BIPARAMETRIC PERTURBATION SOLUTIONS OF LARGE DEFLECTION PROBLEM OF CANTILEVER BEAMS

The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach. This kind of substitution can transform the basic equation, an integral differential equation into nonlinear algebraic ones, thus simplify computational process. Compared with present results, it indicates that the large deflection problem solved by using pseudolinear analysis can lead to simple and precise results.     

有摩擦时悬臂细长大杆大挠度弯曲的解

在专用汽车开发中,遇到有磨擦时细长杆受集中载荷时大挠度弯曲变形件的设计问题,本文利用数值积分法对此进行讨论,提出有摩擦时细长杆悬臂梁所受最大弯矩计算方法,同时就磨擦力对变形的影响进行了分析,为此类杆件的强度计算提供依据。     

悬臂梁大挠度变形的近似估计法

研究了悬臂梁自由端受集中力作用时的大挠度变形问题,对大挠度的界定方法做出了一些讨论,并从计算数据分析和理论推导两方面归纳出一种不通过复杂计算就能对大挠度变形进行定量估计的方法. 分析表明,由挠曲线近似微分方程得出的自由端挠度值与梁长度之比值的平方,可以近似表示小挠度法计算挠度值偏离精确挠度值的误差,并由此得出大挠度变形的估计值. 该方法避免了复杂的微分方程求解和数值计算,有一定的工程实际意义.     

A new technique for large deflection analysis of non-prismatic cantilever beams

This paper studies the very large deflection behavior of prismatic and non-prismatic cantilever beams subjected to various types of loadings. The formulation is based on representing the angle of rotation of the beam by a polynomial on the position variable along the deflected beam axis. The coefficients of the polynomial are obtained by minimizing the integral of the residual error of the governing differential equation and by applying the beam’s boundary conditions. Several numerical examples are presented covering prismatic and non-prismatic cantilever beams subjected to uniform, non-uniform distributed loads and tip concentrated loadings in vertical and horizontal directions. The loads considered in this study are restricted to the non-follower type loads. Cases with different loadings and geometries are compared with MSC/NASTRAN computer package. However, for some very large deflection case, the MSC/NASTRAN failed to predict the deflected shape due to divergence problems.     

Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force

A realistic beam structure often exhibits material and geometrical non-linearity, in particular for those made of metals. The mechanical behaviors of a non-linear functionally graded-material (FGM) cantilever beam subjected to an end force are investigated by using large and small deformation theories. Young's modulus is assumed to be depth-dependent. For an FGM beam of power-law hardening, the location of the neutral axis is determined. The effects of depth-dependent Young's modulus and non-linearity parameter on the deflections and rotations of the FGM beams are analyzed. Our results show that different gradient indexes may change the bending stiffness of the beam so that an FGM beam may bear larger applied load than a homogeneous beam when choosing appropriate gradients. Moreover, the bending stress distribution in an FGM beam is completely different from that in a homogeneous beam. The bending stress arrives at the maximum tensile stress at an internal position rather than at the surface. Obtained results are useful in safety design of linear and non-linear beams.     

The complete process of large elastic-plastic deflection of a cantilever

An extension of the Elastica theory is developed to study the large deflection of an elastic-perfectly plastic horizontal cantilever beam subjected to a vertical concentrated force at its tip. The entire process is divided into four stages: I.elastic in the whole cantilever; II.loading and developing of the plastic region; III.unloading in the plastic region; and IV.reverse loading. Solutions for stages I and II are presented in a closed form. A combination of closed-form solution and numerical integration is presented for stage III. Finally, stage IV is qualitatively studied. Computed results are given and compared with those from small-deflection theory and from the Elastica theory.     

海洋管线在有摩擦的弹性地基上铺设时的大变形分析

本文在[1]文献的基础上,进一步考虑了地基的弹性变形和摩擦的影响,分析和计算了海洋管线在铺设工况下的大变形.文中采用奇异摄动技术和幂级数解相结合,并针对几种不同的地基模型,提出了含二参数和四参数两类非线性方程组的迭代格式,成功地求得了问题的解.     

ELASTIC EFFECT IN DYNAMIC RESPONSE OF PLASTIC CANTILEVER BEAMS TO IMPACT

A lumped masses-springs model is proposed to analyze the dynamicresponse of an elastic-plastic cantilever beam resulting from impact. The numericalresults are in good agreement with those by finite-element approaches. The simplifiedmodel can catch the most essential features of elastic-plastic response of beams; inparticular, it demonstrates the effect of elastic deformation on the distribution ofbending moment and energy dissipation, and provides valuable quatitative results.     

弹塑性悬臂梁结构动力响应中的弹性效应

本文提出由一组质量－弹簧构成的力学系统来研究弹塑性悬臂梁的动力响应问题，其数值结果与有限元解吻合得相当好，这种简化模型能够反映出梁动力响应中的本质特性，还特别显示出梁中弹性对弯矩分布和能量耗散的影响，提供了很有价值的计算结果．     

弹性地基上双层叠合梁的解

将双层叠合梁之间的接触状况拟合为一符合Ｇｏｏｄｍａｎ假设的弹性夹层,导出了Ｗｉｎ ｋｌｅｒ弹性地基上双层叠合梁的微分方程组及其解析解．通过引入“广义夹层反应模量”计入了夹层水平和竖向反力引起的梁截面的剪切和拉压形变效应,它有效地提高了计算精度,尤其是在双层梁结构有间断的场合．     

嵌入薄膜传感器悬臂梁三向力测量技术研究

以薄膜传感器悬臂梁作为等效模型,通过传感器的应变效应对三向力测量技术进行了研究。为提高薄膜传感器的应变输出响应,对悬臂梁上布放薄膜传感器的位置加设弹性结构,研究了三向力测力模型输出电压与传感器所在位置应变的关系;分析了受力位置对测力模型输出响应的影响关系,结合实验验证了其工作原理、测力模型应变输出响应与可控尺寸参数的关系。研究表明:该测力模型可实现三向力测量,各个方向最大测量误差均在9%以内,悬臂梁宽度方向x和高度方向z的交叉干涉误差分别为2.84%和3.37%;当悬臂梁自由端受力位置发生变化时,测力模型输出响应只在梁长度方向y上发生变化。     

用高阶剪切变形理论研究双模量梁的弯曲

利用高阶剪切变形理论研究了双模量梁的弯曲变形问题,推导出了双模量梁的挠曲线方程及弯曲正应力公式．讨论分析了翘曲函数的指数n对挠度、正应力的影响．研究结果表明：拉压弹性模量的差异对梁的弯曲应力有较大影响．把高阶剪切变形理论的计算结果与弹性理论计算结果进行比较,可知该方法计算精度非常高．     

一端外伸梁对称弯曲弹性位移的置换法确定

置换法应用于求解一端外伸梁,在对称弯曲的条件下,根据直梁挠曲线所在平面内其与切线所成图形的边角几何关系,推导出求解该形梁的挠度和转角的置换法位移方程,其变量是相应的置换梁自由端的挠度、梁长、梁轴线位置坐标等. 对具体载荷梁的求解过程是：先以具体量值填充左、右置换梁自由端的挠度,再将其代入该置换法位移方程的统一表达式,即得到所求梁段的挠度、转角的方程全解. 所用的计算为代数方程的分式四则运算,只需挠曲线和叠加原理概念,无需积分,一般无需查挠度表,结果精确. 给出工程背景的算例.     

大变形复合材料柔性梁静,动特性的试验研究

本文对两种铺层的复合材料柔性梁进行了静、动特性的试验研究,重点研究了挠度、结构耦合、梁的根部安装角等对变形、固有频率的影响。得出的结论有助于直升机旋翼桨叶的设计和发展,并且验证了大挠度复合材料柔性梁的分析模型     

梁式构件动态弹性模量的实验研究及振动分析中梁的有效长度问题

本文根据实验资料,用不同方法求得加重乳胶梁的前四阶动态弹性模量,加重乳胶材料的动态弹性模量随着振动阶次的提高而提高。在振动问题中,不能以梁的实际长度与梁高之比来划分梁的类型。在低阶振动时,粱的“平截面”假定可能满足精度要求,随着振动阶次的提高其误差会迅速增大,本文讨论了梁的有效长度问题。     

考虑轴力二阶效应悬臂梁的支承及裂纹参数识别

建立了轴向压力作用下悬臂裂纹梁边界支承和裂纹损伤程度识别方法．首先,将悬臂梁边界非完整支承等效为竖向和扭转弹簧、梁中开裂纹等效为内部扭转弹簧,利用Laplace变换,得到了边界弹性支承、考虑轴向压力二阶效应、具有任意裂纹数目Euler-Bernoulli悬臂梁弯曲挠度的解析解．其次,提出了边界弹性支承弹簧柔度和裂纹等效扭转弹簧柔度的识别方法．最后,通过数值试验,考察了轴向压力,裂纹深度以及测量误差等对识别结果的影响,说明了本文考虑轴向压力二阶效应的悬臂梁边界支承弹簧柔度及裂纹等效扭转弹簧柔度识别方法的适用性和可靠性,结果表明：相比于应变测量误差,挠度测量误差对裂纹损伤程度识别结果影响更加敏感,且轴向压力对裂纹损伤程度识别影响较小,因此,应严格控制挠度的测量误差．同时,边界支承扭转弹簧柔度的识别误差大于其竖向弹簧柔度识别误差．这些结果为实际工程中边界非完整支承悬臂裂纹梁的参数识别提供了指导．     

集中载荷作用下弹性地基圆薄板大挠度问题的精确解

本文处理了winkler型弹性地基上圆板受集中载荷作用的大挠度问题,第一次获得了这类问题的精确解的解析式,并用此精确解进行了具体求解,其结果可供工程直接使用,这较之已有文献中的近似处理方法具有更好的可靠性,同时也为研究大挠度理论提供了可靠的依据。     

弹性模量的发现历程

尽管弹性模量以英国科学家托马斯·杨（Thomas Young,1773—1829）的名义命名,被称为杨氏模量,然而,弹性模量的发现并非由托马斯·杨一人独立完成。本文通过文献梳理,重点分析了雅各布·伯努利（Jacob Bernoulli,1655—1705）、欧拉（Leonhard Euler,1707—1783）、里卡蒂（Giordano Riccati,1709—1790）、托马斯·杨、纳维（Claude-Louis Navier,1785—1836）等人在弹性模量发现过程中的贡献,通过勾勒弹性模量概念的发现历程,探索力学概念在其发展过程中的内在逻辑性。