空间弹性细杆在扭矩作用下的屈曲

用有限元方法研究了三维弹性细杆在扭矩作用下的屈曲．利用自然坐标形式的细长空间曲杆的能量方程和2节点12个自由度的自然坐标形式的三维曲梁单元，采用特征值分析方法，研究分析了同时受有轴力和扭矩作用时的空间弹性细杆的屈曲问题．数值结果与存在的理论解极为吻合．具有一定曲率和挠率的空间细长曲杆，其临界扭矩值与扭矩的指向有着极其明显的关系．     

浅海内孤立波动态传播过程中声波模态强度起伏规律

内孤立波是一种常见于浅海海域的非线性内波,具有振幅大、周期短和流速强等特点,它通过扰动水体中的温盐分布使声速剖面产生明显的距离依赖性,进而影响水下声传播特性.内波自生成后通常以1 m/s量级的速度传播,运动的内波使声传播路径上的声波模态能量在空间和时间上剧烈起伏.本文定义模态强度为模态系数模值(模态幅度)的平方,并用其衡量各阶模态所含声能量的大小.文中基于耦合简正波理论,推导了内波运动时声波模态强度起伏的表达式,将模态强度表征为振荡项和趋势项的线性叠加.以往的工作大多局限于单独从时域或频域研究内波运动时声波模态强度的时变规律,本文则结合短时傅里叶变换在时频平面上揭示了模态强度的起伏机理.理论推导和数值仿真均表明内孤立波使各阶声波模态之间发生能量交换,即模态耦合.内波的动态传播进一步引起模态干涉,这种干涉效应表现为模态强度中的振荡项并使模态强度随时间快速起伏.受模态剥离效应(不同阶模态之间衰减系数的差异)的影响,趋势项的幅度随时间不断变化,进而对模态干涉引起的振荡叠加了时变的偏置.模态强度的整体走势和振荡项中各频率分量振幅的时变特征均与模态衰减密切相关.同时,本文使用深度积分声强作为总接...     

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.     

小球与均质自由杆的碰撞

讨论了小球与自由杆碰撞过程中所遵从的物理规律,明确了完全非弹性碰撞过程的能量特征,指出完全非弹性碰撞后两物体不一定粘在一起共同运动的事实.     

小球与均质定轴杆的碰撞

讨论了小球与定轴转动杆碰撞过程中所遵从的物理规律,进一步明确了完全非弹性碰撞过程的能量特征,指出完全非弹性碰撞后两物体不一定粘在一起共同运动的事实.     

带缺口加强圈的圆柱壳屈曲特性分析

以低温液体罐车外筒体为原型,采用有限元方法研究了带缺口加强圈的圆柱壳的屈曲特性。着重考察了加强圈缺口间的夹角、加强圈之间的间距、边界条件对此类结构屈曲载荷的影响。计算结果表明:圆柱壳的屈曲载荷与加强圈缺口间夹角不是简单的线性关系,当加强圈缺口间夹角增大到一定程度后,圆柱壳的屈曲载荷几乎不再变化;加强圈布置的均匀度不但会影响到圆柱壳的屈曲载荷,同时也对其屈曲模态产生影响;在不同的边界条件下,圆柱壳也表现出不同的屈曲特性。     

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.     

黏性流体中超细长弹性杆的动力学不稳定性

基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.     

基于能量修正法进行大尺寸指数型超声变幅杆准确设计

基于能量修正法修正了大尺寸变幅杆纵振动共振频率方程，得出了其修正频率表达式，分析了大尺寸指数型变幅杆的共振频率修正值，并利用有限元软件ANSYS对一组大尺寸指数变幅杆进行了模态分析。结果表明，比起一维理论值，修正后的频率值更接近于有限元仿真分析结果，变幅杆的尺寸越大（即径长比越大）这种修正效果越明显。     

金属铜的晶体结构与热力学性质的第一性原理计算

基于第一性原理,利用密度泛函理论(DFT)和密度泛函的微扰理论(DFPT),以及广义梯度近似(GGA),研究了过渡金属Cu的晶体结构、能量、电子能带和态密度、声子的能带结构和态密度,以及其在298.15 K下的热容,体积模量,格林艾森参数和体胀系数等热力学函数并与实验值作了对比.通过分析Cu的晶格几何与能量之间的关系,讨论了金属Cu的固-液相变与晶格声子振动能量之间可能的内在联系,首次提出直接得到Cu熔化温度T_m的静力学方法,研究了熔化温度与压强的关系.计算结果与实验值符合较好,明显优于分子动力学模拟的结果.     

Force chain buckling,unjamming transitions and shear banding in dense granular assemblies

Force chain buckling, leading to unjamming and shear banding, is examined quantitatively via a discrete element analysis of a two-dimensional, densely-packed, cohesionless granular assembly subject to quasistatic, boundary-driven biaxial compression. A range of properties associated with the confined buckling of force chains has been established, including: degree of buckling, buckling modes, spatial and strain evolution distributions, and relative contributions to non-affine deformation, dilatation and decrease in macroscopic shear strength and potential energy. Consecutive cycles of unjamming–jamming events, akin to slip–stick events arising in other granular systems, characterize the strain-softening regime and the shear band evolution. Peaks in the dissipation rate, kinetic energy and local non-affine strain are strongly correlated: the largest peaks coincide with each unjamming event that is evident in the concurrent drops in the macroscopic shear stress and potential energy. Unjamming nucleates from the buckling of a few force chains within a small region inside the band. A specific mode of force chain buckling, prevalent in and confined to the shear band, leads to above-average levels of local non-affine strain and release of potential energy during unjamming. Ongoing studies of this and other buckling modes from a structural stability standpoint serve as the basis for the formulation of internal variables and associated evolution laws, central to the development of thermomicromechanical constitutive theory for granular materials.     

Stability of rod-shaped nanoparticles embedded in an elastic matrix

In many biological tissues as well as in some technical materials we find nano-sized rod-shaped particles embedded in a relatively soft matrix. Loss of stability of equilibrium, i.e. buckling, is one of the possible failure modes of such materials. In the present paper different kinds of load transfer between matrix and reinforcing particles, which are typical for rod-shaped nanostructures in biological tissues, are considered with respect to stability of equilibrium. Two regimes of matrix stiffnesses leading to different modes of buckling, and a transition regime in between, have been found: soft matrix materials leading to the so-called ‘flip mode’ (also called ‘tilt mode’) and hard matrix materials resulting in ‘bending mode’ buckling. The transition regime is of particular interest for biological tissues. Numerical and semi-analytical as well as asymptotic concepts are employed leading to results for estimating the critical load intensities both in the form of closed form solutions and diagrams. The analytical solutions are compared with results of finite element analyses. From these comparisons indications are gained for deciding which of the different analytical approaches should be chosen for a particular nanostructure configuration in terms of the associated buckling modes.     

考虑介质膨胀速率的锂离子电池管状电极中扩散诱导应力及轴向支反力分析

硅作为锂离子电池阴极材料相对于传统负极材料具有高比容量,价格低廉等优势.本文针对充电过程中锂离子电池中电极建立力学模型和扩散模型,并在扩散模型引入考虑介质膨胀速率的影响.以硅空心柱形电极为例,分析了恒流充电下介质膨胀速率对电极中扩散诱导应力分布的影响,并研究了不同内外半径比、充电速率、材料参数以及锂化诱导软化系数(lithiation induced softening factor,LISF)对轴向的支反力达到临界欧拉屈曲力所需时间的影响.结果表明,随着电极中锂浓度上升,介质膨胀速率对应力分布的影响增大,对轴向的支反力影响较小.弹性模量和应力成正比,但其与轴向的支反力达到临界欧拉屈曲力所需时间无关;扩散系数与所需时间成反比;偏摩尔体积增大时,达到临界屈曲力所需时间减少;随着LISF绝对值增大,完全锂化时轴向力降低.     

Deformation of copper-filled single-walled boron-nitride nanotubes under axial compression

The buckling behaviors of copper–filled single-walled boron-nitride nanotubes (BNNTs) under axial compression are studied by molecular mechanics simulations. This study shows that the stability of this composite nanostructure (Cu@BNNT) gets better with the decrease of the tube diameter. An obvious decrease of the strain energy and vdW energy is observed at the onset of the global compressive buckling. Comparison of the axial compressing behavior between the Cu@BNNT(7,7) and Cu@BNNT(11,11) reveals that they have different buckling deformation and energy loss. Moreover, the stability of a BNNT filled with larger number of atoms is better than the one filled with small number of atoms.     

Stability and vibration of isotropic,orthotropic and laminated plates according to a higher-order shear deformation theory

A higher-order shear deformation theory is used to determine the natural frequencies and buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia. Exact solutions of simply supported plates are obtained and the results are compared with the exact solutions of three-dimensional elasticity theory, the first-order shear deformation theory, and the classical plate theory. The present theory predicts the frequencies and buckling loads more accurately when compared to the first-order and classical plate theories.     

Exact dynamic and static stiffness matrices of shear deformable thin-walled beam-columns

Total potential energy of non-symmetric thin-walled beam-columns in the general form is presented by introducing the displacement field based on semitangential rotations and deriving transformation equations between displacement and force parameters defined at the arbitrary axis and the centroid-shear center axis, respectively. Next, governing equations and force-deformation relations are derived from the total potential energy for a shear-deformable, uniform beam element and a system of linear eigenproblem with non-symmetric matrices is constructed based on 14 displacement parameters. And then explicit expressions for displacement parameters are derived and exact dynamic stiffness matrices are determined using force-deformatin relationships. In addition, the modified numerical method to eliminate multiple zero eigenvalues and to evaluate the exact static stiffness matrix is developed for spatial stability analysis. Finally, in order to demonstrate the validity and the accuracy of this study, the spatially coupled natural frequencies and buckling loads are evaluated and compared with analytical solutions or results analyzed by thin-walled beam elements and ABAQUS's shell elements.     

热力联合作用弹性薄圆板的弯曲与屈曲

 导出了热力联合作用下弹性薄圆板的弯曲动力响应控制方程,讨论了其弯曲变形特点及影响失效的因素。分析表明在短时热能沉积作用下,热屈曲是弹性薄板失效的主要方式之一;反鼓包或反冲塞是热屈曲的后继行为;增加外载和热能沉积功率水平都将加速热屈曲的发生;材料的温度相关性与热能沉积的时空分布对薄板的力学行为都有重要影响,同为产生和影响热剪切失效(反冲塞)的重要因素。     

Cascade processes of energy loss by emission of hard phonons

The method of cascade equations is used for studying the dynamics of the energy loss process (struggling) during passage of particles through a substance. Special attention is paid to multiphoton processes of emission of relativistic electrons in amorphous media and in oriented crystals. New analytic solutions to cascade equations are obtained and a method is developed for solving these equations, which makes it possible to express the results in terms of rapidly converging integrals. It is shown that the relatively simple Landau equation for the energy loss distribution function can be used for analyzing processes of energy loss commensurate with the initial energy of particles. The experimental data for 150-GeV electrons in oriented crystals are thoroughly analyzed.