Effects of imperfections on the buckling response of compression-loaded composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The results identify the effects of traditional and non-traditional initial imperfections on the non-linear response and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The non-traditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, non-uniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity non-linear shell analysis procedure that accurately accounts for the effects of these traditional and non-traditional imperfections on the non-linear responses and buckling loads of the shells is described. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable response characteristics.     

轴压层合结构脱层屈曲及其扩展研究进展

脱层及其进一步扩展可以降低层合结构的强度．首先简单介绍了脱层的一般概念、起因及其分类．从一维脱层、二维脱层和柱壳脱层三个方面介绍了脱层问题的研究概况．指出拉弯耦合和横向剪切效应对脱层结构的屈曲载荷和后屈曲特性影响很大;对于不同的材料特性和尺寸比率,脱层结构的屈曲模态和最终承载能力也不同．最后提出了需进一步深入研究的问题      

预应力杂交结构的屈曲分析

含有预应力索的半刚性大跨度空间结构是一种非常有生命力的杂交钢结构形式,对应用日益广泛的空间杂交结构的正确分析是保证结构安全设计的前提,屈曲分析通常是这类结构分析的主要内容之一,结构的屈曲分析可分为特征值屈曲分析和非线性屈曲分析。论文首先阐述了结构特征值屈曲分析和非线性屈曲分析中的分枝屈曲分析的基本理论,提出了含有恒定荷载的预应力结构特征值的求解方法,明确正确应用屈曲理论对保证工程安全设计的重要性,然后应用有限元软件ANSYS对待建的安徽大学体育馆新型弦支网壳屋盖结构进行了特征值屈曲分析和分枝屈曲分析,提出应用通用有限元程序跟踪结构分枝屈曲路径的方法,本文结论对预应力杂交结构的屈曲分析具有指导意义。     

含内埋圆形或椭圆形脱层复合材料层合板的屈曲分析

用瑞里-李兹方法来建立含内埋圆形或椭圆形脱层板的屈曲分析模型．首先利用Heaviside阶梯函数，假定一种适合于脱层板的位移模式．然后由变分原理并进行线性化得出了含内埋圆形或椭圆形脱层板的屈曲特征方程．最后通过将含表面脱层的各向同性和各向异性板的屈曲载荷与其它文献进行比较，验证了该文分析方法的正确性，并分析了含内埋圆形或椭圆形脱层的各向同性、正交各向异性和角铺层层合板各种参数对屈曲载荷的影响．     

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。     

Buckling load of non-linear systems with multiple eigenvalues

For structural systems with a coincident lowest eigenvalue λ_c, the influence of imperfections on the buckling of the systems depends to a very large extent upon the distribution of the imperfections. Moreover, the system may buckle either at a limit point or at a bifurcation point before this limit point is reached. Considering both possibilities, a lower bound to the buckling load of the system, for a given root mean square of the imperfections, is obtained. Furthermore, with reference to a set of particular, normalized co-ordinates, it was found that the absolute minimum buckling load is given by an imperfection vector parallel to the steepest of all post-buckling paths intersecting at λ_c. At this absolute minimum buckling load the critical point is a limit point. As an example, the lower bound to the buckling load of an imperfect cylindrical shell under axial compression was calculated.     

含脱层损伤复合材料层合梁冲击动力响应实验研究

对纤维增强复合材料层合梁在受轴向冲击时的动力响应问题进行了实验研究。实验以单向玻璃纤维布和环氧树脂材料制作试件,在层间预埋薄铜箔模拟脱层损伤。采用激光测速仪测量子弹速度,动态应变仪和TDS420A数字示波器记录应变时程曲线进行动力响应分析。实验结果表明铺层角度是决定材料性能的主要原因,脱层损伤的存在及大小对动力响应和发生动力屈曲有重要影响。此外,初始缺陷的影响也是不可忽视的重要因素。     

有初始几何缺陷的壳体弹塑性大变形分析

本文在等温小变形弹塑性内时本构方程偏量形式的基础上，导出了适用于大位移、大转动、小应变分析的弹塑性内时本构方程，进一步推导出了带有初始几何缺陷的非线性弹塑性问题的有限元方程，可用于分析缺陷对结构非线性弹塑性反应的影响，也可用于带缺陷的非线性问题求解及稳定性分析．     

考虑周长约束的圆柱薄壳初始几何缺陷随机场建模方法

利用随机场对圆柱薄壳结构的初始几何缺陷进行建模，并据此建立了一种用于含初始几何缺陷轴压圆柱薄壳屈曲分析的随机分析方法。首先，指出已有将圆柱薄壳初始几何缺陷表征为二维高斯随机场的方法会导致与实际不相符的初始几何缺陷，如圆柱周长显著增大或缩小的几何缺陷。其次，提出一种考虑周长不变约束的随机场建模方法，以剔除与实际不相符的随机几何缺陷。最后，基于所建立的初始几何缺陷随机场模型，利用非干涉多项式混沌展开法进行圆柱薄壳的随机屈曲分析，给出临界屈曲载荷的概率分布。数值试验结果表明，基于随机场理论的初始几何缺陷建模方法可有效刻画几何缺陷对结构承载能力的影响，而提出的约束随机场建模方法又能有效减小结果的分散性。     

A Motion Amplifier Using an Axially Driven Buckling Beam: II. Modeling and Analysis

In this paper, the nonlinear behavior of a motion amplifier used to obtain large rotations from small linear displacements produced by a piezoelectric stack is studied. The motion amplifier uses elastic (buckling) and dynamic instabilities of an axially driven buckling beam. Since the amplifier is driving a large rotary inertia at the pinned end and the operational frequency is low compared to the resonant frequencies of the beam, the mass of the buckling beam and the dynamics of the PZT stack are neglected and the system is modeled as a single-degree-of-freedom, nonlinear system. The beam simply behaves as a nonlinear rotational spring having a prescribed displacement on the input end and a moment produced by the inertial mass acting on the output end. The moment applied to the mass is then a function of the beam end displacement and the mass rotation. The system can, thus, be modeled simply as a base-excited, spring–mass oscillator. Results of the response for an ideal beam using this reduced-order model agree with the experimental data to a high degree. Inclusion of loading and geometric imperfections show that the response is not particularly sensitive to these imperfections. Parameter studies for the ideal buckling beam amplifier were conducted to provide guidance for improving the design of the motion amplifier and finding the optimal operating conditions for different applications. An erratum to this article can be found at     

脱层梁屈曲的高阶剪切理论

脱层的存在将会大大降低层合结构的屈曲载荷。该文将含任意位置脱层的两端固支梁分成多段子层,用厚度的三次多项式模拟脱层梁屈曲时子层的轴向位移,利用变分原理和欧拉方程导出了脱层梁的屈曲方程和定解条件,并用状态空间方法进行求解。通过与一阶剪切理论和经典理论的比较,指出了它们各自的适用范围;考虑了脱层梁三种不同的屈曲模态。分析了脱层长度、深度、位置和材料的铺层方向对脱层梁屈曲载荷的影响;最后给出了多处简单脱层的屈曲分析。     

Nonlinear delamination buckling and expansion of functionally graded laminated piezoelectric composite shells

In this paper, an analytical method is presented to investigate the nonlinear buckling and expansion behaviors of local delaminations near the surface of functionally graded laminated piezoelectric composite shells subjected to the thermal, electrical and mechanical loads, where the mid-plane nonlinear geometrical relation of delaminations is considered. In examples, the effects of thermal loading, electric field strength, the stacking patterns of functionally graded laminated piezoelectric composite shells and the patterns of delaminations on the critical axial loading of locally delaminated buckling are described and discussed. Finally, the possible growth directions of local buckling for delaminated sub-shells are described by calculating the expanding forces along the length and short axis of the delaminated sub-shells.     

圆弧拱考虑一般缺陷的面内屈曲

研究了几何缺陷、荷载非均匀分布和支座沉陷对圆弧拱面内屈曲的影响.基于能量的变分原理推导了考虑缺陷的微分方程,得到了外荷载和轴力的关系式以及径向位移的表达式.从微分方程出发用摄动法对屈曲荷载的缺陷敏感性进行了分析,得到了屈曲荷载的近似表达式.结果表明近似解与精确解吻合良好;正对称屈曲荷载对正对称缺陷参数十分敏感;反对称缺陷参数对反对称屈曲荷载影响显著而正对称缺陷参数影响很小.     

弹性基础上的杆在轴压下的二次屈曲

本文研究弹性基础上受轴向加载的两端铰支杆当其最低两屈曲荷载很近时的后屈曲行为。首先,使用Liapunov-Schmidt约化并借助稳定性分析,揭示了杆的二次屈曲现象;基于分叉方程给出了原始后屈曲分支及二次分支的渐近展开。其次,我们使用作者建立的二次分叉的计算方法对杆的二次屈曲做了数值计算,数值结果与渐近展开符合得很好     

Columns with Random Imperfections and Associated Bracing Requirements

Abstract

The imperfections in the form of initial displacement in structural columns are important factors to be reckoned with. To investigate the effect of imperfections and to obtain the results of general valadity, imperfections in columns should be considered as random in nature. In this paper, the effect of imperfection on column behavior and load carrying capacity is examined. The imperfections are modeled by a stochastically stationary random process with a known autocorrelation function. The results for the expected reduction in column capacity and the bending moments due to imperfection are obtained. The problem of lateral bracings, provided in columns to prevent buckling in their weaker planes and thereby increase their load carrying capacities, is also examined probabilistically: the effect of random initial displacements on the strength and stiffness requirements of a bracing is investigated.     

On stability of cylindrical shells of variable thickness with initial imperfections

The paper outlines a numerical method for stability analysis of cylindrical shells with initial imperfections. We solve a nonlinear buckling problem for a cylindrical shell with variable wall thickness under surface pressure. The imperfections of the shell are modeled as the first buckling mode. A probabilistic approach is used to determine the reliability against buckling of the cylindrical shell with the probability density of initial imperfections represented by uniform distribution, triangular distribution, or Gaussian distribution     

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通过对拱顶储罐罐壁承受轴向载荷、初始几何缺陷及轴压失稳状况研究,指 出在固定顶罐设计、建造和运行各阶段都应进行罐壁轴压稳定性校核. 根据圆柱薄壳稳定性 理论和轴压失稳临界应力数值分析计算结果,提出固定顶罐罐壁轴压稳定性校核方法和数学 模型,并运用回归分析方法建立罐壁轴压失稳临界应力计算公式. 对几种常用规格的拱顶罐 有初始挠度缺陷罐壁轴压稳定性分析表明：随储罐容积和罐壁初始挠度增大,罐壁轴压稳定 性呈减弱趋势.     

Nonlinear buckling optimization of composite structures considering “worst” shape imperfections

Nonlinear buckling optimization is introduced as a method for doing laminate optimization on generalized composite shell structures exhibiting nonlinear behaviour where the objective is to maximize the buckling load. The method is based on geometrically nonlinear analyses and uses gradient information of the nonlinear buckling load in combination with mathematical programming to solve the problem. Thin-walled optimal laminated structures may have risk of a relatively high sensitivity to geometric imperfections. This is investigated by the concepts of “worst” imperfections and an optimization method to determine the “worst” shape imperfections is presented where the objective is to minimize the buckling load subject to imperfection amplitude constraints. The ability of the nonlinear buckling optimization formulation to solve the laminate problem and determine the “worst” shape imperfections is illustrated by several numerical examples of composite laminated structures and the application of both formulations gives useful insight into the interaction between laminate design and geometric imperfections.     

Buckling analysis of two layer delaminated beams with bridging

Stitching has been used as through-thickness reinforcement to reduce the effects of delamination. In stitching, the delamination will be held by stitches in the form of crack/interface bridging. In the present work, the reinforcement of stitching threads is assumed to provide continuous linear restoring tractions opposing the delamination opening. A generalized mathematical model is developed to study the buckling analysis of two layer delaminated beams with bridging by using Rayleigh–Ritz energy method. The delaminated beam is analyzed as four interconnected beams using the delamination as their boundary. Lagrange multipliers are used to enforce the boundary and continuity conditions between the junctions of the interconnected beams. The developed mathematical model is solved as an eigenvalue problem in which the lowest eigenvalue gives the buckling load. Effective-bridging modulus, a new nondimensionalized parameter, is introduced to study the influence of bridging on the delamination buckling. It is shown that bridging strongly influences the buckling load of the delaminated beams and a monotonic relation is observed between the buckling load and the effective-bridging modulus. Parametric studies in terms of delamination sizes and locations along spanwise and thicknesswise positions on the buckling load have been carried out. The bridging is found to be effective for shallow delaminations of moderate length, and for deep and long delaminations. Spanwise positions of delamination strongly influence the buckling loads. In addition, an analytical model for obtaining upper bounds of the buckling load is developed by using Euler–Bernoulli beam theory. Effective-slenderness ratio, a new nondimensionalized parameter is defined and it is found to be controlling the buckling mode configurations, i.e., local, global and mixed modes.     

Mode Interaction in Thin-Walled Structural Members∗

Thin-walled structural members are susceptible to failure by interaction of local and overall modes of buckling. A comprehensive analytical approach that employs finite strips and the theory of mode interaction is outlined for study of the problem. Theoretical predictions of collapse loads agree well with the experimental results, despite the uncertainty caused by the lack of data on local imperfections of experimental specimens. Illustrative examples explore to some extent the following specific questions: optimality of design for simultaneous buckling, imperfection-sensitivity of compression members having unstiffened plate elements, and the nature of interaction of local and lateral-torsional buckling.