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分析人体双足步行的动态稳定性以及跳跃运动的动力学过程. 讨论与竞走和跑步运动有关的 力学问题.     

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简要介绍伯努利家族在力学上的贡献. 在19世纪力学3项最突出的进展:分析力学、连 续介质力学和统计力学方面,伯努利家族的成就起着奠基和先行者的作用.     

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一 1957年1月,我在清华园第一次见到郭永怀先生.当时郭先生承担主讲清华大学和力学研究所合办的力学研究班‘流体力学'讲座,他对我们几个流体力学辅导教员说:实验工作很重要,今后你们的主要工作就是准备并指导实验.为此他亲自带我们去北京航空航天大学参观风洞实验室并拜访陆士嘉先生.     

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等截面直梁受纯弯曲作用,其挠曲线精确解为圆弧线,然而用图乘法和重积分法求得的却都 是抛物线. 分析了用图乘法和重积分法求解纯弯曲梁的挠曲线均是抛物线而不是圆弧线的原 因,给出了用抛物线代替圆弧线的误差.     

全应变梯度挠曲电纳米梁有限单元法研究

挠曲电效应是一种存在于所有电介质材料中的特殊的力电耦合效应,本质上是应变梯度与电极化之间的线性耦合。然而,应变梯度会引入位移的高阶偏量,常给挠曲电问题的理论求解带来困难。且已有研究表明应变梯度弹性项会影响纳米结构中的力电耦合响应,但是现有的挠曲电研究大多忽略了应变梯度弹性的影响。因此,本文提出了一种既考虑应变梯度弹性,又考虑挠曲电效应的有效数值方法。基于全应变梯度弹性理论,建立了包含3个独立材料尺度参数的纳米欧拉梁的理论模型和有限元模型,提出了满足C₂弱连续的两节点六自由度单元。基于本文的有限单元法,以简支欧拉梁为例,通过分析讨论挠度、电势和能量效率,得到了挠曲电效应和应变梯度弹性项对梁的力电响应的影响。结果表明,挠曲电效应存在尺寸依赖性,且应变梯度弹性项在纳米电介质结构的挠曲电研究中的影响不可忽略。     

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以晚清数学家李善兰和西方传教士丁韪良译著中出现的符号为代表, 对其在图形和计算过程中的应用规律、特点作一些分析对比, 进一步归纳总结, 探讨晚清力学译著中的符号系统. 揭示晚清时期符号系统在力学学科的发展和使用状况.      

连续阶梯梁影响线方程的奇异函数法研究

 介绍了奇异函数的特性，通过奇异函数给出了单跨梁的影响线表达式， 建立了连续阶梯梁影响线计算公式，形式简单统一，便于编制程序进行电算. 最后 给出了该方法的应用实例.     

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简述了多刚体系统接触及碰撞动力学的研究方法，详细回顾了考虑库仑摩擦的多刚 体系统的能量不协调、Painlev\'{e}疑难及碰撞恢复系数等该领域中难点问题的研 究进展，探讨了解决该难点问题的研究思路，指出了未来该领域的研究方向.     

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本文阐述时变力学这一新的研究方向,对其基本课题、特征及力学、数学方法与进展作了较为系统概述,并结合工程实践说明时变固体力学方向研究的重要性与发展前景．     

任意支承梁的固有频谱和模态的定性性质

确定了任意支承方式下欧拉梁横振动时其频谱和位移、转角、应变模态的一些重要特性，阐明了梁的位移模态的充分必要条件．     

Method of equilibrium differential equation for analysis of strength of large deflection drill string

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An integral equation approach to finite deflection of elastic plates

The present paper concerns an approximate integral equation approach to finite deflection of elastic plates with aribitrary plan form. With the combined help of the Berger equation governing non-linear bending and a weighted residual technique for boundary-value problem, a boundary integral equation is formulated for immovable edge conditions. We here clarify the formulation and show that the calculation can be performed, with a slight modification, through a procedure similar to that conventionally employed in the linear bending analysis. Availability of the derived integral equation and the solution scheme is shown by way of simple numerical examples.     

On the equation of deflection of a thick plate

Summary Approximate equations of the deflection of a thick plate are derived from fundamental equations of a three-dimensional elastic body, by expanding components of displacement into power series in platethickness h and then by truncating at appropriate terms of 0(h ⁿ ).The method proposed here enables us to give a systematic treatment to obtain approximate equations with any desired accuracy in the sense of increasing order of h. As an example, a thick plate is treated under distributed pressure acting at its upper surface.

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Über die Gleichung zur Durchbiegung einer dicken Platte

Übersicht Näherungsgleichungen für die Durchbiegung einer dicken Platte werden aus den drei-dimensionalen Fundamentalgleichungen der Elastizität hergeleitet, wobei die Verschiebungen erst nach Potenzreihen der Plattendicke h entwickelt und danach an passenden Termen von 0(h ⁿ ) abgebrochen werden.Die hier präsentierte Methode ermöglicht uns ein systematisches Verfahren, um die Näherungsgleichungen mit einer beliebig gewünschten Genauigkeit im Sinne zunehmender Ordnung von h zu gewinnen. Als ein Beispiel wird eine dicke Platte unter verteilter Belastung an ihrer Deckfläche behandelt.

     

The difference methods for the solution of singular-perturbation for the elliptic-parabolic differential equation

In this paper it is discussed the difference method for the solution of singular perturbation problems for the elliptic equations, involving small parameter in the higher derivatives. As ε= 0 the original equations are degenerated into the parabolic equations.Authors constructed special difference schemes by means of the boundary layer properties of the solutions of these problems as well as investigated the convergence of this scheme and asymptotic behaviour of the solutions. Finally, a numerical example is given.     

The exponential asymptotic solution of differential equation

In this paper, the exponential asymptotic solution (E.A.S.) of differential equation is discussed. Firstly, E.A.S. of the second-order differential equation is studied and the orthogonal conditions of the uniformly valid E.A.S. are found out. Next, E.A.S. in matched asymptotic method is discussed. Finally, some examples are given.     

The differential solution to the flyinc locus equation of the shot and its application

This paper establishes a locus equation of the shot according to kinematical principes. By using differential and integral calculus and trigonometric function, we have found the extreme valve of the angles of delivery and the best flying distances, with the falling points of t’ short considered. Thus a simple expression showing the relationships among the bes’ angle o delivery, the best flying distance, the height of delivery point and its initial velocity can be attained and a diagram can be made by calculating, showing the best angle of delivery and the best flying distance.     

The corner solution for quasilinear differential equation with two parameters

I.IntroductionWeconsiderinthispaperboundaryvalueproblemofquasilineardifferentialequationby# pi(x,y)y' g(x,y)=0,a相似文献   

Applications of the integral equation method to delay differential equations

In this paper, we compare two approaches for determining the amplitude equations; namely, the integral equation method and the method of multiple scales. To describe and compare the methods, we consider three examples: the parametric resonance of a Van der Pol oscillator under state feedback control with a time delay, the primary resonance of a harmonically forced Duffing oscillator under state feedback control with a time delay, and the primary resonance together with 1:1 internal resonance of a two degree-of-freedom model. Using the integral equation method and the method of multiple scales, the amplitude equations are obtained. The stability of the periodic solution is examined by using the Floquet theorem together with the Routh–Hurwitz criterion (without time delay) and the Nyquist criterion (with time delay). By comparison with the solution obtained by the numerical integration, we find that the accuracy of the integral equation method is much better.     

A direct method for constructing solutions of the Hamilton-Jacobi equation

Summary A new method that allows to establish the existence of global solutions of the classical Hamilton-Jacobi equation for a Hamiltonian H(y, x), periodic in (x₁,,x_d), is presented.

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Sommario Si presenta un nuovo metodo che permette di Stabilire l'esistenza di soluzioni globali dell'equazione classica di Hamilton-Jacobi per Hamiltoniane H(y, x), periodiche in (x₁,,x_d).