连续跨越多个支座的阶梯梁(轴)的三弯矩方程

阶梯状悬臂梁自由端的挠度和转角有一阶梯梁(如图1),在自由端处受集中力P作用时,自由端的转角和挠度可用叠加法求得: ...     

基于改进SPH方法的平面动态应力模拟

为了探讨在动态激励作用下材料的局部力学行为,本文将改进的光滑粒子流体动力学方法(Smoothed Particle Hydrodynamics)应用于平面应力问题求解.引入速度、密度及应力修正项,对在简谐外部激励作用下的弹性悬臂梁运动及应力情况进行模拟.本文通过编写FORTRAN程序,计算了弹性悬臂梁的运动周期、运动幅值,并将悬臂梁自由端中点的位移情况与有限元计算结果进行了对比.此外,本文还对梁内典型位置处的正应力及密度变化情况进行显示跟踪.研究结果表明,本文采用的改进光滑粒子流体动力学方法不仅能够较为准确的模拟悬臂梁振动问题,且能持续显示跟踪各物质点的物理量,对结构强度的长期监测有一定的工程应用潜力与现实意义.     

磁耦合悬臂梁双稳动力学分析与实验

研究了一个自由端附加小磁铁的悬臂梁在磁力作用下的双稳态动力学行为．首先,利用Hamilton原理和Euler-Bernoulli梁的基本方程建立了系统在非零平衡点处做微幅振动的动力学方程．其次,利用多尺度法对建立的模型进行理论分析,得到悬臂梁在非零平衡点处振动的幅频方程和位移解,并对解进行了稳定性分析．最后,通过建立实验装置,得到悬臂梁不同运动形式下的参数平面分类和悬臂梁在非零平衡点处振动的幅频关系,通过观察系统在非零平衡点处振动的理论预测,实验结果验证了非零平衡点处振动的理论分析的正确性．对照理论、实验和数值结果得到：在不同的外激励幅值和频率作用下,悬臂梁有三种不同的运动形式：在非零平衡点处的微幅振动;大范围往返运动;在两个非零平衡点之间的无规律运动．     

自由端受集中力作用下压电悬臂梁弯曲问题解析解

本文对由横观各向同性压电介质构成的悬臂梁，在自由端受集中力作用下的弯曲问题进行了研究。首先根据问题的特点，得到简化的线弹性压电悬臂梁的基本方程。然后根据正交各向异性材料悬臂梁应力分布特点，采用逆解法，建立了该问题的应力函数与电势分布函数，进而得到精确多项式解析解。该解析解形式简单，便于应用。文中对自由端受集中力的常规材料和压电材料悬臂梁的挠度也进行了比较。     

横向冲击载荷下伪弹性TiNi合金矩形悬臂梁结构响应的实验研究

利用改装的霍普金森压杆装置对伪弹性TiNi合金矩形截面悬臂梁进行了横向冲击实验研究.结果表明:冲击自由端时,只在根部附近产生一个相变铰,冲击梁中间某位置时,则可能在多处形成相变铰;相变铰形成时拉伸和压缩两侧应变存在一定的不对称性,但是差别并不明显;相变铰的形成与发展过程中,应变并不是单调增加的,而是带有波动性;卸载后相变铰消失,TiNi悬臂梁形状完全回复;自由振动前期,应变的平衡位置与挠度的平衡位置有一定偏离,并且这种偏离随着梁的振动逐渐减小直至消失.TiNi悬臂梁的冲击特性受热弹性马氏体相变和逆相变的支配,不同于传统的弹塑性机制.     

三种典型边界条件下受集中载荷梁大挠度弯曲精确解

利用Jacobi椭圆函数得到了自由端受集中载荷悬臂梁大挠度弯曲问题的显式精确解,不同于由传统椭圆积分公式得到的解,该显式精确解给出梁中任意点的转角,由此可方便的得到梁弯曲后各点的位移.研究表明:由该解出发,可得到任意位置受集中载荷悬臂梁问题的解;对称性分析表明该解可直接用于两端简支或两端固支梁中点受集中载荷的情况.最后分别给出了载荷取一系列值时以上三种边界条件下梁弯曲的挠度曲线.     

关于材料力学中一处结论的修正

关于材料力学中一处结论的修正刁海林（广西农业大学林学院，南宁５３０００１）文［１］在“动载荷”一章中给出了自由落体冲击下，考虑受冲击杆件质量时的动荷系数笔者认为这一结果是错误的。如图１所示，不能忽略质量的悬臂梁在自由端Ｂ受重物ｍｇ冲击的问题为例分析之...     

关于材料力学中一处结论的修正

关于材料力学中一处结论的修正刁海林（广西农业大学林学院，南宁５３０００１）文［１］在“动载荷”一章中给出了自由落体冲击下，考虑受冲击杆件质量时的动荷系数笔者认为这一结果是错误的。如图１所示，不能忽略质量的悬臂梁在自由端Ｂ受重物ｍｇ冲击的问题为例分析之...     

阶梯形悬臂梁在脉冲载荷作用下塑性动力响应的完全解

本文采用双塑性铰模型,分析了阶梯形悬臂梁自由端受矩形脉冲载荷作用时的刚塑性动力响应,给出了整个响应过程封闭形式的完全解,讨论了一些主要参数对最终挠度的影响。     

基于MATLAB的悬臂梁大变形分析

主要研究悬臂梁大变形的挠度求解问题.通过推导悬臂梁自由端受集中力时的绕曲线方程,得出一种较为简便的大变形问题求解方法.编写程序利用黎曼积分配合二分法迭代出解,并和传统小变形解法进行了比较.同时,利用ANSYS软件建模证明了本文方法在一定范围的正确性.     

Average increase in vertical stress due to uniform embedded rectangular loadings in cross-anisotropic materials

This study derives the closed-form solution for the average increase in vertical stress at the corner of uniform embedded rectangular loadings on cross-anisotropic materials. The solution is obtained by integrating the vertical point load solution of Wang and Liao, which is affected by the dimensions of the loaded rectangular area, the depth of the loading embedment, the depth below the loading, and the five elastic cross-anisotropic engineering constants. Additionally, to estimate the consolidation settlement at a particular cross-anisotropic layer due to embedded rectangular loadings, the average increase in vertical stress is obtained by applying the principle of superposition.     

梁中复合应力波的传播

采用有限差分法讨论了梁中复合应力波的传播．给出了粘塑性悬臂梁当自由端受突加弯矩载荷作用时梁内复合应力波传播的基本图象。指出，在冲击早期响应阶段．截面横向转动惯性效应起着重要作用，是不可忽视的。标志弹塑性边界的塑性效，一开始由自由端向固定端运动，但在反射卸载波的迎面作用下，会出现回退现象。在波动早期阶段，固定端主要处于弹性变形状态。此外，还对弹塑性梁中复合应力波的控制方程进行了必要的讨论。     

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slender,non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed continuous load and a concentrated load at the free end of the beam.The material of the cantilever is assumed to be nonlinearly elastic.Different nonlinear relations between stress and strain in tensile and compressive domain are considered.The accuracy of numerical solutions is evaluated by comparing them with results from previous studies and with a laboratory experiment.     

提高强冲击荷载作用下平板式防护门门框墙抗力的方法

在强冲击波荷载作用下门框墙转角处会产生明显的应力集中,影响门框墙体系甚至整个防护结构的安全。为解决该问题,提出在迎爆面门框墙和衬砌结合部位设置薄弱层的构造方法,从而减小冲击荷载引起的过大的拉应力。运用考虑了剪切变形的悬臂梁理论分析表明,梁端部约束刚度的变化可以影响结构的破坏形态以及结构的内力分布,降低端部的约束刚度可以有效降低端部区域的内力峰值,延缓结构发生破坏的时间。利用有限元模拟的方法,分析了在出入口门框墙位置设置薄弱层对门框墙动力响应和破坏规律的影响。分析结果表明,设置薄弱层可以有效降低门框墙转角处的应力,降低门框墙结构破坏的风险,进而提高门框墙的抗力水平。     

Investigation of the size effects in Timoshenko beams based on the couple stress theory

In this paper, a size-dependent Timoshenko beam is developed on the basis of the couple stress theory. The couple stress theory is a non-classic continuum theory capable of capturing the small-scale size effects on the mechanical behavior of structures, while the classical continuum theory is unable to predict the mechanical behavior accurately when the characteristic size of structures is close to the material length scale parameter. The governing differential equations of motion are derived for the couple-stress Timoshenko beam using the principles of linear and angular momentum. Then, the general form of boundary conditions and generally valid closed-form analytical solutions are obtained for the axial deformation, bending deflection, and the rotation angle of cross sections in the static cases. As an example, the closed-form analytical results are obtained for the response of a cantilever beam subjected to a static loading with a concentrated force at its free end. The results indicate that modeling on the basis of the couple stress theory causes more stiffness than modeling by the classical beam theory. In addition, the results indicate that the differences between the results of the proposed model and those based on the classical Euler–Bernoulli and classical Timoshenko beam theories are significant when the beam thickness is comparable to its material length scale parameter.     

Elasticity solutions for plane anisotropic functionally graded beams

This paper considers the plane stress problem of generally anisotropic beams with elastic compliance parameters being arbitrary functions of the thickness coordinate. Firstly, the partial differential equation, which is satisfied by the Airy stress function for the plane problem of anisotropic functionally graded materials and involves the effect of body force, is derived. Secondly, a unified method is developed to obtain the stress function. The analytical expressions of axial force, bending moment, shear force and displacements are then deduced through integration. Thirdly, the stress function is employed to solve problems of anisotropic functionally graded plane beams, with the integral constants completely determined from boundary conditions. A series of elasticity solutions are thus obtained, including the solution for beams under tension and pure bending, the solution for cantilever beams subjected to shear force applied at the free end, the solution for cantilever beams or simply supported beams subjected to uniform load, the solution for fixed–fixed beams subjected to uniform load, and the one for beams subjected to body force, etc. These solutions can be easily degenerated into the elasticity solutions for homogeneous beams. Some of them are absolutely new to literature, and some coincide with the available solutions. It is also found that there are certain errors in several available solutions. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a functionally graded anisotropic cantilever beam.     

Dual extremum principles relating to optimum beam design

Of concern is a cantilever beam resting on an elastic foundation and supporting a load at the free end. The beam is of rectangular cross section and of constant height but variable width. It is required to taper the beam for maximum strength. This means that the beam is to support a maximum vertical load W at the free end when the free end is given unit deflection. The constraint is that the weight of the beam should not exceed a given bound K. It is shown that the optimum taper should be so chosen that the curvature of the beam is constant. This yields the solution of the problem in terms of explicit formulas. For more general constraints, an inequality is found which gives upper and lower bounds for the maximum load W even though explicit formulas are not available.This paper was prepared under Research Grant DA-ARO-D-31-124-71-G17, U.S. Army Research Office (Durham).     

Furthest reach of a uniform cantilevered elastica

A uniform elastic cantilever is subjected to a uniformly distributed load or a concentrated load at its tip. The angle of the fixed end with the horizontal is varied until the maximum horizontal distance (projection) from the fixed end to the horizontal location of the tip is attained. The beam is modeled as an inextensible elastica, and numerical results are obtained with the use of a shooting method. For the optimal solution (furthest reach), the tip is below the level of the fixed end. Experiments are conducted to verify the analysis for a heavy cantilever (i.e., only subjected to its self-weight).