弹性屈曲大挠度杆纵横变形的计算

弹性屈曲大挠度杆纵横变形的计算刘传芬（兰州铁道学院，兰州７３００７０）两端铰支的弹性屈曲杆纵横变形的计算，根据压杆弹性稳定的大挠度理论，其中点最大挠度δ和两支座间距离Ｄ（见图１）的精确解为￣［１］上述３个公式中，ｐ为轴向载荷，ＥＩ为抗弯刚度；分别为第...     

屈曲杆最大挠度的近似计算

利用特殊函数公式,得到第一类全椭圆积分在ρ→１时的近似展开,然后将近似展开式应用于屈曲杆问题,得到求解屈曲杆最大挑度的近似公式．该公式优于已有的屈曲籽大挠度的近似公式．     

关于屈曲杆最大挠度的各种近似公式的比较

关于屈曲杆最大挠度的各种近似公式的比较刘俊杰（西北农业大学水建学院，陕西杨陵７１２１００）关于两端铰支细长压杆最大挠度的近似计算，除了材料力学的经典著作［１］中所推荐的公式外，近年来又有文献发表了多种形式［２～４］的其它近似公式，本文也来推导一个近似...     

Pade逼近在力学中的应用

本文应用Ｐａｄｅ逼近给出单摆的大幅运动周期及屈曲杆的大挠度的有理近似公式，这些公式给出了相当好的逼近结果．     

屈曲杆最大挠度近似公式的再改进

屈曲杆最大挠度近似公式的再改进朱华满（大连铁道学院大连１１６０２２）两端铰支细长压杆最大挠度近似公式已有多种形式￣［１－３］，精度较高、适用范围较大的当数文献［３］推荐的公式。本文导出的近似公式在精度和适用范围方面又有新的改进。欧拉从曲率精确式出发，...     

对材料力学中屈曲杆最大挠度近似公式的改进

<正> 根据两端铰支屈杆大挠度精确微分议程■，弹性屈曲杆中点最大度δ的精确解为■式中P=sin(а/2)，а为杆端转角■     

简支梁大挠度弹性后屈曲载荷与变形的优化算法

针对简支梁结构大挠度后屈曲载荷与变形的计算问题,本文提出了一种直接求解其后屈曲载荷和变形的优化算法。在简支梁处于大挠度屈曲平衡状态下,将梁结构划分为有限子段,以待求后屈曲载荷为设计变量,根据起点的边界条件和每个子段满足的弯矩变形公式,累积计算出其他各个节点的坐标,以得到的终点坐标满足的边界条件构建目标函数模型。在此基础上,通过MATLAB编制优化程序分析了两个典型算例,并将理论结果与相关软件的计算结果进行对比,从而证明了本文算法的正确性。本文算法求解过程简单、快速,具有一定的实用性,为变截面结构大挠度弹性屈曲稳定性问题的研究提供了参考。     

弹性圆板的热过屈曲

基于精确的圆薄板轴对称大挠度变形几何方程，建立了均匀加热圆板轴对称热弹性屈曲问题位移形式的控制方程，采用打靶法和解析延拓法获得了连续依赖于温度载荷的圆板过屈曲状态解，给出了相应的数值结果。     

弹性薄板的后屈曲特性

文章用三维弹性理论的非线性应变公式研究了弹性薄板的后屈曲特性，旨在探讨冯·卡门平板大挠度方程的可靠性范围。计算结果表明，当板中薄膜力较大时，用冯·卡门方程描述后屈曲问题会产生较大的误差。     

黏弹性板的大挠度蠕变屈曲

研究了具有初始小挠度受轴向压载黏弹性板的蠕变屈曲问题，在建立控制方程时，利用了von Karman非线性应变-位移关系，并考虑了初始挠度，用标准线性固体模型描述材料的黏弹性特性，在求解非线性积分方程时，利用梯形公式计算记忆积分式，将非线性积分方程化为非线性代数方程进行数值求解，得到了结构的蠕变变形过程，又将问题退化到小挠度情况进行研究，得到了挠度随时间扩展的解析解，分析了瞬时失稳临界载荷、持久临界载荷的物理意义，讨论了考虑几何非线性对黏弹性板蠕变屈曲的影响。     

均布压力下正交异性圆锥扁壳的后屈曲分析

基于Ｋａｒｍａｎ型大挠度方程,用修正迭代法分析了均布压力下夹支正交异性圆锥扁壳的几何非线性的后屈曲行为,给出二阶近似的荷载挠度特征关系式及临界荷载,给出了三种正交异性参数对应数值结果,分析了正交异性参数对壳体变形和屈曲荷载的影响。     

AN EXPERIMENTAL STUDY ON POST-BUCKLING BEHAVIOR OF SLENDER COLUMN WITH FIBER REINFORCED COMPOSITE MATERIAL

Equilibrium paths of post-buckling are measured for large slenderness column specimensmade of the fiber reinforced composite material. The influence of the initial curvature is investigatedexperimentally and compared with the result of the initial post-buckling theory. Both the theoreticaland experimental results reveal that the column with the initial curvature has stable post-buckling be-haviors and is not sensitive to the imperfection in the form of initial curvature. The experimental re-sults show that when the lateral buckling displacement is less than 20 percent of the column length, theexperimental results agree with the results from the theory of initial post-buckling quite well, whilethey agree with the results from the large deflection theory in a quite large range.     

Bucklewaves

Motivated by a selection of results on the plastic buckling of column members within a sandwich plate core where one face of the sandwich is subject to an intense impulse, the problem addressed is one where lateral buckling takes place simultaneously as a compressive axial wave propagates down the member. The bucklewave problem is modeled as an infinitely long column (or wide plate) which is clamped against lateral deflection at the end where velocity is imposed and has a moving clamped condition coinciding with the front of the plastic compression wave. The model reveals that a column or plate suddenly compressed into the plastic range is dynamically stabilized against lateral buckling for lengths that are significantly longer than the corresponding length at which the member would buckle quasi-statically. This stabilization has significant implications for energy absorption under intense dynamic loading. The analysis method is benchmarked against a simpler, but mathematically analogous problem, for which closed form solutions are available: the dynamics of a guitar string lengthening at constant velocity.     

Buckling of thin-walled columns accounting for initial geometrical imperfections

The paper is devoted to the effect of some geometrical imperfections on the critical buckling load of axially compressed thin-walled I-columns. The analytical formulas for the critical torsional and flexural buckling loads accounting for the initial curvature of the column axis or the twist angle respectively are derived. The classical assumptions of theory of thin-walled beams with non-deformable cross-sections are adopted. The non-linear differential equations are derived and the critical buckling loads are approximated by means of the Galerkin’s method. Comparison of analytical results to numerical analysis of simply supported I-columns by means of finite element method (FEM) is provided. Moreover the analytical formulas is adapted to I-columns with lipped flanges and satisfactory agreement of analytical and numerical results of stability analysis is observed.     

结构随机分析的Monte Carlo加权残值法

本文提出一种结构随机分析的Monte Carlo加权残值法。文中建立了这种方法的基本列式,并通过静力挠度、固有频率和屈曲荷载等算例,表明本文方法理论简捷,计算工程量少,精度较高,是随机结构数值分析的有效方法。     

Buckling and postbuckling behavior of half-loaded shallow spherical shells

Applying the Galerkin procedure to Marguerre's shallow shell equations, reasonably accurate solutions are obtained for the buckling and postbuckling behavior of clamped shallow spherical shells subjected to external pressure distributed over half the surface.For the geometrical parameter λ smaller than 4.5, the half-loaded shells do not buckle. The buckling loads for 6 ≦ λ ≦ 15 lie about 17–30% below those of uniformly loaded shells. However, the lowest loads after buckling are higher than those for uniformly loading. As λ keeps increasing, the buckling mode shows more and more waves along the circumferential direction. The amplitude of the asymmetrical deflection component Δ₁ becomes remarkably large immediately after buckling. After passing the postbuckling lowest equilibrium point, the sinusoidal deflection disappears and the deflection is changed such that only one location on the shell surface, including the non-loaded area, has been deflected almost symmetrically. The effects of initial imperfections are not so great as for the uniformly loaded case.     

夹层扁球壳的非线性稳定性

基于Reissner假设和变分原理,给出夹层扁球壳在均布压力作用下的大挠度方程,采用修正迭代法求得了夹层扁球壳非线性稳定问题的解析解,得到两类边界条件下临界屈曲载荷的表达式,讨论了几何参数和物理参数对临界屈曲载荷的影响     

细长柔韧压杆弹性失稳后挠曲线形状的计算机仿真

采用Maple编程对细长柔韧压杆弹性失稳后挠曲线形状进行了计算机仿真,进行了细长柔韧压杆弹性失稳后最大挠度和挠曲线封闭两种情况下的挠曲线形状仿真和详细的解答.分析计算了失稳后屈曲的力学特征,给出了解析表达式;分析计算了失稳后屈曲的平衡状态曲线的几何特征,绘出了计算机仿真曲线.结果表明:失稳后最大挠度和挠曲线封闭是属于两个完全不同的屈曲状态.     

Buckling analysis of an elastic bar using the Bubnov-Galerkin method

The factors responsible for the errors often encountered in the stability analysis of elastic systems are found by testing the Bubnov-Galerkin method for the buckling problem of a single-layer flexible elastic bar. Refined formulas are obtained for the maximum deflection of a longitudinally compressed hinged three-layer bar. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 148–156, January–February, 2008.