逐段变形效应叠加法的能量法证明及其推广

采用能量法证明了计算静定的梁、刚架和杆系位移的逐段变形效应叠加法,并讨论了对于组合变形和非线性问题的推广.     

计算梁弯曲变形的一种特殊叠加法

梁的弯曲变形是材料力学的核心内容之一。本文基于梁的弯曲变形理论,以悬臂梁的弯曲变形为基础,给出了一种求解梁弯曲变形的“特殊叠加法”,该方法对于计算简支梁、外伸梁以及变刚度梁的变形问题尤为方便和有效。

     

静定刚架弯矩图的叠加法活用与对称性利用

静定刚架弯矩图的绘制是结构力学教学中最为重要和基础的内容, 针对现行教材中讲述该部分知识点较少涉及的弯矩图快速绘制方法, 探讨了叠加法活用与对称性利用的基本思想及其综合应用思路, 并通过多个典型例题展示两种方法的应用技巧及其有效性和便捷性. 实践证明, 在静定刚架弯矩图教学中引入这两种方法, 充分体现了结构力学的思维性和趣味性特征, 不仅提高了学生绘制复杂刚架结构弯矩图的能力, 同时也增加了他们对结构力学的兴趣.     

关于逐段变形效应叠加法的证明与讨论

提出逐段变形效应叠加法适用于含有悬臂梁部分的结构,一般不适用于简支梁. 对于简支梁,用荷载叠加法比较方便. 用相当简单的方法证明了逐段变形效应叠加法. 讨论了该方法在静定结构与静不定结构中应用的可能性. 由于该方法适用于含有悬臂部分的结构,提议将该方法改称为分段悬臂梁叠加法.     

变截面悬臂梁的刚度叠加法

利用梁的弯曲刚度与位移成反比的关系, 可较为方便地计算变截面悬臂梁端截面的位移．该 方法是区别于载荷叠加法和逐段变形效应叠加法的叠加方法．     

阶梯梁的位移计算方法对比

为了加深学生对位移法及阶梯梁位移计算的理解,以阶梯式简支梁为例,分别利用积分法、常规图乘法、刚度叠加法及位移法求解了阶梯式简支梁的位移。计算结果表明：利用位移法求解阶梯式简支梁的位移具有独特的优势,可显著减少计算工作量并提高计算准确率,值得在教学过程中推广。

     

关于位移法计算有侧移斜梁的研究

针对用位移法计算有侧移斜梁时遇到的几个问题进行了研究,利用运动学原理对斜梁位移进行分析,采用力法对几种常见载荷作用下的斜梁进行理论推导,得到了几个重要结论: 一是斜梁的侧移计算公式,二是一端固定、一端定向支承(支杆与斜梁斜交时)的有侧移单跨斜梁的转角位移方程、固端弯矩分别与两端固定支承的水平梁的相同,所以计算此类斜梁时可以按两端固定支承的单跨水平梁处理.     

叠加法求变刚度弹性板大变形下最大挠度的研究

利用逐段变形效应叠加法推导出求解变刚度弹性板大变形下最大挠度的解析方程,扩大了叠加法的应用范围。在此基础上,本文以典型变刚度弹性板——滑雪板为例,对解析方程作了进一步阐述。最后利用解析方程解,求出滑雪板在滑雪转弯时最大挠度和速度之间的耦合方程。此方程对滑雪运动具有指导意义。     

无约束反对称静不定刚架截面相对位移的解法

从虚功原理出发,重点讨论了在求解无约束反对称静不定刚架截面相对位移时,单位载荷状态的构造方法与原则,可以启发教师和学生在进行该部分内容的讲授与练习时,从本质上理解并灵活运用单位载荷法.     

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提出计算弯曲变形的虚悬臂梁法. 利用变形等效概念将非固端杆件转化为悬臂杆件(悬臂梁或一端固支刚架), 仅借助悬臂梁受集中力和均布载荷下的位移公式, 即可求得受复杂载荷非固端杆件任意截面的广义位移. 给出了把非固端杆件转化为虚悬臂梁的解法和算例. 该法规范, 易于编程, 有独特的优越性.     

Forced vibrations and accumulation of plastic displacements of a compressed beam

Summary Using the theory of plastic hinges the equations of motion for a clamped beam made of elastic-plastic material are derived. As examples the response of the system to impact and harmonic excitation are discussed. The analytical results are compared with experimental investigations.

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Wachstum plastischer Deformationen eines Druckstabes bei Zwangserregung

Übersicht Unter Verwendung der Fließgelenktheorie werden die Bewegungsgleichungen des eingespannten, gedrückten Stabes aus elastisch-plastischem Material hergeleitet. Als Beispiele werden die Antwort des Systems auf Stoß- und harmonische Erregung diskutiert und die analytischen Ergebnisse mit Experimenten verglichen.

     

On the choice of the reference frame for beam section stiffness properties

This work discusses the choice of a reference frame for beam section stiffness properties. Established concepts as the center of elasticity, the center of stiffness and the center of compliance are discussed and contextualized. An interpretation of univocally defined generalized strain transformations is given in terms of minimization of appropriate norms of the stiffness and compliance matrices of the beam section that univocally define special reference points. Transformations of generalized strain perturbations that preserve the angular strain are sought. They are subsequently constrained to represent a change of reference point, and further restricted to lie in the plane of the section. Each transformation is univocally defined and given a clear mathematical and geometrical interpretation. It is recognized that transformations that decouple forces and linear strains from moments and angular strains cannot be described as a mere change of reference point.     

Relative displacements of the two sides of a plane crack

We consider a two dimensional deformation of an infinite anisotropic elastic material which contains a plane crack. When tractions are specified over the crack faces, we give a formula for the corresponding relative displacements of the two sides of the crack. We also consider the inverse problem of determining the elastic constants by measuring the tractions and the corresponding relative displacements on the crack.     

二层刚架动静态综合性实验设计研究

 根据学科的发展并结合作者的实践，设计了二层刚架动静态综合性教学实验，包 括最大静态应力应变、最大动态应力应变的测试. 通过一组综合性实验作为示范，介绍二层 刚架的教学实验要求、实验把握、实验讨论等，说明了二层刚架具有使学生理论融会贯通、 培养学生思维形象化和综合分析能力及动手能力的特点，亦反映了二层刚架适合于教学实验 的特色.     

Stability analysis for two kinds of equations in two-species population dynamics

In this paper we study the stability for equilibrium points of equations in two-population dynamics.We discuss two predator-prey-patch models.Model1 is described by a differential equation.Model2 is described by an integral differential equation.We obtain the conditions for the stability of their equilibrium points.The results show that the overall population stability despite local extinction is realizable.     

新型发射药爆炸TNT当量系数的实验研究

TNT当量系数是危险品工程抗爆设计和安全距离确定的重要依据。为确定H1和H2两种新型高能发射药的TNT当量系数,分别开展了10 kg TNT和新型发射药的空气自由场静爆实验。基于修正的当量系数计算方法和测量得到的不同爆心距离处冲击波超压时程曲线,确定了不同比例距离处两种高能发射药的超压和比冲量TNT当量系数。研究结果表明,发射药爆炸产生的冲击波传播规律与TNT炸药爆炸产生的冲击波传播规律相同,符合爆炸相似律,相同质量发射药爆炸产生的冲击波超压和比冲量都显著高于TNT的。随着比例距离的增大,H1的超压当量系数先增大后减小,最大值为1.34;H2的超压当量系数逐渐减小,最大值为1.26。两种新型发射药的比冲量TNT当量系数均随比例距离的增大先减小后增大,H2的比冲量TNT当量系数大于H1的,最大值为1.38。本文中修正的计算方法能更准确计算被试样品的TNT当量系数,实验结果可为提高抗爆结构安全性设计提供参考。     

Application of nonlocal beam models for carbon nanotubes

Investigations of wave and vibration properties of single- or multi-walled carbon nanotubes based on nonlocal beam models have been reported recently. However, there are numerous inconsistencies in the handling of the governing equations, applied forces, and boundary conditions based on some of the reported nonlocal beam models. In this paper, the consistent equations of motion for the nonlocal Euler and Timoshenko beam models are provided, and some issues on the nonlocal beam theories are discussed. The models are then applied to the studies of wave properties of single- and double-walled nanotubes. The wave and vibration properties of the nanotubes based on the presented nonlocal beam equations are studied, and scale effects are discussed.     

The new solutions for two kinds of axially symmetrical laminar boundary layer equations

The transformations, which are similar to Mangier's transformation, are given in this paper, and make the two kinds of entrance region flow of axially symmetrical laminar boundary layer in internal way into the flow of two-dimensional boundary layer, and simplify the proboems. The simplified equations can be solved by the 2-D boundary layer theory. Therefore, a new way is opened up to solve the axially symmetrical flow in the entrance region of internal way.Project Supported by the Scientific Fund of Chinese Academy of Science.