Effect of In-Plane Deformation on Lateral Buckling

ABSTRACT

In the classical analysis of the flexural-torsional buckling of beams, beam columns and rigid-jointed plane frames, it is assumed that the major axis rigidity is very large, so that the small in-plane deformations can be neglected. The effects of the in-plane deformations on lateral buckling are investigated in this paper for determinate beams and cantilevers, beam columns, continuous beams, and portal frames. This is done by deriving more accurate governing differential equations, and by obtaining closed form or numerical solutions of these. The results obtained indicate that the classical critical loads or moments are generally conservative, except for the members which are highly restrained laterally. The sources of error in the classical analysis are also studied, and their effects are demonstrated. The results of experiments on small scale beams, which are in close agreement with the theoretical predictions, are reported.     

复合板旋转约束刚度推导及箱型结构屈曲分析

基于结构稳定性理论,推导出正交各向异性纤维树脂增强复合材料箱型结构各板连接处旋转约束刚度的近似表达式．与以往的经验公式相比,考虑了材料的正交各向异性和截面尺寸的影响．通过对箱型结构的正交各向异性比、截面属性以及纵横比对旋转约束刚度的影响进行参数研究,验证了旋转约束刚度新公式的精确性和适用范围．通过比较采用不同近似表达式得到的结果与有限元计算结果的对比,表明本文的旋转约束刚度新公式可以更精确地用来计算箱型结构的临界屈曲载荷．     

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。     

正交各向异性薄板的弹塑性屈曲分析

本文应用混合硬化正交各向异性塑性理论和屈曲的能量法则，推导了正交各向异性薄板在面内压缩情况下的弹塑性稳定方程，计算了相应的临界荷载，并讨论几何形状、边界条件及诱导荷载比等对临界应力的影响。分析表明材料的各向异性性质对弹塑性临界应力的有较大的影响。     

Effect of Lateral Linear Stiffness on Nonlinear Characteristics of Hunting Motion of a Railway Wheelset

Railway wheelset experiences the problem of hunting above a critical speed, which is a kind of self-excited oscillation. At the critical speed, it is known that the system undergoes a subcritical Hopf bifurcation. Therefore, for clarifying the nonlinear characteristics of hunting it is very important to detect, for example, the nonlinear forces in the wheelset due to the creep forces acting between the wheels and rails, and the nonlinear component of the resorting forces by the suspensions. However, it is impossible to determine each force quantitatively. In the present paper, it is first shown, by using the center manifold theory and the method of normal form, that the nonlinear characteristics of the bifurcation in a wheelset model with two degrees of freedom are governed by a single parameter, hence each nonlinear force need not be detected when examining the nonlinear characteristics. Also, a method of determining the governing parameter from experimentally observed radiuses of the unstable limit cycle is proposed. Next, we experimentally investigate the variation of the parameter due to the presence of linear spring suspensions in the lateral direction and discuss the variation of the nonlinear characteristics of the hunting motion, which depends on the lateral stiffness. As a result, the improvement of the stability of the wheelset against the disturbance by the linear spring suspensions is clarified.     

复合材料脱层梁的屈曲分析

本文研究了具有任意位置透型脱层的复合材料梁的屈曲问题。基于弹性理论建立了复合材料脱层梁的基本方程式。对脱层梁进行了分区处理,利用B样条函数作为位移型函数的基函数,方便地描述了脱层长度、脱层位置。考虑边界条件、区间位移连续性条件和弯矩剪力的平衡条件以及纵向内力的附加条件,对基本方程式进行了求解。得出了脱层位置不同,脱层长度不同的屈曲荷载的变化规律,并与轴对称脱层时的屈曲荷载进行了比较,认为层合梁考虑脱层对屈曲的影响是非常必要的。     

Buckling of a Rod Undergoing Direct or Reverse Martensite Transformation under Compressive Stresses

Analytical solutions of the problem of buckling of a compressed rod made of a shape-memory alloy, which undergoes direct or reverse martensite phase transition under compressive stresses, are obtained with the use of various hypotheses. Specific features of the experimentally observed buckling phenomenon caused by martensite transformations are described. It is found that the hypotheses of continuing phase transition and continuing loading give the minimum critical loads.     

Axisymmetric Deformations of Buckling and Barrelling Type for Cylinders Under Lateral Compression – The Linear Problem

We consider the nonlinear boundary value problem of specifying the displacement of the lateral surface of a cylindrical body subject to zero normal stresses on the top and the bottom and sliding conditions (i.e. no tangential components of the surface traction) at the lateral surface. We restrict our analysis to study the existence of axisymmetric deformations assuming that the material of the body is homogeneous, isotropic and hyperelastic. We study the linearization of the nonlinear equations about a trivial solution and show that smooth solutions of the linear problem must be separable. We classify the nontrivial axisymmetric solutions of the linearized problem in two types that we call buckling and barrelling like solutions. We characterize the eigenvalues for both solutions types as well as those displacements of the lateral surface at which the complementing condition for the linearized equations fails to be satisfied. For a class of Blatz–Ko type materials we give a complete characterization of the existence, multiplicity and disposition of the corresponding eigenvalues. We show, for such material, that the eigenvalues of buckling and barrelling types are simple, and that they form monotone sequences (decreasing for the former and increasing for the latter) both of which converge to a value at which the complementing condition fails. Moreover, it is shown that the cylinder looses stability first to buckling rather than to barrelling.     

单变量有限元的新思考:精化直接刚度法

对单变量有限元和多变量有限元进行了综合分析和比较。其中包括有限元法的单元的可靠性问题:收敛性,坐标不变性,伪零能模式;单元的性能:计算精度,对畸变网格的适应性及解除闭锁、解的晃动现象等问题。进一步对单变量有限元提出新的思考,用精化直接刚度法发展单变量有限元,使之能兼备单变量有限元与多变量有限元之长,克服两者之短。     

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．     

Application of a Direct Stiffness Method to Wave Propagation in Multiphase Poroelastic Media

In this paper, it is demonstrated how a direct stiffness method for wavepropagation in multilayered saturated poroelastic media, based on integraltransform techniques, can be modified to account for a small amount of gasin the pores. Unsaturated media with small gas fractions can be treatedusing Smeulders extension of Biots poroelastic theory. The effect of thepresence of gas bubbles on the fluid bulk modulus and the dispersioncharacteristics of a water-saturated sand of Mol is demonstrated. Thedirect stiffness method is illustrated with a numerical example wheretransient wave propagation in a dry, saturated and unsaturated halfspaceis considered.     

屈曲型数字微镜结构的机电动力学分析

设计一种基于压杆屈曲原理的数字微镜装置，针对该装置建立机电动力学模型，应用龙格-库塔法和有限元数值方法求解其动力学模型中的隐函数。通过对该模型的完整机电动力学微分方程数值求解所作的运动仿真，得到了微镜基板的连续角位移曲线，表明该装置具有良好的光束稳定特性。     

涉及肌肉作用影响的髓内钉屈曲分析

在骨折的修复过程中，常发生髓内钉断骨内的情况。其主要原因是涉及肌肉影响后，髓内钉不是单钝的受压杆件，而是多种组合变形的屈曲问题。文中利用有限元法对目前较新结构的髓内钉在骨折治疗中涉及肌肉作用影响进行多方面的压、弯曲与扭转组合变形屈曲分析。得出了三叶瓣型髓内钉在涉及肌肉影响时的屈曲临界压力比单纯受压时髓内钉的屈曲临界压力小51％。并得出髓内钉只能额外承受15Nm左右的外来扭力。这些结果可供髓内钉进一步发展及临床应用参考。通过有限元的分析还可以对髓内钉受力状态的薄弱环节有一个全面的认识，为髓内钉合理设计、材料的选择等进行优化设计提供依据。     

有初始缺陷的矩形板非线性屈曲分析

推导出几何非线性和物理非线性且存在初始缺陷的矩形薄板在纵向荷载作用下增量形式的基本微分方程，并用伽辽金配点法求解该方程。数值计算结果与已有文献的理论和实验结果相当一致。     

U型波纹管及相关结构环向屈曲的有限元分析(Ⅱ）--半圆环壳的屈曲

环壳不仅是U型波纹管的一个组成部分，更是一类重要的结构，在航天、核能和海洋工程中有重要的应用，其屈曲是人们关注的问题之一，其中对半圆环壳的分析还较为少见。本文采用文[7]的有限元法（考虑了屈曲前的弯曲和屈曲时载荷的转动并按线性化特征值问题处理）计算了正Gauss曲率半圆环壳在均匀外压作用下的屈曲，将所得结果与已知的近似解进行了对比、并讨论了其中的差异。本文除了给出临界载荷和子午线的屈曲模态外，还给出了前屈曲弯曲应力分布，以便仔细了解屈曲问题。     

关于结构刚度方程病态问题的疑难分析

本文围绕矩阵位移法求解结构位移的误差,讨论了结构刚度矩阵的病态问题,指出了计算上的病态常常是结构刚度分布和结构拓扑的不合理,而不一定是计算本身的问题。首先,文章依据误差界的概念和范数的性质推导了衡量结构刚度矩阵病态程度的条件数的公式。然后,阐明了基于不同范数的条件数在衡量矩阵病态程度上的等价性。最后,通过两个具有代表性的算例,分别从结构构件的刚度差异和结构几何拓扑两方面,计算和分析了结构刚度矩阵的病态程度随结构本身性质的改变而改变的规律。在特定的算例中,还有使结构刚度矩阵的病态程度降到最低的最佳刚度分布。     

粗糙薄层弹性体接触刚度分析

薄层弹性体功能结构表面在工程领域有着广泛的应用前景,薄层弹性体的接触特性分析对功能结构表面设计与应用非常重要.采用随机粗糙表面模拟生成技术和有限元分析技术建立了粗糙薄层弹性体表面的接触刚度确定性分析模型,研究了薄层弹性体的接触特性,对基于半数值确定性分析方法的粗糙层-基体层串联模型用于粗糙薄层弹性体接触刚度计算的适用性进行了讨论,进一步分析了粗糙薄层弹性体串联模型接触刚度的误差来源.研究结果表明:当薄层弹性体的基体层厚度小于10倍表面均方根粗糙度时,由传统粗糙层-基体层串联模型分析获得的粗糙薄层弹性体刚度误差将超过15%,误差主要来源于粗糙峰的大变形和基体层的局部变形不均匀的共同作用.     

矩形板非线性蠕变损伤屈曲特性分析

基于Von Karman非线性板理论和Kachanov-Rabotnov损伤理论,建立了在横向和面内载荷共同作用下考虑蠕变损伤效应的矩形板的非线性控制平衡方程,采用有限差分法和时间增量算法对未知变量进行离散,对整个问题进行迭代求解,分析了几何非线性、荷载等因素对板非线性蠕变损伤特性的影响。     

底部两层框剪砖房层间侧移刚度比的合理取值

底部框剪结构多层砖房在城市建设中应用广泛。这种房屋的特点是由两种承重和抗侧力体系构成的。以典型房屋为基础。编制了剪切型结构弹塑性动力时程分析通用程序，通过减小剪力墙厚度。数量或材料标号的方法，基佗层的质量和刚度不变，采用多种层间侧移刚度比以及多种层数进行了弹塑性动力分析。讨论了这类房屋相邻层间侧移刚度比的合理取值问题，可供工程设计和编制有关的规范，规程参考。