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.     

提高能量法确定压杆临界荷载精度的一种方法

通过杆件的弯矩位移关系消去能量法确定压杆临界荷载公式中的位移导数项,大大地提高了其计算精度,文后给出的两个算例证明了这一结论.     

用加权残值法求压杆的临界载荷

用加权残值法求压杆的临界载荷刘悦藏（河北工学院材料力学教研室,天津３００１３２）加权残值法是一种求解微分方程的方法。它不是严格地求微分方程的解析解,而是直接从微分方程得出问题的近似解。与其它数值法相比,它没有完全抛弃已有的理论解。由于此法原理简单、方...     

压杆稳定性的平衡视角与刚柔渐近

为了阐述弹性压杆稳定性的内涵,本文采用力矩平衡视角展示了压杆稳定性问题中各力矩的变化;利用多刚杆-碟形弹簧模型讨论了压杆稳定性的刚柔渐近,揭示了两种压杆稳定性模型的关系以及弹性压杆稳定性临界载荷的物理意义。     

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.     

压杆临界力实验方法

将Southwell的方法[1]加以分析后,得到一个既简便又更精确的用实验测压杆临界力的方法。     

考虑剪切效应时压杆临界载荷的新数值方法

熟知,计入剪切效应时压杆临界载荷的求解归为某些常微分方程的特征值问题,本文提出一种求解该种问题的新数值方法.此种方法的思想是基于将特征值问题转化为同一方程的初值问题,要点为:(1)首先在积分始端取一个补充的初值,(2)又取一个暂设的特征值,(3)数值求解此微分方程的一个初值问题,(4)多次试凑和改变暂设特征值,让终端条件得到满足.数值算例已在文中给出.     

用能量法求细长压杆临界荷载

用能量法求细长压杆临界荷载薛福林（哈尔滨工业大学，哈尔滨１５０００１）文［１］第２．９节在对图１压杆用能量法求临界荷载近似解时，得出两个变形能△Ｕ的算式：并有如下两个论述：Ⅰ．如果我们是以真实的挠度曲线进行计算，则（１）与（２）两式都是精确的，但当我...     

??????????????????????

通过对拉压杆概念的回顾以及出现在教科书中几个实例的分析,一方面说明规范化载荷平衡分析的必要性,另一方面展示杆件分析类型的标准与意义.     

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.     

A direct method of obtaining the critical load of inelastic columns

Experimental Techniques -     

行星运动轨道方程的又一推导方法

 提出了推导行星运动轨道方程的一种新方法------ 矢量分析法, 较先推导比耐公式, 再求解微分方程的传统方法简单, 所得结果与传 统方法一致.     

细长压杆临界压力欧拉公式的统一推导

利用细长压杆微小弯曲的平衡条件，得到了压杆挠曲线近似微分方程，将挠曲线的初参数解用于几种常见支承条件的细长压杆，可以方便地求得相应的临界压力欧拉公式。     

A nondestructive dynamic method for the determination of the critical load of elastic columns

A dynamic method for predicting the buckling load of an elastic column is formulated. The method is based on the integral-equation representation of a column with varying cross section and elastic springs at the boundaries. The experimental inputs are the dynamic properties of the unloaded column (trequencies, mode shapes and masses). The buckling loads predicted for three tested configurations agreed well with loads defined by other static and dynamic methods.     

A lower bound estimate of the critical load for compressible elastic solids

We determine lower bound estimates for the critical load for hyperelastic solids under monotonic dead load processes. By considering the Hadamard criterion of infinitesimal stability, we first determine a lower bound for the Hadamard stability functional; then, we develop a procedure for optimal lower bound estimates for the critical load. As examples, we apply our procedure to generalized Blatz-Ko solids under simple extension, simple compression and rectilinear shear, and compare our results with other proposals contained in the literature.     

The asymptotic behavior of solutions to the Kirchhoff equation with a viscous damping term

We study the asymptotic behavior of solutions to an equation describing non-linear vibration of a string with viscosity. In the case when the string is unstretched (the degenerate case), we determine the decay order of solutions by investigating the dynamics near an infinite-dimensional center manifold. Moreover, we classify the asymptotic behavior of all solutions from a dynamical systems point of view. We also deal with the case where the string is stretched (the nondegenerate case).     

Post-buckling of cantilever columns having variable cross-section under a combined load

Post-buckling of a cantilever column is examined under a combined load consisting of a tip-concentrated load and a distributed axial load, through dynamic formulation. The formulation of the problem is based on the moment–curvature relationship. The two-point boundary value problem described by the governing equations is dependent on the frequency parameter and the two load parameters. The buckling loads are those loads at which the eigencurve, namely, the load versus frequency curve of the column meets the load axis. A simple and reliable iterative procedure to convert the two-point boundary value problem into an initial value problem is followed and solved the non-linear differential equations utilizing a fourth-order Runge–Kutta integration scheme. To demonstrate the potentiality of the adopted numerical scheme, linear vibration frequencies of truncated, tapered cantilever wedges and cones are determined and compared with the published analytical and test results. Buckling and post-buckling loads of a simply supported stepped column are obtained and compared with the published test results. The loads and deflections of non-uniform cantilever columns are obtained for various slopes at the tip. The interaction of load parameters for a free–free truncated conical column has also been examined. The numerical results indicate that the path represented by the two load parameters turns out to be nearly a straight line.     

Finding the buckling load of non-uniform columns using the iteration perturbation method

The aim of this study is to calculate the critical load of variable inertia columns. The example studied in this paper can be used as a paradigm for other non-uniform columns. The wavelength of equivalent vibratory system is used to calculate the critical load of the trigonometrically varied inertia column. In doing so, the equilibrium equation of the column is theoretically studied using the perturbation method. Accuracy of the calculated results is evaluated by comparing the solution with numerical results. Effect of improving the initial guess on the solution accuracy is investigated. Effects of varying parameters of the trigonometrically varied inertia and the uniformly tapered columns on their stability behavior are studied. Finally, using the so-called “perfectibility” parameter, two design goals, i.e., being lightweight and being strong, are studied for the discussed columns.