锥壳的轴压屈曲

依据新的精确的锥壳屈曲分支方程 ,研究承受轴向压力的刚性圆顶夹支截锥壳的稳定性。构造的屈曲模态接近分支点变形。应用 Galerkin法计算了各种截锥比壳体在全锥度的临界特征值、屈曲荷载和临界应力。结果表明 ,轴压屈曲临界应力σcr 随几何参数ν的减小和截锥比λ的增大而减小。     

轴压圆柱壳后屈曲的有限元分析

采用流动的曲线坐标建立了大位移下的样条曲壳元，利用它分析了轴压圆柱壳的后屈曲问题。一个跨越和求取分支点的技巧和对弧长法的一个改进在文中提出。计算所得的载荷－轴向缩短曲线较解析解更接近于实验结果，所得的后屈曲波形也和实验相当符合。     

安全壳中钢衬壳热屈曲问题理论与实验研究(Ⅱ)──实验部分

钢衬壳热屈曲问题是核工程安全壳设计中的主要问题,但实验研究方面的文章发表得不多文中以200兆瓦核电站安全壳中钢衬壳为研究对象,采用局部1：1模型,测得了钢衬壳热屈曲温度和应变载荷,给出了钢衬壳屈曲和初始后屈曲过程中挠度和温度关系、以及膜应变和温度关系,实验测得钢衬壳具有局域屈曲的现象,实验屈曲载荷与理论结果符合较好     

安全壳中钢衬壳热屈曲问题理论与实验研究(II)--实验部分

钢衬壳热屈曲问题是核工程安全壳设计中的主要问题,但实验研究方面的文章发表得不多.文中以200兆瓦核电站安全壳中钢衬壳为研究对象, 采用局部1:1模型,测得了钢衬壳热屈曲温度和应变载荷, 给出了钢衬壳屈曲和初始后屈曲过程中挠度和温度关系、以及膜应变和温度关系, 实验测得钢衬壳具有局域屈曲的现象, 实验屈曲载荷与理论结果符合较好.     

金属圆柱壳受大质量低速冲击的屈曲变形

对钢质和铜质金属圆柱壳的轴向冲击动力响应进行了实验研究,记录了两种不同材料圆柱壳在大质量低速冲击下的冲击力时程曲线,得到其屈曲模态。采用高速摄像及模拟技术给出了钢质圆柱壳渐进屈曲的全过程,为理解钢质圆柱壳的屈曲机理提供了直观的结果。黄铜质圆柱壳在大质量低速冲击下, 出现整个壳面滿布屈曲波纹的塑性动力屈曲现象,说明高速冲击不是产生塑性动力屈曲的充要条件。像铜这样具有高密度的韧性材料,在大质量低速冲击下,会在轴向产生持续的压缩塑性流作用而出现塑性动力屈曲现象。     

安全壳中钢衬壳热屈曲问题理论与实验研究(I)———理论分析部分

钢衬壳热屈曲问题是核工程安全壳设计中的主要问题把铆固之间的钢衬壳视为钢衬板的特殊缺陷形式，利用Ｋｏｉｔｅｒ初始后屈曲理论分析了完善和具有初始缺陷钢衬壳的弹性热后屈曲性态给出了用挠度－温度载荷表示的钢衬壳的后屈曲平衡路径表达式和屈曲临界载荷表达式具体分析了三种钢衬壳模型：四点铆固钢衬壳、四边固支钢衬壳和五点铆固钢衬壳给出了钢衬的初始缺陷、锚钉间距、钢衬厚度等参数对钢衬热屈曲载荷的影响结果对安全壳中钢衬壳的设计有很好的参考价值     

钢衬壳后屈曲问题分析

本文用两种方法分析了核电站预应力混凝土安全壳中的内衬壳（钢衬壳）在温度应力作用下的后屈曲问题。认为钢衬壳模型是钢衬板模型的一种特殊缺陷形式，用Ｋｏｉｔｅｒ初始后屈曲渐近分析理论研究了钢衬壳的后屈曲问题。另外，本文从大挠度偏微分方程出发导出控制钢衬壳后屈曲的带有参数的非线性方程组，且用伪弧长法追踪其后屈曲平衡路径。文中用两种方法分析了四点铆固钢衬壳的后屈曲性态，并进行了比较。     

含内埋矩形脱层复合材料圆柱壳屈曲分析的混合变量条形传递函数方法

提出了一种分析含内埋矩形脱层正交各向异性圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于Mindlin一阶剪切壳理论,通过定义圆柱壳的广义力变量和混合变量,建立了壳的改进混合变量能量泛函;然后,为了便于脱层壳的分区求解,通过引入条形单元,创建了基于混合变量条形传递函数解的含脱层和不合脱层两种超级壳单元;在此基础上,将含内埋矩形脱层的复合材料层合壳划分成两种超级壳单元的组合体,通过各超级壳单元相互之间连接结点处的位移连续和力平衡条件得到脱层壳的屈曲方程;最后由屈曲方程计算含内埋矩形脱层壳的屈曲载荷和屈曲模态。算例分析的结果验证了本方法的正确性,并给出了几种因素对屈曲载荷和屈曲模态的影响。     

圆柱壳在静水压力作用下的塑性屈曲

由于航空和造船等部门大量采用板壳结构,所以,板壳的塑性屈曲问题引起了广泛的注意。所采用的理论大体上为塑性形变理论和塑性流动理论,在建立板壳的塑性屈曲方程时,有的考虑卸载,有的不考虑卸载。由于板壳的塑性屈曲实验结果与不考虑卸载的形变理论的结果比较接近,所以,大部分板壳塑性屈曲工作采用不考虑卸载的形变理论。对于圆柱壳在静水压力作用下的塑性屈曲问题也有过不少研究,      

基于弧长法的受压球壳稳定性分析

对受压球壳进行特征值屈曲分析,得到了前6阶屈曲模态及线性屈曲临界载荷;采用弧长法进行非线性有限元分析,对理想球壳施加初始扰动,通过2次扰动值折半的方法求得引起结构屈曲的最小扰动值,追踪到了屈曲分支点和全过程载荷-位移路线。基于前6阶屈曲模态位移,在受压球壳中分别引入2.5mm和1mm两种缺陷值,分析缺陷对球壳屈曲特性的影响。结果表明:取壳厚的0.5%即0.05mm时,得最小扰动值,近似模型与完善结构极值载荷的差值为0.93%;球壳是缺陷敏感性结构,缺陷的幅值和分布都对其极限载荷有影响,缺陷幅值与厚度比为0.1时,缺陷球壳承载力相对理想结构下降了约11%,缺陷幅值与厚度比为0.25时,承载力相对下降了约30%,说明提高球壳稳定性需要提高球壳加工精度。     

Dynamic torsional buckling of multi-walled carbon nanotubes embedded in an elastic medium

In this paper the dynamic torsional buckling of multi-walled carbon nanotubes （MWNTs） embedded in an elastic medium is studied by using a continuum mechanics model. By introducing initial imperfections for MWNTs and applying the preferred mode analytical method, a buckling condition is derived for the buckling load and associated buckling mode. In particular, explicit expressions are obtained for embedded double-walled carbon nanotubes （DWNTs）. Numerical results show that, for both the DWNTs and embedded DWNTs, the buckling form shifts from the lower buckling mode to the higher buckling mode with increasing the buckling load, but the buckling mode is invari- able for a certain domain of the buckling load. It is also indicated that, the surrounding elastic medium generally has effect on the lower buckling mode of DWNTs only when compared with the corresponding one for individual DWNTs.     

Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions

The paper studies the axisymmetric compressive buckling behavior of multi-walled carbon nanotubes (MWNTs) under different boundary conditions based on continuum mechanics model. A buckling condition is derived for determining the critical buckling load and associated buckling mode of MWNTs, and numerical results are worked out for MWNTs with different aspect ratios under fixed and simply supported boundary conditions. It is shown that the critical buckling load of MWNTs is insensitive to boundary conditions, except for nanotubes with smaller radii and very small aspect ratio. The associated buckling modes for different layers of MWNTs are in-phase, and the buckling displacement ratios for different layers are independent of the boundary conditions and the length of MWNTs. Moreover, for simply supported boundary conditions, the critical buckling load is compared with the corresponding one for axial compressive buckling, which indicates that the critical buckling load for axial compressive buckling can be well approximated by the corresponding one for axisymmetric compressive buckling. In particular, for axial compressive buckling of double-walled carbon nanotubes, an analytical expression is given for approximating the critical buckling load. The present investigation may be of some help in further understanding the mechanical properties of MWNTs.     

关于结构限制失稳的研究进展

限制失稳是指构件失稳时其屈曲变形不能自由发展而受到某种限制性约束的失稳,有时又称单向失稳、接触失稳、约束失稳.这类问题在工业中有大量应用,也是固体力学中的一个经典问题.最常见的实例如应用于地下管道、隧道、压力容器、核反应堆安全壳中的薄衬壳,当薄衬壳发生屈曲时,由于受到外壁的约束,其屈曲行为和一般的壳体屈曲行为不同,这就需要我们发展新的研究方法.另外如受钻井套管横向约束的钻柱的屈曲,复合材料的分层屈曲,电子元器件中的镀层屈曲等也属于限制失稳的范畴.限制失稳问题因其涉及接触问题、单向屈曲、非保守问题等而显得十分复杂,一直没有得到很好的解决.从近年来文献看,限制失稳的研究多集中在压杆、圆环的研究,板、壳的研究相对较少.本文首先简单介绍了限制失稳的一般概念,指出存在的限制约束对结构屈曲特性的影响.然后分别介绍了对于杆、环、板、壳的受限制失稳的研究进展.最后提出了需要进一步深入研究的问题.图11参75      

In-plane stability of arches

Classical buckling theory is mostly used to investigate the in-plane stability of arches, which assumes that the pre-buckling behaviour is linear and that the effects of pre-buckling deformations on buckling can be ignored. However, the behaviour of shallow arches becomes non-linear and the deformations are substantial prior to buckling, so that their effects on the buckling of shallow arches need to be considered. Classical buckling theory which does not consider these effects cannot correctly predict the in-plane buckling load of shallow arches. This paper investigates the in-plane buckling of circular arches with an arbitrary cross-section and subjected to a radial load uniformly distributed around the arch axis. An energy method is used to establish both non-linear equilibrium equations and buckling equilibrium equations for shallow arches. Analytical solutions for the in-plane buckling loads of shallow arches subjected to this loading regime are obtained. Approximations to the symmetric buckling of shallow arches and formulae for the in-plane anti-symmetric bifurcation buckling load of non-shallow arches are proposed, and criteria that define shallow and non-shallow arches are also stated. Comparisons with finite element results demonstrate that the solutions and indeed approximations are accurate, and that classical buckling theory can correctly predict the in-plane anti-symmetric bifurcation buckling load of non-shallow arches, but overestimates the in-plane anti-symmetric bifurcation buckling load of shallow arches significantly.     

结构动力屈曲研究进展

本文系统介绍了结构的振动屈曲、冲击屈曲研究进展,阐述了作为冲击屈曲极端情况的阶跃载荷下的动力屈曲问题。同时,结合所讨论的动力屈曲问题,对其屈曲准则和分析方法也进行了一般性讨论。     

Buckling of nano-fibre reinforced composites: a re-examination of elastic buckling

Elastic buckling of layered/fibre reinforced composites is investigated. Assuming the existence of both shear and transverse modes of failure, the fibre is analysed as a layer embedded in a matrix. Interacting stresses, acting at the interfaces are determined from an exact derived stress field in the matrix. It is shown that buckling can occur only in the shear buckling mode and that the transverse buckling mode is spurious. As opposed to the well known Rosen shear buckling mode solution (predicated on an infinite buckling wavelength), shear buckling is shown to exist under two régimes: buckling of dilute composites with finite wavelengths and buckling of non-dilute composites with infinite wavelengths. Based on the analysis, a model is constructed which defines the fibre concentration at which the transition between the two régimes occurs. The buckling strains are shown to be (approximately) constant for dilute composites and, in the case of very stiff fibres, to have realistic values compatible with elastic behaviour. For the case of non-dilute composites, the strains are found to be in agreement with those given by the Rosen shear buckling solution. Numerical results for the buckling strains and stresses are presented and compared with the Rosen solution. These reveal that the Rosen solution is valid only for the case of non-dilute composites. The investigation demonstrates that elastic buckling may be a dominant failure mechanism of composites consisting of very stiff fibres fabricated in the framework of nano-technology.     

等曲率井中有重钻柱屈曲的非线性有限元分析

建立了等曲率井中有重钻柱屈曲的平衡方程及对应的泛函表达式,用有限元法对等曲率井 中有重钻柱屈曲过程进行了分析,给出了钻柱正弦屈曲和螺旋屈曲临界载荷的定义. 力学模 型中考虑了重力、钻柱上端井斜角和井眼轨迹曲率半径对屈曲的影响. 分析结果表明：载荷 增大时,钻柱的下端先出现局部屈曲,随后屈曲向钻柱上部扩展,导致钻柱发生整体屈曲, 屈曲位移、井壁约束力线密度和钻柱弯矩都呈周期性变化;重力对等曲率井中钻柱的屈曲有 较强的抑制作用,其影响不可忽略;井眼轨迹曲率半径越小,钻柱上端井斜角越大则对钻柱 屈曲的抑制作用越强.     

弹性圆柱壳在轴向应力波传播过程中的非对称屈曲

讨论弹性圆柱壳端部受冲击载荷作用，在应力波传播过程中的非对称屈曲问题。通过求解扰动方程得到了动态屈曲的分叉条件、临界载荷和屈曲模态。数值结果表明，当壳壁厚不很薄时，轴对称屈曲临界载荷比非对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低。不同的冲击载荷，屈曲模态也将不同。     

薄宽带材局部纵向屈曲的辛弹性力学求解方法

局部纵向屈曲是普遍存在于薄宽带材生产过程的板形缺陷,是屈曲研究的难点,精确的解析求解方法对局部纵向屈曲形成机理的研究和板形质量的提高具有重要意义。本文将任意位置的局部纵向屈曲分为带材边部和内部两类,采用辛弹性力学方法直接推导得到了局部纵向屈曲区域承受不同边界约束条件时的临界屈曲应力和屈曲挠度函数,并将求解结果与有限元和相关文献结果进行了对比。结果表明：辛弹性力学方法与有限元方法相比具有相同计算精度和更高的计算效率,计算精度高于传统能量法;带材边界的约束条件对临界屈曲应力、屈曲区域几何形状和屈曲挠度函数均存在显著影响,验证了传统能量法求解的不足,有利于提高局部屈曲计算精度。     

DYNAMIC BUCKLING OF DOUBLE-WALLED CARBON NANOTUBES UNDER STEP AXIAL LOAD

An approximate method is presented in this paper for studying the dynamic buckling of double-walled carbon nanotubes （DWNTs） under step axial load. The analysis is based on the continuum mechanics model, which takes into account the van der Waals interaction between the outer and inner nanotubes. A buckling condition is derived, from which the critical buckling load and associated buckling mode can be determined. As examples, numerical results are worked out for DWNTs under fixed boundary conditions. It is shown that, due to the effect of van der Waals forces, the critical buckling load of a DWNT is enhanced when inserting an inner tube into a single-walled one. The paper indicates that the critical buckling load of DWNTs for dynamic buckling is higher than that for static buckling. The effect of the radii is also examined. In addition, some of the results are compared with the previous ones.