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...     

再论压杆失稳与Lyapunov稳定性

进一步分析了弹性杆平衡的Euler稳定性和Lyapunov稳定性的概念和意义，指出了两的异同，表明不能用Euler稳定性的概念去理解弹性杆平衡的Lyapunov稳定性，并用例子予以说明。     

大柔度型钢压杆的稳定性设计计算公式

对大柔度型钢压杆稳定性设计,本文导出一个简便计算公式,从而能够直接选定型钢型号....     

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.     

弹性细杆螺旋线平衡的动态稳定性

本文从动力学观点讨论具有初扭率的非圆截面弹性细杆的螺旋线平衡稳定性。弹性杆平衡的动态稳定性建立在以弧坐标s和时间坐标t为双自变量的离散系统的Lyapunov稳定性概念基础上。对于两端约束状况固定不变的弹性杆,若静态稳定性条件已满足,其与弧坐标对应的本征值可根据端部约束条件确定。则螺旋线平衡的动态稳定性由时间域的本征值判断。在缓慢受扰运动条件下,引入尺度缩小的时间变量T=εt,可将动力学过程视为对平衡状态的摄动。证明在ε^2计算精度范围内,当螺旋线平衡的一次近似静态稳定性条件得到满足时,考虑动力学因素的稳定性条件必也同时满足。     

局部削弱压杆的稳定性实验研究

因为缺乏相关的理论和实验研究,局部削弱压杆的临界载荷通常按无削弱压杆处理.工程中,局部削弱压杆的使用极为普遍.对局部削弱压杆的稳定性的定量研究结果,无论是工程中,还是材料力学教学中都是迫切需要的.本文在前人理论研究的基础上,对局部削弱压杆的临界载荷作了定量的实验研究.试验结果表明,对细长压杆,即使削弱部分的刚度下降达到38.9%,对失稳临界载荷的影响仍可忽略;试验结果与黄玉珊提出的对局部削弱压杆稳定性的定量计算方法也比较接近.研究结果对部分工程问题和材料力学教学都具有一定的指导意义.     

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。     

压杆稳定性设计的数学分析

通过对压杆稳定性设计的分析, 将截面设计转化为计算分段函数关于柔度的不动点问题, 用数值分析方法中的二分法处理. 以圆截面压杆为算例, 利用Matlab 中的fzero(@fun, x0) 函数求解. 与传统方法相比, 本文所述方法准确度高, 且更为方便实用.     

受轴向力和扭矩作用的直杆的平衡稳定性

以受轴向力和扭矩作用的具有原始扭率的两端铰支圆截面直杆为对象，讨论其平衡的Lyapunov稳定性和欧拉稳定性．在Kirchhoff方程及线性化扰动方程基础上计算其欧拉载荷．压杆的欧拉载荷为其特例．     

To the problem of stability of a cylindrical shell under axial compression

The classical problem of stability of a thin elastic cylindrical shell loaded by axial compressions forces is considered. The axially symmetric and non-axisymmetric buckling modes of isotropic and orthotropic shells are studied. In contrast to the traditional approach, the well-known expressions for the critical load are obtained by analyzing the equations for the shell behavior and are independent of the boundary conditions.     

The stability of a finitely inflated cylindrical elastic membrane under axial compression

The stability under overall axial compression of a finitely inflated cylindrical membrane composed of highly elastic material is investigated. The critical loads for inflated tubes with closed ends and with either simply-supported or fixed ends are determined in terms of the material properties of the membrane. For long tubes the results are compared with the Euler formulae for the buckling load for struts in compression. An equivalent Young's modulus is derived, and it is shown that the critical loads can be obtained from the Euler formulae by using the dimensions of the inflated state and the equivalent Young's modulus.     

Simplified variant of calculation of the stability of cylindrical shells under axial compression

Design formulas for calculating the critical stresses of unreinforced and reinforced cylindrical shells in axial compression are derived by analyzing experimental data. The curves obtained with the formulas bound the experimental data from below. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 11, pp. 75–78, November, 1999.     

Thin rod under longitudinal dynamic compression

The paper contains a short survey of the papers on the static and dynamic longitudinal compression of a thin rod initiated by Morozov and and carried out in 2009–2016 with his direct participation. We consider linear and nonlinear problems related to the propagation of longitudinal waves in a rod and the transverse vibrations generated by these waves; parametric resonances; beating due to energy exchange between longitudinal and transverse vibrations; the rod shape evolution as the load exceeds the Euler critical value; the possibility of buckling of the rod rectilinear shape under a load less than the Euler load; and the rod dynamics at the initial stage of motion. The prospects of further investigations related to the complication of the models are considered, in particular, the problem of longitudinal impact by a body on a rod and the transverse vibrations generated by it.     

Nonlinear deformation and stability of noncircular cylindrical shells under internal pressure and axial compression

Stability analysis of noncircular shells is performed with allowance for nonlinear subcritical deformation. Explicit expressions for the rigid displacements of elements of noncircular cylindrical shells are obtained and used to construct shape functions of an effective quadrilateral finite element of natural curvature. A finiteelement algorithm for solving problems of nonlinear deformation and stability of shells is developed. Stability problem of an elliptic cylindrical shell is considered. The effect of the ellipticity and subcritical nonlinear deformation of the shell on the critical load is studied. Results obtained are compared with available experimental data.