含刚性段复合压杆的稳定性分析

压杆稳定性实验是材料力学中一个重要实验内容.然而,压杆稳定性实验中压杆两端的约束往往需要附加刚性的夹持件来实现.为了讨论压杆端部夹持件对测试结果的影响,本文基于弹性系统的稳定性理论,采用欧拉方法,分析了两端包含刚性段的复合压杆的稳定性,并通过数值求解讨论了刚性段不同占比情形下压杆的临界载荷.同时,采用有限元数值模拟方法...     

考虑轴向均布载荷时压杆的稳定性计算

为了求得压杆同时承受轴向均布载荷和集中载荷时,临界载荷的计算公式,首先对仅承受轴向均布载荷的压杆,用初参数法,导出了临界载荷特征方程,由软件分析特征方程发现, "固支--定向"、"固支--自由"、"铰支--定向"支承的压杆,轴向均布载荷对其稳定性有明显影响,并求得了临界载荷的近似解;其次采用载荷换算与叠加的方法,求得了压杆同时承受轴向均布载荷和集中载荷时,临界载荷计算的经验公式;最后就"固支--自由"支承的压杆,与其他一些研究结果进行了比较,本文结果与"平均结果"较吻合.     

计及轴向和剪切变形时压杆的Euler公式

依据平面截面假定, 在计及拉/压和剪切变形的情况下研究压杆的稳定性. 利用线性化 扰动方程, 导出了压杆的挠曲线方程; 根据各种端部约束的边界条件及其积分常数 存在非零解的条件,得到了 Euler临界载荷计算公式. 结果表明, 拉/压和剪切变形对稳定性的影响取决于它们的柔度差.     

细长压杆临界挠度的一级非线性解

 给出细长压杆临界挠度的一级非线性解, 从而简 单明了地解释了材料力学教学中细长压杆临界挠度不能 确定的原因.     

轴向受压螺旋杆的平衡稳定性

在Kirchhoff动力学比拟基础上讨论端部受轴向压力作用的圆截面弹性细杆的螺旋线平衡稳定性问题．弹性杆的平衡状态由Euler角描述的弹性杆平衡方程的特解确定．从Lyapunov或Euler的不同稳定性概念出发,对弹性杆的平衡稳定性的判断可得出不同的结果．根据一次近似扰动方程判断,弹性杆的螺旋线状态和圆环状态恒满足Lyapunov稳定性条件．但螺旋杆在轴向压力到达临界值时,圆环杆在扭转数到达临界值时将产生屈曲而丧失Euler稳定性．导出临界载荷和临界扭转数的计算公式．螺旋杆的临界载荷取决于螺旋线的高度和螺旋角：螺旋角趋近于π／2时螺旋杆转化为带扭率的直杆,其临界载荷的极限值与压杆的Euler载荷一致．文中对两类不同稳定性概念的区别和联系作出解释．     

由Kirchhoff方程导出压杆的临界载荷

用Kirchhoff方程讨论压杆的稳定性,导出了适合任意端部约束的、直杆的 线性化扰动方程及其通解;根据积分常数非零解的存在条件,分别导出了不同端部约束压杆 的临界载荷.     

测量压杆临界压力的理论与实验

从细长压杆临界压力的定义出发，分析了实验测定压杆临界压力的困难，阐述了用振动方法测量细长压杆临界压力的理论，介绍了在轴向拉力和压力状态下用振动方法测量压杆临界压力的实验，并与材料力学中通常的压杆稳定实验------测量压溃载荷的实验进行了比较,得出结论：用振动方法可以比较准确地测得细长压杆的临界压力.     

压杆稳定的机理性认识

<正> 在近代工程设计中,结构的稳定性一直成为一个相当突出的问题.从土建类材料力学的一些后续专业课程来看,无论是结构力学、钢筋混凝土结构、钢结构及一些结构设计课程,其中很多稳定性问题实质上都可归结为压杆稳定问题.而后者也一直是多学时材料力学教学全过程中的难点之一.从我们对工民建专业的教学情况来看,问题并不在于对一般压杆临界荷载值的数学推导以及对一些稳定问题的具体计算,而在于对稳定性本身的理解,特别是对于“压弯”与“失稳”     

谈细长压杆稳定性问题

谈细长压杆稳定性问题薛福林（哈尔滨工业大学，哈尔滨１５０００６）为什么在材料力学中细长压杆临界挠度是“不确定值”，为什么用挠曲线近似微分方程能得到临界力的精确解答，笔者愿谈谈自己的看法．不失一般性，本文以图１的压杆为例．首先我们应该明确什么是压杆的临...     

谈细长压杆稳定性问题

谈细长压杆稳定性问题薛福林（哈尔滨工业大学，哈尔滨１５０００６）为什么在材料力学中细长压杆临界挠度是“不确定值”，为什么用挠曲线近似微分方程能得到临界力的精确解答，笔者愿谈谈自己的看法．不失一般性，本文以图１的压杆为例．首先我们应该明确什么是压杆的临...     

组合截面轴压短柱的非线性有限元分析

圆管或方管内填充另一种工程材料构成的组合截面构件（如钢管混凝土）在工程结构中得到了广泛的应用。本文借助商用有限元分析软件ABAQUS，利用软件子程序接口，引入应力场变量，来考虑两种材料本构关系的非线性以及受力过程中Poisson比、模量的变化等因素，建立了组合截面短柱在轴心压力作用下的非线性有限元计算模型。并通过数值算例，计算了组合截面短柱在轴心压力作用下两种材料共同受力工作的荷载－变形曲线，与试验结果基本符合，同时得到了管材对核心材料约束的变化规律。     

The shape of the strongest column

The problem of determining that shape of column which has the largest critical buckling load is solved, assuming that the length and volume are given and that each cross section is convex. The strongest column has an equilateral triangle as cross section, and it is tapered along its length, being thickest in the middle and thinnest at its ends. Its buckling load is 61.2% larger than that of a circular cylinder. For columns all of whose cross sections are similar and of prescribed shape-not necessarily convex—the best tapering is found to increase the buckling load by one third over that of a uniform column. This result, which was independently obtained by H. F. Weinberger, is originally due to Clausen (1851). For a uniform column, triangularizing is shown to increase the buckling load by 20.9% over that of a circular cylinder. The results lead to isoperimetric inequalities for the buckling loads of arbitrary columns. The research reported in this paper has been sponsored by the Office of Naval Research under Contract No. (285) 46.     

光伏支架柱平面内有侧移失稳计算长度系数研究

光伏支架是一种典型的不等高单层框架,有侧移失稳的光伏支架柱计算长度系数需考虑多方面因素的影响,无法直接套用现有规范公式．综合考虑了光伏支架短柱和长柱的刚度比γ、短柱和长柱的高度比β以及梁柱线刚度比K1的影响,进行了理论推导,得出了不等高单层框架柱有侧移失稳计算长度系数的计算公式,并制作表格以便工程人员查阅使用．然后以某典型光伏支架实际工程为算例,建立了有限元数值分析模型,并分别进行了线性屈曲分析和考虑几何非线性以及材料非线性的极限承载力分析．分析结果表明,提出的理论公式和计算表格能够精确地计算光伏支架有侧移失稳的极限承载力．     

On the applicability of the Southwell plot to plastic buckling

A completely forgotten paper by C.T. Wang on the extension of the Southwell plot to inelastic buckling of columns is revived, rederived and amplified. A theoretical justification is presented for the application of the Southwell method to plastic buckling of columns made of a strain-hardening material, showing that it predicts the double (or reduced) modulus buckling load. Typical experimental verifications are recapitulated. This puts practical applications of the Southwell method in the plastic region on firmer ground.     

Theoretical approach on the dynamic global buckling response of metallic corrugated core sandwich columns

A theoretical (semi-analytical) approach was proposed to estimate the dynamic in-plane response of corrugated core sandwich columns against suddenly applied loads with a compression rate less than 5 m/s. The model has been constructed so as to effectively include various dynamic effects such as stress wave propagation, material rate dependence and lateral inertia. The practical and theoretical complexities caused from the dynamic phenomena and the established governing equations (e.g. coupled non-uniform axial force distribution) have been resolved by employing Galerkin׳s method. The proposed approach was validated by comparing the calculations from the theoretical model and Finite Element Method (FEM): the load history and deformation shape of extruded Al6061-T6 corrugated core sandwich columns and bending/brazed SS304 corrugated core sandwich columns. The model successfully yielded the imperfection-sensitive, velocity-dependent dynamic response and appearance of higher buckling modes. In addition, it has been demonstrated that the sandwich columns with periodic cellular metals outperform their weight-equivalents, monolithic solid columns, under dynamic conditions. The proposed approach as an efficient tool to explore the dynamic global buckling response in design space can make preliminary studies of weight minimization for dynamic applications.     

Buckling optimization of flexible columns

A novel approach to the optimization of flexible columns against buckling is presented. Previous published studies, considering either continuous or discrete finite element models, are always constrained to specific relations between stiffness and mass distributions of the column. These, besides yielding impractical configurations that do not conform to manufacturing and production requirements, result in designs that are certainly suboptimal. The present model formulation considers columns that can be practically made of uniform segments with the true design variables defined to be the cross-sectional area, radius of gyration and length of each segment. Exact structural analysis is performed, ensuring the attainment of the absolute maximum critical buckling load for any number of segments, type of cross section and type of boundary conditions. Detailed results are presented and discussed for clamped columns having either solid or tubular cross-sectional configurations, where useful design trends have been recommended for optimum patterns with two, three and more segments. It is shown that the developed optimization model, which is not restricted to specific properties of the cross section, can give higher values of the critical load than those obtained from constrained-continuous shape optimization. In fact, the model has succeeded in arriving at the global optimal column designs having the absolute maximum buckling load without violating the economic feasibility requirements.     

Selected local stability problems of channel section flanges made of aluminium alloys

The paper addresses the issue of local buckling of compressed flanges of cold-formed thin-walled channel columns and beams with nonstandard flanges composed of aluminium alloys. The material behaviour follows the Ramberg–Osgood law. It should be noted that the proposed solution may be also applied for other materials, for example: stainless steel, carbon steel. The paper is motivated by an increasing interest in nonstandard cold-formed section shaping in local buckling analysis problems. Furthermore, attention is paid to the impact of material characteristics on buckling stresses in a nonlinear domain. The objective of the paper is to propose a finite element method (FEM) model and a relevant numerical procedure in ABAQUS, complemented by an analytical one. It should be noted that the proposed FEM energetic technique makes it possible to compute accurately the critical buckling stresses. The suggested numerical method is intended to accurately follow the entire structural equilibrium path under an active load in elastic and inelastic ranges. The paper is also focused on correct modelling of interactions between sheets of cross section of a possible contact during buckling analysis. Furthermore, the FEM results are compared with the analytical solution. Numerical examples confirm the validity of the proposed FEM procedures and the closed-form analytical solutions. Finally, a brief research summary is presented and the results are discussed further on.     

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．     

An experimental investigation of the influence of stiffener torsional rigidity on buckling of compression panels

The influence of torsional ridigity of the stiffeners on the buckling of reinforced aluminum-alloy panels has been investigated. Experimental results reveal that stiffener torsional rigidity must be introduced in the analysis of compressed panels, for, if the stiffener has a closed cross section, the stiffener shape may change the buckling mode shape essentially and increase the critical load considerably.José María Mínguez was Postgraduate Student in Engineering, Metallic Structures Group, University of Bath, United Kingdom     

Buckling of an elastic column containing a fatigue crack

Results of an experimental program conducted in order to study the residual buckling strength of an elastic column containing a fatigue crack are presented in this paper. Tests were performed on bars of rectangular cross section, made from 2024-T351 aluminum-alloy plate and containing a fatigue crack at the midsection. Results obtained show a reduction in buckling strength of 8 percent under highed-highed end conditions, in apparent tentative accord with data obtained from columns containing machined notches. Although it is small, the reduction in buckling strength is thought to be significant for design and requires further investigation.