不圆度对圆环和圆管静水压力下临界荷载的影响

采用最小二乘法求解曲率半径对称波动变化的非理想圆环在均匀静水压力作用下的平面内稳定性问题,分别求得了反对称屈曲和对称屈曲的临界荷载系数。当不圆度参数β=0．4时,反对称屈曲的临界荷载系数降低67．71％。用最小相对误差拟合法得到了精度较高的临界荷载系数拟合公式,其最大相对误差仅为土0．76％。采用平面应变假设,推广得到...     

反对称横向荷载作用下钢梁的弹性弯扭屈曲研究

为了建立反对称横向荷载作用下双轴对称截面简支钢梁弹性弯扭屈曲的设计理论,考虑荷载比例系数ψ的影响,推导了反对称横向荷载作用下钢梁的弯扭屈曲总势能方程。采用Rayleigh-Ritz法得到了反对称横向荷载作用下钢梁弹性临界弯矩M_(cr)的通用计算式以及系数C_1、C_2的计算式,并总结了荷载比例系数ψ对临界弯矩的影响规律。采用有限元法对本文理论公式进行了验证,当0≤ψ≤4时,临界弯矩M_(cr)的理论解与有限元解吻合良好;当ψ4时,临界弯矩收敛于ψ=4时的值。在此基础上,通过线性回归分析,拟合出了等效弯矩系数C_b与荷载比例系数ψ以及跨长影响系数ξ之间的近似关系式,C_b的近似解与有限元解吻合较好,最大误差为6.5%,大部分工况下误差控制在5%以内。该拟合公式适用性较强,精度较高。     

四种非正交边界板考虑初始荷载效应的后期荷载位移近似解

基于考虑初始荷载效应情况下板的一般形式的静力平衡微分方程,运用坐标变换得到了轴对称情形,考虑初始荷载效应后圆形板的极坐标形式的静力平衡微分方程。运用Galerkin法解得了简支等边三角形板、固支椭圆板、固支圆形板和简支圆形板四种非正交边界板考虑初始荷载效应的后期荷载位移近似解。运用相关文献提出的有限元法验证了近似解的正确性。各位移近似解表达式简单、物理意义明确,清楚地反映了初始荷载及相关因素对后期荷载位移的影响。计算分析表明：初始荷载效应提高了板的弯曲刚度,减小了板的后期荷载位移;板的初始荷载效应主要受初始荷载、跨厚比及边界条件等因素的影响。     

撑杆式预应力钢压杆屈曲形态函数研究

基于撑杆式预应力钢压杆正对称和反对称两个基本屈曲模态, 给出了相应的 屈曲形态函数, 通过3个典型算例并变化关键参数着重研究了模拟曲线项数, 同时 给出了不对称屈曲的形态函数. 研究表明, 取形态函 数模拟项数为预应力钢压杆节间数, 可以很好满足工程精度.     

反对称铺设复合材料层合板非线性后屈曲分析

基于层合板壳理论,考虑反对称铺设层合板的拉弯耦合效应和后屈曲过程中的非线性几何变形,推导了由应力函数和挠度表示的复合材料层合板的后屈曲控制方程。引入无量纲参数对控制方程和边界条件进行无量纲化,以消除材料参数及几何尺寸对分析结果的影响。采用摄动法将无量纲的非线性控制方程及边界条件展开成一系列非齐次线性摄动方程组,分析各阶摄动方程的通解与特解的构造,并逐次求解,建立了反对称铺设复合材料层合板受单向均布压力作用的临界屈曲荷载及后屈曲平衡路径的理论解。进而运用ABAQUS软件对复合材料层合板在面内压缩载荷作用下的屈曲和后屈曲进行有限元分析,结果表明理论解与ABAQUS结果十分接近,验证了理论解的正确性。在此基础上进一步讨论了铺设角度、铺设层数和拉弯耦合效应等对层合板后屈曲性能的影响。研究发现层合板的屈曲载荷受铺设角度与层数的影响较为显著,而拉弯耦合效应使板的屈后强度大大降低。     

均布压力作用下圆弧双铰拱对称和反对称失稳的折迭突变和尖点突变模型

建立了径向均布压力作用下圆弧双铰拱正对称失稳和反对称失稳的折迭和尖点突变模型，模型可以很好地描述这两个失稳过程的各种性态，求解拱失稳时的临界荷载，给出拱屈曲后路径与荷载的初步关系。     

考虑横向剪切变形矩形底中厚扁壳的屈曲研究

基于考虑横向剪切变形直角坐标下矩形中厚扁壳的几何方程、本构关系、平衡方程,建立了关于三个中面位移和两个中面转角为独立变量的矩形中厚扁壳小挠度屈曲的基本微分方程。该方程可退化为矩形中厚板屈曲的基本微分方程,从而说明本文推导过程的正确性及一般性。文中矩形中厚扁壳小挠度屈曲的基本微分方程是一组耦合的变系数二阶偏微分方程,对常曲率扁壳使用双重三角级数并将其作为广义坐标对该方程组进行解耦,进一步建立中厚扁壳小挠度屈曲的特征方程,并得到了简支矩形中厚壳屈曲的临界荷载表达式,最后获得了其屈曲的临界荷载曲线及其相应的临界荷载值。该临界荷载曲线及其相应的临界荷载值可以退化为矩形中厚板的临界荷载曲线及临界荷载值。结果表明：本文提出的算法求解过程简便,矩形中厚扁壳临界荷载收敛较快。     

中厚夹层圆柱扁壳的屈曲分析

基于一阶剪切变形中厚圆柱壳理论,考虑夹心层的面内刚度,根据中厚夹层圆柱扁壳的几何方程、本构关系、平衡方程,建立了中厚夹层圆柱扁壳小挠度屈曲的微分方程;应用广义傅里叶级数解法,得到了四边简支条件下中厚夹层圆柱扁壳屈曲的临界荷载表达式。该表达式可以退化为硬夹心夹层板的表达式,表明本文推导过程的正确性。本文还讨论了夹心层的弹性模量和泊松比以及中厚夹心圆柱扁壳的长宽比和厚度对扁壳屈曲荷载的影响。结果表明:临界荷载与夹心层的弹性模量和泊松比成正比,与扁壳的长宽比和厚度成反比。     

S型功能梯度扁球壳非线性屈曲的渐近分析

本文利用渐近迭代法获得了边界弹性支撑的功能梯度扁球壳的非线性屈曲问题的理论解．假设材料组分体积分数沿壳体厚度方向呈sigmoid幂函数变化,边界上考虑一般的弹性支撑约束．基于经典的薄壳理论和几何非线性关系,导出了S型功能梯度扁球壳的非线性屈曲问题的控制方程．采用渐近迭代法通过两次迭代得到了无量纲挠度和均布荷载之间的非线性特征关系．通过与已有有限元方法和其他数值方法的结果对比,验证了本文解的有效性和高精度．同时,通过计算阐述了缺陷因子、材料参数、边界约束系数及特征几何参数对壳体临界屈曲荷载的影响．     

初始纵横向荷载效应对薄板自振频率的影响分析The analysis for the effect of both initial in-plane and transverse loads on the natural frequency of plates

首先基于能量变分原理,给出了同时考虑初始纵向、横向荷载效应情况下板的应变能表达、动力平衡微分方程及单元刚度矩阵。再以动力平衡微分方程为基础,运用伽辽金法解得四种典型板同时考虑初始纵向、横向荷载效应的基频近似解,并运用瑞利法解得简支矩形板考虑初始纵向、横向荷载效应的前三阶频率近似解。然后相互验证了考虑初始纵向、横向荷载效应的板单元刚度矩阵和频率近似解的正确性,并进一步分析了初始纵向、横向荷载及相关因素对板自振频率的影响。结果表明,考虑初始纵向、横向荷载效应后,板的自振频率主要受初始纵向荷载、初始横向荷载、板的厚度及边界条件等因素的影响;初始纵向、横向荷载效应对板的基频影响明显于高阶频率;初始纵向、横向荷载对板的自振频率影响分别呈线性和抛物线规律。     

Imperfection sensitivity of curved panels under combined compression and shear

The initial buckling load of curved panels under compressive loads is substantially reduced by the existence of imperfections, in particular geometric imperfections. It is therefore essential that these imperfections are considered in analysing components which incorporate such panels in order to accurately predict their buckling behaviour. Finite element analysis allows fully non-linear analysis of shells containing geometric imperfections, however, to obtain accurate results information is required on the exact size and shape of the imperfection to be modelled. In most cases this data is not available. It is therefore generally recommended that the imperfections are modelled on the first eigenmode and have an amplitude selected according to the manufacturing procedure. This paper presents the effects of varying imperfection shape and amplitude on the buckling and postbuckling behaviour of one specific case, a curved panel under combined shear and compression, to test the accuracy of such recommendations.     

Thermomechanical postbuckling of composite laminated cylindrical shells with local geometric imperfections

The effect of local geometric imperfections on the buckling and postbuckling of composite laminated cylindrical shells subjected to combined axial compression and uniform temperature loading was investigated. The two cases of compressive postbuckling of initially heated shells and of thermal postbuckling of initially compressed shells are considered. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of the nonlinear prebuckling deformation, the nonlinear large deflection in the postbuckling range and the initial geometric imperfection of the shell. The analysis uses a singular perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of cross-ply laminated cylindrical shells with or without initial local imperfections, from which results for isotropic cylindrical shells follow as a limiting case. Typical results are presented in dimensionless graphical form for different parameters and loading conditions.     

Imperfection sensitivity of coincident buckling systems

A two-degree of freedom structural system with both buckling loads equal or nearly so is examined, allowing for the presence of small imperfections specified by the values of two general imperfection parameters. A discrete generalized coordinates energy method is used, and the system considered is non-symmetric in the two modes of deflection. Conclusions regarding the types of behaviour possible are obtained by examination of all possible equilibrium path shapes. Comparison is made to behaviour of idealized systems. Change in buckling load value with imperfection size, or imperfection sensitivity, is established and imperfection sensitivity surface forms are sketched.     

基于模态缺陷的受压球壳屈曲特性研究

针对受压球壳非线性屈曲过程，对含初始缺陷受压球壳的稳定性进行研究。根据EN1993-1-6（2007）规范，给出不同制造等级壳体的等效缺陷值计算方法；基于线性特征值分析的模态构型给出初始缺陷的分布。利用非线性有限元弧长法对球壳受压失稳过程进行数值模拟，得到屈曲前后球壳变形情况及全过程载荷-位移曲线。计算一致缺陷模态法和N阶缺陷模态法对应的球壳屈曲临界载荷，结果表明，受压球壳对缺陷较敏感，承载能力随缺陷值增大而降低；一致缺陷模态法计算便捷，在工程应用上具有合理性，N阶缺陷模态法考虑高阶模态缺陷构型，结果更加全面，可以为工程中缺陷结构稳定性设计提供参考。     

Postbuckling and imperfection sensitivity of fixed-end and free-end struts on elastic foundation

Summary A study of the postbuckling and imperfection sensitivity of fixed-end and free-end struts on a Winkler elastic foundation is carried out. The configuration and stability of the postbuckling paths bifurcating from the critical points are analysed. For the most part of foundation stiffness, the corresponding postbuckling paths are shown to be falling with respect to load and be unstable. This indicates that, for almost all values of foundation stiffness, the buckling loads of the struts will be sensitive to imperfections. We also obtain imperfection sensitivity of the struts with respect to geometric imperfections having the shape of buckling modes. Received 30 October 1998, accepted for publication 30 March 1999     

Effect of multiple localized geometric imperfections on stability of thin axisymmetric cylindrical shells under axial compression

Stability of imperfect elastic cylindrical shells which are subjected to uniform axial compression is analyzed by using the finite element method. Multiple interacting localized axisymmetric initial geometric imperfections, having either triangular or wavelet shapes, were considered. The effect of a single localized geometric imperfection was analyzed in order to assess the most adverse configuration in terms of shell aspect ratios. Then two or three geometric imperfections of a given shape and which were uniformly distributed along the shell length were introduced to quantify their global effect on the shell buckling strength. It was shown that with two or three interacting geometric imperfections further reduction of the buckling load is obtained. In the ranges of parameters that were investigated, the imperfection wavelength was found to be the major factor influencing shell stability; it is followed by the imperfection amplitude, then by the interval distance separating the localized imperfections. In a wide range of parameters this last factor was recognized to have almost no effect on buckling stresses.     

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.     

Experimental investigation of the buckling of shallow spherical shells

In the present paper, the buckling behavior of clamped thin shallow spherical shells under external pressure is studied. Seventy-nine plastic shells formed by thermovacuum process were tested. The distributions of initial geometrical imperfections and vertical displacements were minutely measured with a differential transformer. It was possible to control the symmetrical initial geometrical imperfection of each specimen.Results indicate that the buckling phenomena of shallow spherical shells vary greatly with the symmetrical initial imperfection parameter η. In the case of the geometrical parameter λ larger than 5.5, the amplitude of the asymmetrical displacement component with the bifurcation buckling wave calculated by Huang becomes large immediately before buckling. The validity of Huang's theory for an initially perfect shell is experimentally demonstrated.     

薄壁圆筒壳初始几何缺陷不确定性量化的极大熵方法

针对薄壁圆筒壳结构轴压屈曲载荷的缺陷敏感性以及真实几何缺陷的不确定性,提出一种基于实测缺陷数据和极大熵原理的初始缺陷建模与屈曲载荷预测方法。首先,将初始几何缺陷视为二维随机场,并利用实测缺陷数据和Karhunen-Loève展开法将初始缺陷的随机场建模转化为随机向量的建模;其次,利用极大熵方法确定随机向量的概率分布;最后,基于所构建的初始缺陷随机模型,利用MCMC抽样方法和确定性屈曲分析方法,进行随机屈曲分析并给出基于可靠度的屈曲载荷折减因子。数值算例表明,与直接假设随机场相关结构的方法相比,本文方法的结果是对薄壁圆筒壳屈曲载荷的一个更无偏估计。     

Buckling of imperfect functionally graded cylindrical shells under axial compression

Buckling behaviors of axially compressed functionally graded cylindrical shells with geometrical imperfections are investigated in this paper using Donnell shell theory and the nonlinear strain-displacement relations of large deformation. The analysis is based on the nonlinear prebuckling consistent theory. Both the prebuckling effects and the temperature-dependent material properties are taken into account. The buckling condition for imperfect functionally graded cylindrical shells is obtained by using the Galerkin method. Numerical results show various effects of imperfection, structural type, power law exponent, temperature and dimensional parameters on buckling. The present theoretical results are verified by those in literature.