U型波纹管及相关结构环向屈曲的有限元分析(Ⅰ)--基本方程及环板的屈曲

U型波纹管是现代管道系统中最常见的一种位移补偿器 ,它由环板和具有正、负Gauss曲率的半圆环壳组成 ,在管道所传输的介质的压力作用下会发生屈曲。其中环向屈曲最为复杂 ,精确的理论分析非常困难 ,有限元分析也不多见。作者在分析前人工作的基础上 ,以圆环壳段为单元 (特定的旋转壳段单元 ,能自动退化成环板单元 ) ,限于弹性范围和线性化特征值问题 ,对介质压力作用下U型波纹管及其相关结构 (圆环板、圆环壳、半圆环壳 )的环向屈曲问题进行了分析。考虑了结构屈曲前的弯曲 ,计及压力的二次势能 ,导出的应力刚度矩阵和载荷刚度矩阵是非对称的。全部工作分为三部分 :(Ⅰ )基本方程 ,环板的屈曲 ;(Ⅱ )圆环壳、半圆环壳的屈曲 ;(Ⅲ )波纹管平面失稳的机理。本文为第一部分 ,除推导公式外 ,对不同边界和不同内外径之比的环板在径向均匀压力作用下的环向屈曲进行了计算 (轴对称的径向屈曲作为特例得到 ) ,给出了前屈曲应力分布、临界载荷及相应的屈曲模态 ,并将临界压力的值与前人基于vonK偄ｒｍ偄ｎ大挠度板的精确解进行了比较 ,吻合良好。     

U型波纹管及相关结构环向屈曲的有限元分析(Ⅲ)--波纹管平面失稳的机理

波纹管无论是在内压还是在外压作用下都会发生环向屈曲或平面失稳,问题很复杂至今未得到妥善解决。本文首先指出了现行的有关“塑性铰”概念的某些不足之处,然后按文[8]的有限元法(考虑了屈曲前的弯曲和屈曲时载荷的转动并按线性化特征值问题处理)对波纹管的环向屈曲进行了计算,并与前人的有关实验进行了对比分析,在此基础上解释了波纹管平面失稳的原因和发展过程。     

45钢柱壳爆炸膨胀断裂的SPH模拟分析

金属柱壳爆炸膨胀断裂存在拉伸、剪切及拉剪混合等多种断裂模式,目前其物理机制及影响因素还不清晰。本文中采用光滑粒子流体动力学方法（smoothed particle hydrodynamics, SPH）对45钢柱壳在JOB-9003及RHT-901不同装药条件下的外爆实验进行了数值模拟,探讨柱壳在不同装药条件下发生的剪切断裂、拉剪混合断裂模式及其演化过程,模拟结果与实验结果一致。SPH数值模拟结果表明:在爆炸加载阶段,随着冲击波在柱壳内、外壁间来回反射形成二次塑性区,沿柱壳壁厚等效塑性应变演化呈凸形分布,壁厚中部区域等效塑性应变较内、外壁大;在较高爆炸压力（JOB-9003）作用下,柱壳断裂发生在爆轰波加载阶段,损伤裂纹从塑性应变积累较大的壁厚中部开始沿剪切方向向内、外壁扩展,形成剪切型断裂模式;而在RHT-901空心炸药加载下,虽然裂纹仍从壁厚中部开始沿剪切方向扩展,但随后柱壳进入自由膨胀阶段,未断区域处于拉伸应力状态,柱壳局部发生结构失稳,形成类似“颈缩”现象,裂纹从剪切方向转向沿颈缩区向外扩展,呈现拉剪混合断裂模式。拉伸裂纹占截面的比例与柱壳结构失稳时刻相关。可见,柱壳断裂演化是一个爆炸冲击波与柱壳结构相互作用的过程,不能简单将其作为一系列膨胀拉伸环处理。     

THE DETERMINATION OF BUCKLING POINT AND CRITICAL LOAD OF COMPRESSIVE MEMBER

为了分析压杆失稳的临界力与失稳后杆件屈服形态的关系,在理论推导和试验研究的基础上,提出了通过捕捉细长压杆失稳时的失稳点来确定压杆临界力的分析方法,通过测量细长压杆失稳时微弯状态下杆端的纵向位移,求得临界压力的大小. 文中将该方法的实验结果与直接用欧拉公式计算的临界压力进行了比较,结果表明,考虑细长压杆微弯状态时杆端的纵向位移所得到的失稳的临界压力值大于利用欧拉公式计算的临界压力值.     

有环壳过渡段的锥—柱组合壳的应力和稳定性

用解析方法计算了受静水外压载荷作用的有环壳过渡段的锥—柱组合壳中的应力值，并用瑞利法计算了其失稳临界载荷。计算结果说明，利用环壳过渡值锥—柱壳形成光滑连接，可使连接部位的局部应力值显著降低，并使失稳临界载荷有所提高     

易拉罐在轴-侧-扭-内压联合作用下的屈曲地貌

柱壳结构广泛应用于各个领域, 但由于其对初始缺陷较为敏感, 容易发生灾难性的屈曲失稳. 本文利用非线性有限元分析程序ABAQUS研究了柱壳屈曲问题, 并应用到了易拉罐的屈曲分析. 首先采用数值模拟的方法验证了Virot等学者的易拉罐屈曲试验结果, 然后为了获得屈曲的一些普适结果, 进一步考察了柱壳的屈曲表现. 对柱壳结构在不同载荷组合、不同几何参数作用下进行了细致分析. 为了讨论的直观, 本文绘制了柱壳结构在受到侧压-轴压载荷作用下外力-屈曲载荷-位移三维屈曲地貌图(称为landscape). 结果表明: 在侧压-轴压-扭转载荷作用下, 试件力-位移曲线出现了"cliff"(断崖)现象; 扭转载荷的施加不利于试件整体稳定性, 并造成了试件对初始缺陷的敏感性; 对于受到轴压-扭转载荷作用的试件, 本文定义承载力为零的平面为"sea level"(海平面)来区分试件破坏模式; 通过对不同边界条件的试件进行分析, 发现试件两端固定可以有效地增加结构的承载能力, 提高稳定性. 对柱壳结构内部充气可以大幅度提升结构的承载能力和稳定性, 减小对初始缺陷的敏感度.      

考虑范德华力曲率效应的双壁碳纳米管外压屈曲

针对双壁碳纳米管外压屈曲问题，研究了层间范德华力的曲率效应对临界外压的影响。应用弹性双层圆柱壳模型，考虑层间范德华力不仅与层间距有关而且与挠度曲率的变化有关，导出了外压屈曲临界压力解析公式。计算得出在不同半径、不同长细比下，外压屈曲临界压力的数值结果，并与经典壳的结果和忽略范德华力曲率效应的结果做了比较。结果显示，对于小半径的双壁碳纳米管曲率效应对外压屈曲有效明显的影响。     

均匀外压圆柱薄壳弹性稳定性的实验研究

本文提供十个精车圆柱薄壳在全面外压作用下弹性稳定性的实验研究结果.着重于描述壳体的失稳过程,基于实验现象,讨论了结构稳定性特征和弹性失稳概念. 实验给出“前波”现象的大致规律,并确认,应用渐近线准则,可以不破坏而又精确地确定临界载荷. 实验发现了“飘移”,“吃波”,“反跳”以及“超临界压力”等现象.O7试件在临界压力下稳压半小时,观察到应变飘移,波形相继长大以至最终崩溃的“慢放”全过程. 理论计算和实验结果的比较表明,对于精加工的中等长度壳体而言,较小的初挠度对临界压力并无显著影响.     

充内压的整体加劲圆柱壳承受轴压的稳定性

本文概述了充内压整体加劲圆柱壳承受轴压的稳定性的实验和理论研究结果.在非加劲圆柱壳和两种网格型整体加劲圆柱壳稳定性试验的基础上,讨论了充内压的整体加劲圆柱壳在轴压作用下的失稳特点.分析表明,可按过屈曲平衡状态的分歧点,近似地决定实际屈曲的总体失稳载荷.     

圆截面杆在曲线井中的屈曲问题

本文研究了线弹性的圆截面压杆在刚性井壁的曲线井中的屈曲问题。压杆两端为铰支，杆和井壁之间的摩擦力忽略不计，失稳前假设压杆位于曲线井的较低侧。分析了压杆屈曲时的几何变形条件，导出了压杆的曲率，变形能和各项外力势的表达式，用最小势能原理导出压杆失稳的微分方程和边界条件。引入梁单元，用有限单元法求得了压杆失稳时的临界压力和杆轴线状态。结果显示，临界压力随着压杆自重和曲线井半径的增加而增加。自重为零时，杆轴线为半个正弦曲线；自重不为零时，杆轴线为振荡的曲线，且振荡主要集中在压杆顶部。     

六边形桥墩柔性抗船撞装置抗弯刚度

针对中国自主研发的桥梁柔性抗船撞装置，构建该装置模型:由两个相似的六边形梁为内外钢围以及均布且垂直于六边形各边的防撞圈构成。分析该模型得到在冲击载荷作用下六边形梁的控制方程及相应的初边值条件。利用Laplace变换和数值Laplace逆变换对该方程进行求解，揭示六边形梁在冲击载荷作用下的动态响应。并进一步分析外钢围等效抗弯刚度对抗船撞装置动态响应的影响，发现外刚围结构在冲击载荷作用下存在临界等效抗弯刚度。当外钢围等效抗弯刚度达到该临界值后，该外钢围在冲击载荷作用下可以近似为刚性。     

Analysis of microbuckling for monomolecular layers adhering to a substrate

A two-dimensional linear spring model is established to study the microbuckling of a plane monomolecular layer adhering to a substrate. The model is for the layer subjected to a compressive load having an arbitrary angle with the chemical bond of the layer. The effects of the load angle, the strength of adhesion and the bending stiffness and shearing stiffness (the capability of resisting transverse bending and in-plane shearing) of the layer on the minimal buckling force and the critical buckling mode are discussed. It is found that the minimal buckling force increases with increasing load angle and, for a given bending stiffness, increases with increasing strength of adhesion and decreasing shearing stiffness. Furthermore, a critical condition under which the buckling of the layer can just occur is obtained, which is helpful to avoid buckling in an engineering application. The project supported by the National Distinguished Young Scientist Fund, Cheung Kong Scholars Programme, the National Natural Science Foundation of China (10272082, 10172068) and Shanghai Postdoctoral Science Foundation     

Experimental determination of stiffness properties of thin-shell composite cylinders

An experimental determination is made of the in-plane stiffness properties of 11 composite cylinders constructed by filament winding. All the cylinders have in-plane and bending stiffness matrices of orthotropic form. Also, five of the cylinders exhibit an anisotropic coupling between stretching and shear of the form described by Reissner and Stavsky. In-plane stiffness matrices are determined by the classical procedure of using three simple tests: internal pressure, axial tension or compression, and torsion. They provide the data from which to extract composite orthotropic moduli for filament-wound construction. Moduli thus determined are compared with those predicted by the recent theory of S. W. Tsai. Agreement is good when a value of 0.3 is assigned to his contiguity factor.J. Tasi was formerly Associate Research Scientist, Martin Co.; is now Post-Doctoral Fellow in Mechanics, The Johns Hopkins University, Baltimore, Md.Paper was presented at 1965 SESA Spring Meeting held in Denver, Colo., on May 5–7.     

Steady-state vibrations of an elastic beam on a visco-elastic layer under moving load

Summary  The steady-state response of an elastic beam on a visco-elastic layer to a uniformly moving constant load is investigated. As a method of investigation the concept of “equivalent stiffness” of the layer is used. According to this concept, the layer is replaced by a 1D continuous foundation with a complex stiffness, which depends on the frequency and the wave number of the bending waves in the beam. This stiffness is analyzed as a function of the phase velocity of the waves. It is shown that the real part of the stiffness decreases severely as the phase velocity tends to a critical value, a value determined by the lowest dispersion branch of the layer. As the phase velocity exceeds the critical value, the imaginary part of the equivalent stiffness grows substantially. The dispersion relation for bending waves in the beam is studied to analyze the effect of the layer depth on the critical (resonance) velocity of the load. It is shown that the critical velocity is in the order of the Rayleigh wave velocity. The smaller the layer depth, the higher the critical velocity. The effect of viscosity in the layer on the resonance vibrations is studied. It is shown that the deeper the layer, the smaller this effect. Received 22 March 1999; accepted 26 July 1999     

Stiffness threshold of randomly distributed carbon nanotube networks

For carbon nanotube (CNT) networks, with increasing network density, there may be sudden changes in the properties, such as the sudden change in electrical conductivity at the electrical percolation threshold. In this paper, the change in stiffness of the CNT networks is studied and especially the existence of stiffness threshold is revealed. Two critical network densities are found to divide the stiffness behavior into three stages: zero stiffness, bending dominated and stretching dominated stages. The first critical network density is a criterion to judge whether or not the network is capable of carrying load, defined as the stiffness threshold. The second critical network density is a criterion to measure whether or not most of the CNTs in network are utilized effectively to carry load, defined as bending–stretching transitional threshold. Based on the geometric probability analysis, a theoretical methodology is set up to predict the two thresholds and explain their underlying mechanisms. The stiffness threshold is revealed to be determined by the statical determinacy of CNTs in the network, and can be estimated quantitatively by the stabilization fraction of network, a newly proposed parameter in this paper. The other threshold, bending–stretching transitional threshold, which signs the conversion of dominant deformation mode, is verified to be well evaluated by the proposed defect fraction of network. According to the theoretical analysis as well as the numerical simulation, the average intersection number on each CNT is revealed as the only dominant factor for the electrical percolation and the stiffness thresholds, it is approximately 3.7 for electrical percolation threshold, and 5.2 for the stiffness threshold of 2D networks. For 3D networks, they are 1.4 and 4.4. And it also affects the bending–stretching transitional threshold, together with the CNT aspect ratio. The average intersection number divided by the fourth root of CNT aspect ratio is found to be an invariant at the bending–stretching transitional threshold, which is 6.7 and 6.3 for 2D and 3D networks, respectively. Based on this study, a simple piecewise expression is summarized to describe the relative stiffness of CNT networks, in which the relative stiffness of networks depends on the relative network density as well as the CNT aspect ratio. This formula provides a solid theoretical foundation for the design optimization and property prediction of CNT networks.     

复合材料加筋板铺层优化设计的等效弯曲刚度法

借助于等效弯曲刚度法和遗传算法,建立了一种复合材料加筋板铺层顺序优化设计算法.等效弯曲刚度法基于层合板的弯曲刚度与其失稳载荷一一对应的关系,将任意铺层顺序的层合板等效成一个只有8层的对称铺层的辅助层合板,通过优化辅助层合板,得到层合板的最优弯曲刚度参数,最后以获得的最优弯曲刚度参数为约束应用遗传算法进行铺层顺序优化,获...     

硬夹心矩形夹层板的整体稳定性分析

摘要：本文在Reissner型理论给出的位移模式基础上，修正其软夹心假设，考虑夹心层面内刚度，给出了硬夹心夹层板的几何方程、物理方程，建立了硬夹心夹层板结构在面内纵向载荷作用下的平衡微分方程，并对方程进行了简化，通过理论计算得到了四边简支条件下硬夹心矩形夹层板整体失稳临界载荷的解析解，并分别计算了夹心层材料的弹性模量 、厚度 、泊松比 对硬夹心夹层板临界载荷的影响，结果证明，对于硬夹心夹层结构，夹心层面内刚度对硬夹心夹层板整体失稳临界载荷的影响较大，考虑其面内刚度是必要的。     

侧柱对串列双柱脉动压力的干扰

研究了串列双圆柱旁加上一个等直径的圆柱，组成一个等边三角形排列的三圆柱的脉动压力分布．着重研究侧柱对串列双圆柱脉动压力分布的影响．研究的结果表明，绕流等边三角形排列的三圆柱，受影响最严重的是后柱．脉动压力分布出现了严重的不对称，外侧的压力脉动极其强烈，内侧的压力脉动较弱，与时均压力分布，很好的对应关系．另外，侧柱对于串列双圆柱是否达到超过临界间距的绕流流态，有很大的影响     

An experiment for determining the Euler load by direct computation

A direct algorithm is presented for computing the Euler load of a column from experimental data. The method is based on exact inextensional theory for imperfect columns, which predicts two distinct deflected shapes at loads near the Euler load. The bending stiffness of the column appears in the expression for the Euler load along with the column length; therefore, the experimental data allow a direct computation of bending stiffness. Experiments on graphite-epoxy columns of rectangular cross section are reported in the paper. The bending stiffness of each composite column computed from experiment is compared with predictions from laminated plate theory.     

Influence of concentrated lateral loads on the elastic stability of cylinders in bending

The character of the instability and the degradation of the moment-carrying capacity are found by Mylar model experiments for cylinders in bending when subjected to concentrated lateral loads. Lateral loads can seriously degrade the moment capability of cylinders. Critical combinations of moment and lateral load cause two distinct modes of failure—collapse and snapping. Collapse modes exhibit buckles which cover the compression half of the cylinder and are critical for large values of moment and small values of lateral load. Snapping modes of failure involve a single dimple and exist for smaller values of moment and larger values of lateral load.