Torsional buckling of spherical shells under circumferential shear loads

ＩｎｔｒｏｄｕｃｔｉｏｎＩｍｐｏｒｔａｎｔａｐｌｉｃａｔｉｏｎｓｏｆｔｈｅｓｔａｂｉｌｉｔｙａｎａｌｙｓｉｓｏｆｓｈｅｌｓｃａｎｂｅｆｏｕｎｄｉｎｔｈｅｍｏｄｅｒｎｅｎｇｉｎｅｒｉｎｇｒａｎｇｉｎｇｏｖｅｒｔｈｅａｅｒｏｓｐａｃｅ,ｍａｒｉｎｅ,ａｒ...     

薄壳失稳机理浅析

对薄壳失稳问题研究的理论与实验成果进行了总结和讨论，对薄壳后屈曲理论研究结果提出了不同的看法，同时应用动力学原理对薄壳失稳问题进行了探讨，并建立了计算模型。文中应用动力学原理描述了从加载初期的一个呈现静力学特征的薄壳随荷载的增加而逐渐成为一个呈现动力学特征的薄壳的过程，从薄壳受扰振动乃至共振的角度解释了失稳临界荷载实验数据值及其离散并低于失稳临界荷载理论值的原因。     

Axial compression buckling of conical and cylindrical shells

Experiments on the axial compression buckling of high-quality epoxy cylindrical shells with imposed dimpletype defects are described. Additionally, a technique for the manufacture of high-quality epoxy conical shells which buckle at loads approaching the classical critical load is presented. For both types of shells, prebuckling deformations have been monitored optically. The sizes of defects determined from the optical examination when applied in the space-frame approach to shell buckling have led to predicted knock-down factors which are remarkably consistent with measured knock-down factors (i.e., the ratio of actual collapse to classical critical load).     

New Asymptotically Sharp Korn and Korn-Like Inequalities in Thin Domains

It is well known that Korn inequality plays a central role in the theory of linear elasticity. In the present work we prove new asymptotically sharp Korn and Korn-like inequalities in thin curved domains with a non-constant thickness. This new results will be useful when studying the buckling of compressed shells, in particular when calculating the critical buckling load.     

爆炸冲击下复合材料层合扁球壳的动力屈曲

研究计及横向剪切的复合材料层合扁球壳在爆炸冲击载荷作用下的非线性轴对称动力屈曲问题。通过在复合材料层合扁球壳非线性稳定性的基本方程中增加横向转动惯量项并引入R.H.Cole理论的爆炸冲击力,得到爆炸冲击下复合材料层合扁球壳的动力控制方程,应用Galerkin方法得到用顶点挠度表达的爆炸冲击动力响应方程,并采用Runge-Kutta方法进行数值求解,采用Budiansky-Roth准则确定冲击屈曲的临界载荷,讨论了壳体几何尺寸对复合材料层合扁球壳冲击屈曲的影响;数值算例表明,此方法是可行的。     

轴向冲击载荷作用下弹性圆柱壳横向弯曲动态屈曲

研究在轴向冲击载荷下弹性圆柱壳动态屈曲问题.通过构造哈密顿体系,在辛空间中将临界载荷和动态屈曲模态归结为辛本征值和本征解问题.辛本征解反映了局部的压缩屈曲模态和整体的弯曲屈曲模态,特别是在冲击端为自由支承边界时的特殊屈曲方式.数值结果给出了具体的临界载荷和屈曲模态规律.     

Buckling analysis of stringer-stiffened laminated cylindrical shells with nonuniform eccentricity

In this study, the influence of nonuniformity of eccentricity of stringers on the general axial buckling load of stiffened laminated cylindrical shells with simply supported end conditions is investigated. The critical loads are calculated using Love’s First-order Shear Deformation Theory and solved using the Rayleigh-Ritz procedure. The effects of the shell length-to-radius ratio, shell thickness-to-radius ratio, number of stringers, and stringers depth-to-width ratio on the buckling load of nonuniformly eccentric shells, are examined. The research demonstrates that an appropriate nonuniform distribution of eccentricity of stringers leads the buckling load to increase significantly.     

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.      

矩形脉冲作用下复合材料层合扁球壳的冲击屈曲分析

研究了计及横向剪切的复合材料层合扁球壳在矩形脉冲载荷作用下的非线性动力屈曲问题;采用Galerkin方法得到以顶点挠度表达的动力响应方程,并用Runge-Kutta方法进行数值求解,应用Budiansky-Roth准则(简称B-R准则)确定冲击屈曲的临界荷载;讨论了壳体几何尺寸和物理参数对复合材料层合扁球壳冲击屈曲的影响;数值算例表明,该方法是可行的.     

轴向应力波作用下圆柱壳弹性轴对称动力失稳有限元特征值分析

本文运用有限元特征值分析方法对应力波作用下圆柱壳弹性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的有限元特征方程,在此方程中考虑了应力波效应及横向惯性效应,把圆柱壳弹性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳弹性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

局部轴压下圆柱壳的失稳分析

本文用传递矩阵法在初始缺陷法的概念下对圆柱壳的一端有四个类似集中力的局部轴压作用下的失稳问题进行了研究。     

外压对环肋圆柱壳轴向弹塑性动力屈曲的影响

采用增量理论,借助增量数值解法研究了复合加载（轴向流－固冲击载荷＋径向均匀外压）条件下环肋圆柱壳的弹塑性动力屈曲,采用类似B－R准则和Southwell方法来确定临界载荷,讨论了径向均匀外压对结构动力性态及抗轴冲击能力的影响。     

Buckling and Post-buckling Behaviour of Prismatic Aluminium Columns Submitted to a Series of Compressive Loads

The buckling and post-buckling behaviour of prismatic aluminium columns from stocky to very slender shapes is investigated. The unconventional, in terms of buckling tests, displacement control of compressive load and a series of loadings provided an enhanced insight into the buckling process. A phenomenon of buckling load drop has been detected in columns of intermediate slenderness, reaching over 20% of the load early critical value. This newly observed occurrence resembles finite disturbance instability, which until recently was commonly believed to only appear in cases of thin walled cylindrical shells, but not columns. The observation is in contradiction to predicted results from the elasto-plastic buckling models of Engesser or Shanley, with constant or growing values of load during the post-buckling process. Further tests on columns of intermediate slenderness, with strain gauges glued at node and anti-node locations of the buckled profiles, revealed that even minute buckling results in fields of highly non-symmetric residual microplastic strain. The results of the present study indicate that running column buckling tests under displacement control is worthy of being adopted as common practice. The envelope of column post-buckling states can be conveniently determined. This information will in turn allow for the quick and reliable estimation of the safety of a column, which has undergone accidental or deliberate damage in the form of limited buckling when under operational load.     

Nondestructive shell-stability estimation by a combined-loading technique

Accurate nondestructive procedures for cylindrical-shell-stability investigations have long been a goal of experimentalists and practicing engineers. Stability criteria based on stress and deflection have been investigated intensively by researchers, but lateral-stiffness variation has been largely ignored. It is this aspect which is the foundation of the present work. The variation of specimen lateral stiffness with compressive axial loading is studied experimentally and it is demonstrated that buckling loads can be predicted for monocoque shells from such data. A study of the initial specimen geometry is presented and an evaluation is made of its effect on the distribution of stiffness at zero axial load. When the lateral test force used to termine the stiffness is considered as a destabilizing load in combination with the axial compression, it is shown that critical values of the force can be estimated by the “Southwell plat” procedure. These critical forces can be correlated with axial load and extrapolated to yield an accurate estimate of the buckling load. The approach greatly reduces the compressive load necessary for stability predictions over that required for other techniques.     

Koiter circles in the buckling of axially compressed conical shells

As is well known, the elastic stability of shell structures under certain loading conditions is characterised by a severely unstable postbuckling behaviour. The presence of simultaneous buckling modes (‘competing’ modes corresponding to the same critical buckling load) is deemed to be largely responsible for such a behaviour. In the present paper, within the framework of the so-called classical theory (linear bifurcation eigenvalue analysis), the buckling behaviour of axially compressed cylindrical shells is firstly reviewed. Accordingly, doubly periodic eigenvectors (buckling modes) corresponding to the same eigenvalue (critical buckling load) can be determined, and their locus in a dimensionless meridional and circumferential buckling wavenumber space is described by a circle (known as the Koiter circle). In the case of axially compressed conical shells, no clear evidence of the existence of simultaneous buckling modes can be found in the literature. Then, such a problem is studied here via linear eigenvalue finite element analyses, showing that simultaneous doubly periodic modes do also occur for cones, and that their locus in a specifically defined dimensionless wavenumber space can be described by an ellipse (hereafter termed as the Koiter ellipse) whose aspect ratio is dependent on the tapering angle of the cone.     

A numerical calculation of dynamic buckling of a thin shallow spherical shell under impact

Assuming the deformation of the shell has an axial symmetrical form, we transform Marguerre's equations into difference equations, and use these equations to discuss the buckling of an elastic thin shallow spherical shell subjected to impact loads. The result shows when impact load acts on the shells, a jump of the shell takes place dependent on the values λ and the critical buckling load increases with the enlargement of the loading area.     

圆柱壳稳定性问题的研究进展

圆柱壳是工程实际中广泛应用的结构,其主要破坏形式是屈曲失稳．作为力学领域的经典问题,圆柱壳稳定性问题的研究非常之多．其中,受均匀轴向压力的圆柱壳由于临界屈曲载荷的理论预测值与早期试验结果之间的巨大差异,更是推动了壳体稳定性理论的不断发展．本文简要回顾了壳体稳定性理论的发展和分类,并对轴压圆柱壳体试验结果分散且远低于理论预测值的原因及含缺陷圆柱壳体的稳定性研究方法进行了总结,然后综述了地下空间顶管、储油罐、加筋圆柱壳及脱层圆柱壳等实际工程中广泛应用的圆柱壳结构稳定性研究的现状和趋势,最后展望了将来对工程应用中圆柱壳结构的稳定性研究的难点和方向．     

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     

弹性圆柱壳在轴向冲击载荷和温度耦合作用下的屈曲

通过引入哈密顿体系,将临界载荷和临界温度及它们所对应的屈曲模态归结为辛体系下的广义本征值和本征解问题。根据辛本征解的正交性和完备性,给出了全部的且独立存在的屈曲模态。数值结果表明,在轴向冲击载荷和温度耦合作用下,弹性圆柱壳的屈曲呈现出复杂的模式,温度直接影响冲击临界载荷的大小。随着温度的增加,冲击临界荷载降低,最后,文中给出各种条件下的屈曲模态。     

圆柱薄壳的动相变屈曲行为

利用MTS809材料试验机对TiNi圆柱薄壳进行了轴向动渐进相变屈曲实验,对轴向冲击下处于伪弹性状态的TiNi合金柱壳的动相变屈曲行为进行了数值模拟研究。结果表明,不同的加载强度将会激发出柱壳不同的动屈曲响应模态。当冲击速度较高时,柱壳两端首先形成轴对称环形相变屈曲波纹,并产生应力平台;随着马氏体含量不断增加,环形相变屈曲波纹逐渐贯穿整个壳体,名义应力缓慢抬升;当名义应变超过一定阈值时,对称环形屈曲模态突变为非轴对称块状屈曲模态,名义应力大幅下降。撞击速度为40 m/s的算例（含10％随机缺陷）与S.Nemat-Nasser等的实验结果很好吻合,说明本文中计算模型、方法和结果的有效性经过了实验的考核。结果还表明,相变耗能是TiNi柱壳吸收冲击能量的主要机制,适合制作可重复使用的高效吸能元件,并给出了相应的理想厚径比。