关于牛顿力学的力和拉格朗日力学的力------理论力学札记之九

讨论了牛顿力学和拉格朗日力学中的力. 在牛顿力学中着重讨论了主动力, 约束和理想约束力. 在拉格朗日力学中着重讨论了广义力的两种分解方法.     

分析力学的3部经典著作及其作者

介绍分析力学学科的3部经典著作. Whittaker的《分析动力学》、Hamel 的《理论力学》和Lurie的《分析力学》. 概述这些经典著作的主要内容, 考察这些著作对学科发 展的影响, 分析这些著作的特点, 最后介绍各书作者的学术简历、主要贡献和其他著作.     

超细长弹性杆的分析力学问题

超细长弹性杆作为DNA等生物大分子链的力学模型，其平衡和稳定性问题已成为力学与分子生物学交叉的研究热点．虽然在Kirchhoff动力学比拟的基础上，用分析力学方法讨论弹性杆的文章已见诸文献，但尚未形成弹性杆分析力学的严格理论．本文研究了超细长弹性杆分析力学的若干基础性问题．对杆截面的自由度、虚位移、约束方程及约束力等基本概念给出严格的定义和表达式．建立弹性杆平衡的D’Alembert-Lagrange原理、Jourdain原理和Gauss原理；从D’Alembert-Lagrange原理导出Hamilton原理．从变分原理出发导出Lagrange方程、Nielsen方程、Appell方程和Hamilton正则方程；对于受约束的弹性杆，导出了带乘子的Lagrange方程．讨论了Lagrange方程的首次积分．对于杆中心线存在尖点的情形，导出了微段杆平衡的近似方程。     

关于分析力学的定义与内容——分析力学札记之二十五

学习和研究分析力学多年,回过头来看,还是有不少问题值得商讨,如分析力学怎样定义,分析力学哪些概念是不可缺少的,Newton 力学与分析力学的关系等. 该文就分析力学的这些问题做一归纳并提出一些看法.     

The theory of relativistic analytical mechanics of the rotational systems

I'IntroductionThespinningmotionisintrinsicattributeofmicroscopicparticle.In1979,R.BengtssonandS.Frauendorfaccuratlymeasuredthemaximumvolumesofthespinningrotativevelocityof14kindsofnucleons,andtheresultsshowedthatthemaximumvolumesofthespinningrotativevelocityofeachnucleonaredifferent[ll.Withthede\'elopingofmodernscienceandtechnology,moreandmoreexperimentalfactsrelatedtothehighspeedrotationquestions,theEinstein'srelativitytheoryandtherotationaltheoryofclassicalmechanicsarenotsuitabletothesepro…     

An analytical soluion of wave forces on large square cylinder

Wave forces on large square cylinder are determined by using the conformal transformation method. It is found that only for square cylinder, the governing equation is still the Helmholtz equation after the conformal transformation. An analytical solution of wave forces on square cylinder is presented by using the solution of wave forces on a circular cylinder.     

Methods of analytical mechanics in the constrained adaptive identification problems

The application of analytical mechanics methods to the problem of adaptive identification is discussed. The estimated constant parameters satisfy nonlinear equations considered as parametric constraints. Some modifications of identification algorithms are proposed to satisfy such constraints.     

Nielsen's and Euler's operators of higher order in analytical mechanics

In this paper, the definitions of Nielsen’s and Euler’s operators of higher order are presented. These operators are concerned in analysis for systems with holonomic constraints and non-holonomic constraints of higher order. Some theorems that indicating relation between the two operators are established. Moreover, using the theorems, the new equations of mechanical systems with constraints of higher order are derived. Finally, an example is given.     

Experimental and analytical investigation of the mechanics of crawl stroke swimming

A three dimensional analytical model for crawl stroke swimming is developed in which the swimmer is modeled as a body and two arms connected to the body at the shoulder joints. Each arm is assumed to consist of three segments. The numerical results obtained from the model are compared with the results of two sets of experiments performed. In the first series of experiments, the tether forces developed in crawl stroke swimming are measured and a linear correlation between the tether force and the stroke rate is obtained. In the second series of experiments, untethered crawl stroke swimming for different arm position angles is recorded. The results are presented in graphical forms and the effect of stroke rate on swimming velocity is discussed.     

Variational principles and differential inclusions for unilateral constraints in analytical mechanics

Summary The present paper deals with variational principles in terms of hemivariational inequalities and with differential inclusions for unilateral constraints in analytical mechanics. It is discussed how it is possible to describe one-sided constraints in a very general manner by the help of Clarke's generalized gradient.

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Sommario Questo scritto prende in esame i principi variazionali nella forma delle hermivariational inequalities e le inclusioni differenziali per vincoli unilaterali nella meccanica analitica. Si deduce come sia pissobile descrivere vincoli unilaterali, in modo generale facendo uso di gradienti generalizzati di Clarke.

     

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.     

The Okhotsimskii-Pontryagin method in control theory and analytical mechanics. Part I

The Okhotsimskii method for the differentiation of functionals in control theory is discussed on the basis of the Pontryagin formalism. The association of this method with other approaches to solving control problems and with methods of analytical mechanics is studied. Some typical cases of solving optimal control problems are considered.     

固体力学中的统一分析梁与有限节线法

针对现有梁理论不能解决的杆状类工程结构构件和结构体系,本文提出了一种新的梁模型——统一分析梁与一种新的数值分析方法——有限节线法。利用统一分析梁和有限节线法不仅可以解决任意杆状类结构构件或结构体系的力学分析问题,而且当问题的性质与传统梁理论的前提条件一致时,会得出同样精度的解答。算例计算结果证明了统一分析梁的合理性与有限节线法的正确性。     

The Okhotsimskii-Pontryagin method in control theory and analytical mechanics. Part II

The Okhotsimskii method for the differentiation of functionals in control theory is discussed on the basis of the Pontryagin formalism. The relation of this method to other approaches to solving control problems and to other methods of analytical mechanics is studied. Some typical cases of solving optimal control problems are considered. The brachistochrone problem is solved with consideration of viscous friction.     

An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes

An analytical molecular structural mechanics model for the prediction of mechanical properties of defect-free carbon nanotubes is developed by incorporating the modified Morse potential with an analytical molecular structural model. The developed model is capable of predicting Young’s moduli, Poisson’s ratios and stress–strain relationships of carbon nanotubes under tension and torsion loading conditions. Results on the mechanical properties of single-walled carbon nanotubes show that Young’s moduli of carbon nanotubes are sensitive to the tube diameter and the helicity. Young’s moduli of both armchair and zigzag carbon nanotubes increase monotonically and approach Young’s modulus of graphite when the tube diameter is increased. The nonlinear stress–strain relationships for defect-free nanotubes have been predicted, which gives a good approximation on the ultimate strength and strain to failure of nanotubes. Armchair nanotubes exhibit higher tensile strength than zigzag nanotubes but their torsion strengths are identical based on the present study. The present theoretical investigation provides a very simple approach to predict the mechanical properties of carbon nanotubes.     

An analytical method for solving internal forces and deformations of bar-system structure in space

In this paper, based on the idea of finite element method, the initial parametric method in bending problem of a beam is extended to analyse the bar-system structure by employing Dirac function and Heaviside step function.Then a new method for analysing the internal forces and deformations of bar-system structure in space is suggested by improving the mixed method in statically indeterminate structure.The inferred process and obtained answer will be more succinct and accurate when the problem of internal forces and deformations of bar-system structure is analysed by using the new method provided in this paper.     

Nonlinear mechanics of a ring structure subjected to multi-pairs of evenly distributed equal radial forces

Combining the elastica theory,finite element(FE) analysis,and a geometrical topological experiment,we stud-ied the mechanical behavior of a ring subjected to multi-pairs of evenly distributed equal radial forces by looking at its seven distinct states.The results showed that the theoretical predictions of the ring deformation and strain energy matched the FE results very well,and that the ring deformations were comparable to the topological experiment.Moreover,no mat-ter whether the ring was compressed or tensioned by N-pairs of forces,the ring always tended to be regular polygons with 2N sides as the force increased,and a proper compressive force deformed the ring into exquisite flower-like patterns. The present study solves a basic mechanical problem of a ring subjected to lateral forces,which can be useful for studying the relevant mechanical behavior of ring structures from the nano-to the macro-scale.     

Elastic-plastic analytical solutions for an eccentric crack loaded by two pairs of anti-plane point forces

IntroductionTheelastic_plasticanalysisforacrackedplatewithfinitedimensionsisoneofthemostdifficultfieldsofelastic_plasticmechanics .Thenearcracklineanalysismethod ,whichwasfirstproposedbyAchenbachetal.[1,2 ] ,hasbeenimprovedbyYiinRefs.[3,4 ].InRefs.[3,4 ],…