框架结构屈曲的精确有限元求解

基于屈曲微分控制方程的一般解，构造了Euler梁在轴力作用下的精确形函数，建 立了用于框架结构屈曲分析的精确有限单元，得到了单元刚度矩阵和几何刚度矩阵 的显式表达，并提出了基于常规特征值计算的迭代算法以确定屈曲载荷及相应失稳 模态的精确解. 研究表明， 对于线性稳定性分析而言，常规框架有限单元可视为 精确有限单元的一种近似. 若采用精确单元，无需进行网格细分就可以获得精确的 屈曲载荷和失稳模态. 数值算例证明了新单元和算法的效率和精度.     

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。     

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。     

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．     

受弯脱层层板后屈曲有限元分析

脱层是复合材料层板结构中主要的缺陷形式之一。当脱层层板受到压力载荷的作用会造成脱层的局部屈曲和扩展,从而使结构的强度和刚度大为降低。含脱层层板的弯曲问题包含了脱层的压缩问题,却比压缩问题更加复杂。本文对含穿透脱层层板在纯弯载荷作用下的后屈曲问题进行了基于一阶剪切层板理论的几何非线性有限元分析,运用虚裂纹闭合技术求解了纯弯载荷作用下的脱层尖端的能量释放率各型分量,并用脱层扩展判据求解了脱层起始扩展载荷。     

限制失稳模态方程及约束载荷计算

针对受压限制失稳结构,利用点接触、线接触屈曲模型,建立了杆在各种屈曲模态下的挠度曲线方程.通过求解曲线方程,可以得到发生限制失稳结构在各种屈曲模态下,与外部限制失稳构件之间的接触载荷大小,分析了受压结构与限制失稳构件之间的间隙对接触载荷的影响.通过对屈曲模态中各波形的形态进行调整,研究了同一屈曲模态,不同失稳波形下接触载荷的差异.     

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     

基于累积失效法的含损伤格栅加筋板非线性屈曲状态分析

分别采用基于Mindlin一阶剪切理论八节点层合板单元和三节点层合梁单元来模拟蒙皮和肋骨,用累积失效法研究了在压缩载荷作用下蒙皮内含分层损伤复合材料正交格栅加筋板的非线性屈曲性态,分析中考虑了加载过程中蒙皮和肋骨纤维断裂、基体损伤和纤维-基体剪切失效造成的刚度退化,并采用了非线性接触单元模型处理蒙皮分层上下子板间的接触效应。通过典型算例,讨论了蒙皮铺设方式、蒙皮分层的面积和深度、肋骨与蒙皮的刚度比,累积失效行为等因素对格栅加筋板非线性屈曲性态的影响。     

复杂载荷下复合材料对称层合板的椭圆形分层屈曲

应用Ｒａｙｌｅｉｇｈ－Ｒｉｔｚ法对含有单个椭圆形分层的复合材料对称层板在压剪载荷联合作用下的脱层屈曲问题进行了分析计算。给出相应于不同的椭圆长短半轴之比ａ／ｂ值下及不同椭回主轴的偏角时，脱层屈曲的临界应变值。此计算考虑了层板的拉伸剪切藕合刚度影响及子层本身弯曲－扭转耦合刚度，和拉伸－弯曲耦合刚度的影响，给出有工程参考价值的计算结果。     

复合材料多墙盒段弯扭耦合下的屈曲和后屈曲

针对复合材料典型多墙盒段，采用试验和有限元分析相结合的方法，研究了弯扭耦合载荷作用下的稳定性、承载能力及损伤起始、扩展情况．试验采用数字图像相关(Digital Image Correlation, DIC)测量方法捕捉试验件屈曲模态的变化过程，通过载荷-应变曲线获得屈曲和后屈曲破坏载荷．数值仿真基于ABAQUS/Explicit模块，采用Hashin准则结合刚度降的VUSDFLD子程序模拟复合材料的屈曲和后屈曲行为．研究结果表明，多墙盒段在弯扭载荷组合作用下发生屈曲时，扭矩会改变屈曲模态的分布形式和对称性，屈曲鼓包依然保持波峰、波谷交替出现；多墙盒段后屈曲阶段历程较长，屈曲模态由一阶向高阶逐渐发展，直到结构发生过大变形，彻底破坏而失去承载能力．     

受弯脱层层板的局部失稳临界载荷的有限元分析

含脱层的复合材料层板承受弯曲载荷作用会产生跳跃失稳，还常常引起脱层扩展，从而导致结构失效。本文用基于一阶剪切层板理论的几何非线性有限单元法分析了受弯曲曲载荷作用下含脱层板的人稳的临界载荷。本文指出分叉失稳产生了跳跃失稳，而该跳跃失稳与浅圆拱或薄圆柱壳受向心压力作用下的跳跌 同，在整体平衡路径上没有一个极限点。本文对临界载计算结果比使用能量准则的结果要小，文中给出了原因。     

Two-dimensional analyses of delamination buckling of symmetrically cross-ply rectangular laminates

The conventional approach to analysis the buckling of rectangular laminates containing an embedded delamination subjected to the in-plane loading is to simplify the laminate as a beam-plate from which the predicted buckling load decreases as the length of the laminate increases. Two-dimensional analyses are employed in this paper by extending the one-dimensional model to take into consideration of the influence of the delamination width on the buckling performance of the laminates. The laminate is simply supported containing a through width delamination. A new parameter β defined as the ratio of delamination length to delamination width is introduced with an emphasis on the influence of the delamination size. It is found that (i) when the ratio β is greater than one snap-through buckling prevails, the buckling load is determined by the delamination size and depth only; (ii) as the ratio β continues to increase, the buckling load will approach to a constant value. Solutions are verified with the well established results and are found in good agreement with the latter.     

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.     

含分层损伤复合材料层合板剩余压缩强度研究

准确预测含分层损伤层合板的剩余压缩强度,对复合材料具有十分重要 意义。本文基于层合板一阶剪切理论,建立了一种考虑复合材料多种损伤的含分层层合板刚度退化模型,通过数值算例分析了分层屈曲临界载荷与材料强度极限的关系以及刚度退化对含分层层合板前后屈曲行为的影响。     

考虑面内破坏过程的含分层损伤复合材料加筋层合板的动力响应

基于复合材料层合板一阶剪切理论，推导了复合材料层合板单元的刚度阵和质量阵列式；同时采用了Adams应交能法与Rayleigh阻尼模型相结合的方法，构造了相应的阻尼阵列式；为了防止在低阶模态中分层处出现的上、下子板不合理的嵌入现象，建立了含分层损伤复合材料加筋层合板动力分析的分层分析模型和虚拟界面联接模型。在上述模型和理论基础上，采用了Tsai提出的刚度退化准则和动力响应分析的精细积分法，对含分层损伤复合材料加筋层合板结构进行了动力响应和破坏分析。通过算例，分别讨论了外载频率、分层位置，以及破坏过程的刚度退化对含损伤复合材料加筋层合板动力响应特征的影响，得到了一些具有理论和工程价值的结论。     

Buckling of delaminated bi-layer beam-columns

An improved analytical model is presented to analyze the delamination buckling of a bi-layer beam-column with a through-the-width delamination. Both the transverse shear deformation and local delamination tip deformations are taken into consideration, and two delaminated sub-layers as well as two substrates in the intact (un-delaminated) regions are modeled as individual Timoshenko beams. A deformable interface is introduced to establish the continuity condition between the two substrates in the intact regions. Consequently, a flexible joint is formed at the delamination tip, and it is different from the conventional rigid joint given in most of studies in the literature, in which the local delamination tip deformations are completely ignored. In contrast to the local delamination buckling in our previous study (Qiao et al., 2010), the present model accounts for the global deformations of the intact region in the delaminated composite beam-column, thus capable of capturing the buckling mode shape transitions from the global, to global–local coexistent, and to local buckling for asymmetric delamination as the interface delamination increases. Good agreement of the present analytical solutions with the full 2-D elastic finite element analysis demonstrates the local deformation effects around the delamination tip and verifies the accuracy of the present model. Parametric studies are conducted to investigate the effects of loading eccentricity, delaminated sub-layer thickness ratio, and interface compliance on the critical buckling load for the delaminated composite beam-column. Transitions of buckling modes from the global to local delamination buckling are also disclosed as the thickness of one sub-layer reduces from the thick sub-layer to a thin film. The developed delamination buckling solution facilitates the design analysis and optimization of laminated composite structures, and it can be used with confidence in buckling analysis of delaminated composite structures.     

CONTACT ANALYSIS FOR FIBER-REINFORCED, DELAMINATED LAMINATES WITH KINEMATIC NONLINEARITY

A macro-micro analytical approach for the anti-penetrating contact problem at the interfaces of the delamination in symmetrically cross-plied,fiber-reinforced rectangular laminates is presented in this paper.The laminate is simply supported and subjected to a uniform transverse load with a through-width delamination buried at the center position.A contact factor is defined to characterize the contact efect and determined using the micro-mechanics of composite material.By analyzing the kinematics of nonlinear deformation at the interfaces of the delamination,the contact force is derived.Asymptotic solutions from perturbation analysis are presented.It is found that the deformation of the laminate involves a global deflection and a local buckling.The antipenetrating contact efects are characterized by the local buckling and are intrinsic properties of the laminates,relying only on the geometries of the delamination and the material properties.Parametric analyses show that the location and size of the contact areas and the distribution of the contact force are hardly afected by the aspect ratio.     

含分层损伤复合材料层合板分层扩展研究

采用基于Ｍｉｎｄｌｉｎ－阶剪切理论的四节点板单元,分析了含椭圆分层合板分层扩展行为。利用虚裂纹闭合技术计算分层前缘处的总能量释放率,并采用总能量释放率准则作为扩展准则,结合自适应网格移动技术,并考虑了分层前缘闭合接角效应,对 合材料层合板的分层扩展行为进行了模拟分析。结果表明,初始分层形状对其扩展有方式有限大影响。     

Energy release rate analysis of delamination in laminates

Delamination growth caused by local buckling of delaminated laminate under compression may lead the structure to failure. In this paper, a two-dimensional model of delaminated laminates was studied using a combination of post-buckling theory and fracture mechanics. The delaminated laminate under compression is first analysed by the first-order deformable plate thoery. Then, the energy release rateG at every point along the delamination front is derived by means of a variation problem with a moving boundary. Finally, the near-surface elliptical delamination is also discussed. There is a large variation of energy release rateG along the delamination front, the direction in which delamination growth may occur depends upon the delamination aspect ratio, the state of applied load and the orientation of plies.Supported by the Chinese Science Foundation of Aeronautics