. Finally, aspects of tube bifurcation are illustrated using a simple mechanical model, which considers the ovalized pre-buckling state and the effects of pressure.     

Bending of a thin strip by a circular tool

We present a model of transverse bending of a wide thin elastic, elastoplastic, or rigid-plastic strip by a circular tool in the case of large displacements. The bending of the initial rectilinear strip is modeled by small increments in the load on the tool with analysis of the forces, moments, curvature, and the midline equation. The final form of the strip and the residual stresses are determined after elastic unloading. The model describes technological operations of sheet slab bending in dies and on roller-bending machines.     

Buckling analysis of pristine and defected graphene

The buckling behavior of monolayer graphene (pristine and vacancy-defected) and bilayer graphene (pristine) loaded in the armchair direction was simulated for different boundary conditions using a truss FE model, representing the exact atomic lattice of graphene, and a FE model of an equivalent 2D plate. The critical buckling stress of pristine monolayer graphene was derived as a function of aspect ratio. The results from the two FE models coincide and are in very good agreement with established analytical solutions. With increasing the aspect ratio, the critical buckling stress of monolayer graphene decreases until the value of 2 from which the effect starts to diminish. Using the truss FE model, the effect of randomly dispersed vacancies on the critical buckling stress and buckling mode of monolayer graphene was studied. It was found that the critical buckling stress decreases dramatically with increasing the defect density: for a defect density of 10%, the critical buckling stress decreases by almost 50%. Moreover, the presence of defects was found to affect the highest buckling modes (above 3) even at low densities. Bilayer graphene has a totally different critical buckling stress than monolayer graphene due to the effect of van der Waals forces which depends on the applied boundary conditions.     

Effects of inplane constraints and curvature on composite plate behavior

An investigation into the behavior of unsymmetrically laminated anisotropic plates is carried out. Using the basic assumptions of linear plate theory and strain-displacement relations modified to account for small initial curvature, energy formulations are established and the Ritz method utilized to obtain solutions for static deflections and natural frequencies of vibration. The boundary condition with particular inplane restraints and the particular stacking arrangement are shown to have important effects on plate response when bending-extensional coupling is present. Small initial curvature is shown to greatly increase natural frequencies and may obscure the effects of bending-extensional coupling due to nonsymmetrical layering. The increase in lateral stiffness due to curvature is also shown to depend heavily on fiber orientation, orthotropicity and boundary conditions.