关于对动点的动量矩定理------理论力学札记之八

介绍质点系对动点的动量矩定理并讨论它的一些应用.     

关于达朗贝尔原理------理论力学札记之六

介绍d'Alembert原理的原述, 后人对d'Alembert原理的理解, 并给出几点评论.     

关于理想约束和虚位移原理——分析力学札记之二十

 理想约束是分析力学的基本假定, 虚位移原理是分析静力学的基本原理. 本文从经典著作和重要教材中提取一些信息, 期望描述理想约束和虚位移原理的形成和发展, 并发表一些议论.     

关于一阶Lagrange系统------分析力学札记之十七

讨论一阶非奇异和奇异Lagrange系统的方程, 以及它们与Birkhoff方程和广义Hamilton方程的关系.     

理论力学的教学实践

探讨了理论力学教学中, 不同教学内容的讲授方式、教师个人素质的作用以及扬长避短采用多媒体教学手段的问题.     

关于理论力学概念教学模式的一些思考

 通过对理论力学中基本概念的分析与总结, 探讨了如何利用概念教学进行教学方法的研 究, 引导学生通过概念建立力学模型, 进行问题的分析和求解, 提高学生的工程师素质. 对概念教学模式的探讨也为提高课堂教学质量和教学水平提供一些思路和参考.     

关于Emden方程的对称性——————分析力学札记之十一

 研究著名的Emden方程的3种表达在群的无限小变换 下的Noether对称性、Lie对称性和形式不变性. 结果表明, 同一微分方程的不同表达可有不同的对称性.     

关于动力学普遍方程——————理论力学札记之三

 归纳理论力学教材中关于动力学普遍方程的几种典型 表述,对这些表述进行评述, 并给出较全面的表述.     

关于机械能守恒律——————理论力学札记之一

 归纳理论力学教材中关于机械能守恒律的几种典型表述, 对典 型表述进行评述,并给出较全面表述的建议.     

关于经典Appell-Hamel例——————分析力学札记之九

 不可积分微分约束系统动力学有Appell-Chetaev模型和Vacco模型,对经典Appell-Hamel例两个模型有同样解.     

Apparent forces of analytical mechanics

Summary Some extensions of the apparent forces of classical mechanics are expounded, taking the following cases of motion: point referred to general coordinates involving time, point tied to a moving surface and a holonomic system with moving constraints.For a holonomic system with moving constraints and with stationary kinetic energy the apparent forces formally coincide (allowing, obviously, for a conversion ratio) with the ponderomotive forces of a stationary electromagnetic field.Lastly, the apparent forces introduced by the method of ignoration of coordinates are considered and the analogy of this case with the previous one is elucidated.

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Sommario Si mettono in evidenza alcune estensioni delle forze apparenti della Meccanica classica, prendendo in considerazione i seguenti casi di movimento: punto riferito a coordinate generali involgenti anche il tempo, punto vincolato a superficie mobile, sistema olonomo con vincoli mobili.Si rileva in particolare che per un sistema olonomo a vincoli mobili con energia cinetica stazionaria le forze apparenti coincidono formalmente (salvo naturalmente un coefficiente di ragguaglio) con le forze ponderomotrici di un campo elettromagnetico stazionario.Si considerano infine le forze apparenti introdotte dal metodo di ignorazione delle coordinate e si mostra il perchè dell'analogia di questo caso col precedente.

     

Analysis of the structure of generalized forces in the Lagrange equations

Stability of mechanical systems in the sense of Thomson and Tait [1] can be judged from the type of forces applied to them. The forces are usually divided into potential (conservative), circular, dissipative, accelerating, gyroscopic, etc. The decomposition itself of generalized positional forces into conservative and properly nonconservative forces is well known for the case in which these forces linearly depend on the generalized coordinates (e.g., see [1–5]). Such a decomposition is associated with the unique representation of an arbitrary matrix of these forces as the sum of symmetric and skew-symmetric parts. Generalized forces linearly depending on the velocities can in a similar way be divided into dissipative and gyroscopic parts. In the present paper, we show how the same decomposition can be performed in the general nonlinear case.     

Configurational forces and couples in fracture mechanics accounting for microstructures and dissipation

Configurational forces and couples acting on a dynamically evolving fracture process region as well as their balance are studied with special emphasis to microstructure and dissipation. To be able to investigate fracture process regions preceding cracks of mode I, II and III we choose as underlying continuum model the polar and micropolar, respectively, continuum with dislocation motion on the microlevel. As point of departure balance of macroforces, balance of couples and balance of microforces acting on dislocations are postulated. Taking into account results of the second law of thermodynamics the stress power principle for dissipative processes is derived.Applying this principle to a fracture process region evolving dynamically in the reference configuration with variable rotational and crystallographic structure, the configurational forces and couples are derived generalizing the well-known Eshelby tensor. It is shown that the balance law of configurational forces and couples reflects the structure of the postulated balance laws on macro- and microlevel: the balance law of configurational forces and configurational couples are coupled by field variable, while the balance laws of configurational macro- and microforces are coupled only by the form of the free energy. They can be decoupled by corresponding constitutive assumption.Finally, it is shown that the second law of thermodynamics leads to the result that the generalized Eshelby tensor for micropolar continua with dislocation motion consists of a non-dissipative part, derivable from free and kinetic energy, and a dissipative part, derivable from a dissipation pseudo-potential.     

On the method of Lagrange multiplier and others

The fundamentals for the correct use of the method of Lagrange multiplier are presented and illustrated by examples. Some misunderstandings of the method are clarified. Equivalent variational principles are defined. It is pointed out that for a given problem of mechanics, there may be many equivalent and unequivalent variational principles. The functional of the so called generalized variational principles of elasticity with more general forms^[16] are linear combinations of the well known functionals given by Reissner and Hu-Washizu.     

On configurational forces in multiplicative elastoplasticity

The main goal of this work consists in the elaboration of the material or rather configurational mechanics in the context of multiplicative elastoplasticity. This nowadays well-established approach, which is inherently related to the concept of a material isomorphism or in other words to a local rearrangement, is adopted as a paradigm for the general modelling of finite inelasticity. The overall motion in space is throughout assumed to be compatible and sufficiently smooth. According to the underlying configurations, namely the material and the spatial configuration as well as what we call the intermediate configuration, different representations of balance of linear momentum are set up for the static case. The underlying flux terms are thereby identified as stress tensors of Piola and Cauchy type and are assumed to derive from a free energy density function, thus taking hyperelastic formats. Moreover, the incorporated source terms, namely the configurational volume forces, are identified by comparison arguments. These quantities include gradients of distortions as well as dislocation density tensors. In particular those dislocation density tensors related to the elastic or plastic distortion do not vanish due to the general incompatibility of the intermediate configuration. As a result, configurational volume forces which are settled in the intermediate configuration embody non-vanishing dislocation density tensors while their material counterparts directly incorporate non-vanishing gradients of distortions. This fundamental property enables us to recover the celebrated Peach–Koehler force for finite inelasticity, acting on a single dislocation, from the intermediate configuration volume forces.     

????Appell?????????——————?????????????

介绍法国力学家Appell巨著的前两卷,以及他对理论力学的贡献, 并在此基础上给出几点评论.     

On universal relations in continuum mechanics

This paper is devoted to a systematic study of local universal relations in continuum mechanics. We show that it is possible to determine the complete set of independent universal relations whose characterization is obtained by linear universal rules. A historical review of the literature on the topic and various significant examples are given. Received: August 16, 1996     

滚动圆环的力学问题

讨论了带质量偏心的圆环在滚动过程中能否解除约束跳起腾空的问题. 从简单的动力学知识出发,导出圆环离地的充分必要条件.