A discussion of models for the behaviour of gas bearings, particularly of the aspects affecting the stability of the system. The text begins with a discussion of the mathematical models, identifying the stiffness and damping coefficients, and describing the behaviour of the models in unstable regions. It then turns to apply these results to bearings: static characteristics and stability of various rotor systems and an extensive discussion of air rings.

The application of composite materials to engineering components has spurred a ma jor effort to analyze such materials and the structures made from them. Most researchers workin in mechanics of composite structures understand that composite materials pro vide umque advantages but also present complex and challenging problems to researchers. The complex inelastic behavior and variety of failure modes of composite structures are a result of the strength and stiffness properties of constituents and their complex interac tions. Macromechanical constitutive models based on gross composite properties cannot realistically represent local interactions, and thus have serious limitations. The composite materials that are of most interest to engineering applications are often "brittle" in their behavior, in the sense that the strength and life of the material systems is controlled or greatly influenced by events or processes which involve volumes of material whose dimen sions are small compared to the global dimensions of the element. This is also true in ductile systems where local nonlinearity may contribute to local behavior which controls global response."

This book attempts to acquaint engineers who have mastered the essentials of structural mechanics with the mathematical foundation of their science, of structural mechanics of continua. The prerequisites are modest. A good working knowledge of calculus is sufficient. The intent is to develop a consistent and logical framework of theory which will provide a general understanding of how mathematics forms the basis of structural mechanics. Emphasis is placed on a systematic, unifying and rigorous treatment. Acknowledgements The author feels indebted to the engineers Prof. D. Gross, Prof. G. Mehlhorn and Prof. H. G. Schafer (TH Darmstadt) whose financial support allowed him to follow his inclinations and to study mathematics, to Prof. E. Klingbeil and Prof. W. Wendland (TH Darmstadt) for their unceasing effort to achieve the impossible, to teach an engineer mathematics, to the staff of the Department of Civil Engineering at the University of California, Irvine, for their generous hospitality in the academic year 1980-1981, to Prof. R. Szilard (Univ. of Dortmund) for the liberty he granted the author in his daily chores, to Mrs. Thompson (Univ. of Dortmund) and Prof. L. Kollar (Budapest/Univ. of Dortmund) for their help in the preparation of the final draft, to my young colleagues, Dipl.-Ing. S. Pickhardt, Dipl.-Ing. D. Ziesing and Dipl.-Ing. R. Zotemantel for many fruitful discussions, and to cando ing. P. Schopp and Frau Middeldorf for their help in the production of the manuscript. Dortmund, January 1985 Friedel Hartmann Contents Notations ........................................................... XII Introduction ........................................................ .

This book addresses the general theory of motion of mechanical systems with Coulomb friction. In particular, the book focuses on the following specific problems: derivation of the equations of motion, Painleve's paradoxes, tangential impact and dynamic seizure, and frictional self-excited oscillations. In addition to the theoretical results, the book contains a detailed description of experiments that show that, in general, the friction force at the instant of transition to motion is determined by the rate of tangential load and does not depend on the duration of the previous contact. These results are used to develop the theory of frictional self-excited oscillations. A number of industrially relevant mechanisms are considered, including the Painleve-Klein scheme, epicyclic mechanisms, crank mechanisms, gear transmission, the link mechanism of a planing machine, and the slider of metal-cutting machine tools. The book is intended for researchers, engineers and students in mechanical engineering.

Hemorheologic therapy has gained considerably in importance in recent years. This detailed and comprehensive book enumerates, discusses, and critically evaluates those treatment methods in which therapeutic success rests essentially on achieving an improvement in hemodynamics. After a general account of clinical hemorheology, fundamental aspects of hemorheologic methods and the eval- uation and assessment of hemorheologic parameters are discussed and the pathophysiology is described in detail. The treatment methods and substances that bring about improvement of the hemodynamics are described in chronologic order of first publication, and in each case all known later publications are also discussed in the order in which they appeared. This topical account of hemorheologic therapy - the results reported to date and the spectrum of applications - will be a valuable addition to the library both of the specialist and of all interested doctors in hospital and general practice.

Mechanical engineering, an engineering discipline born of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound is sues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series features graduate texts and research monographs intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that will cover a broad range of concentrations important to mechanical engineering graduate ed ucation and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the front page of the volume. The areas of concentration are applied mechanics, biomechanics, compu tational mechanics, dynamic systems and control, energetics, mechanics of material, processing, thermal science, and tribology. Professor Marshek, the consulting editor for dynamic systems and con trol, and I are pleased to present this volume of the series: Mechatronics: Electromechanics and Contromechanics by Professor Denny K. Miu. The selection of this volume underscores again the interest of the Mechanical Engineering Series to provide our readers with topical monographs as well as graduate texts."

Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming "vectorized" (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors they either added' a chapter on tensors or wrote a separate book on the subject."

Micro and nano-fluidics concerns fluid dynamics occurring in devices or flow configurations with minimum design length measured in micrometers or smaller. The behavior of fluids at these scales is quite different from that at the macroscopic level due to the presence of surface tension effects, wetting phenomena, Brownian diffusion and hydrodynamic interactions with immersed particles and microstructures. These effects cannot be generally represented in a classical homogeneous continuum framework. However, this triggers the development of new tools to investigate and simulate problems at the meso-scopic level. This book contains a collection of works presented at the IUTAM Symposium on Advances on Micro and Nano-fluidics held in Dresden in 2007. It covers several subjects of wide interest for micro and nano-fluidics applications focusing on both, analytical and numerical approaches. Topics covered in particular include multi-scale particle methods for numerical simulations, liquid-wall interactions and modeling approaches, modeling of immersed nano-scale structures, organized flow behavior at micro and nano-scales, and methods for control of micro- and nano-scale flows.

Although the problem of tool design - involving both the selection of suitable geometry and material- has exercised the attention of metal forming engineers for as long as this industrial activity has existed, the approach to its solution has been generally that of the 'trial and error' variety. It is only relatively recently that the continuing expansion of the bulk metal-forming industry, combined with an increase in the degree of sophistication required of its products and processes, has focussed attention on the problem of optimisation of tool design. This, in turn, produced a considerable expansion of theoretical and practical investi gations of the existing methods, techniques r,nd concepts, and helped to systematise our thinking and ideas in this area of engineering activity. In the virtual absence, so far, of a single, encyclopaedic, but sufficien tly deep, summation of the state of the art, a group of engineers and materials scientists felt that an opportune moment had arrived to try and produce, concisely, answers to many tool designers' dilemmas. This book attempts to set, in perspective, the existing - and proven - concepts of design, to show their respective advantages and weaknesses and to indicate how they should be applied to the individual main forming processes of rolling, drawing, extrusion and forging.

This volume contains the proceedings of the ICASE/LaRC Work- shop on the "Algorithmic Trends for Computational Fluid Dynamics (CFD) in the 90's" conducted by the Institute for Computer Applica- tions in Science and Engineering (ICASE) and the Fluid Mechanics Division of NASA Langley Research Center during September 15-17, 1991. The purpose of the workshop was to bring together numerical analysts and computational fluid dynamicists i) to assess the state of the art in the areas of numerical analysis particularly relevant to CFD, ii) to identify promising new developments in various areas of numerical analysis that will have impact on CFD, and iii) to establish a long-term perspective focusing on opportunities and needs. This volume consists of five chapters - i) Overviews, ii) Accelera- tion Techniques, iii) Spectral and Higher-Order Methods, iv) Multi- Resolution/ Subcell Resolution Schemes (including adaptive meth- ods), and v) Inherently Multidimensional Schemes. Each chapter covers a session of the Workshop. The chapter on overviews contains the articles by J. L. Steger, H.-O. Kreiss, R. W. MacCormack, O.

When asked to start teaching a course on engineering fracture mechanics, I realized that a concise textbook, giving a general oversight of the field, did not exist. The explanation is undoubtedly that the subject is still in a stage of early development, and that the methodologies have still a very limited applicability. It is not possible to give rules for general application of fracture mechanics concepts. Yet our comprehension of cracking and fracture beha viour of materials and structures is steadily increasing. Further developments may be expected in the not too distant future, enabling useful prediction of fracture safety and fracture characteristics on the basis of advanced fracture mechanics procedures. The user of such advanced procedures m\lst have a general understanding of the elementary concepts, which are provided by this volume. Emphasis was placed on the practical application of fracture mechanics, but it was aimed to treat the subject in a way that may interest both metallurgists and engineers. For the latter, some general knowledge of fracture mechanisms and fracture criteria is indispensable for an apprecia tion of the limita tions of fracture mechanics. Therefore a general discussion is provided on fracture mechanisms, fracture criteria, and other metal lurgical aspects, without going into much detail. Numerous references are provided to enable a more detailed study of these subjects which are still in a stage of speculative treatment."

This book addresses the principles, methods and applications of biodegradable polymer based scaffolds for bone tissue engineering. The general principle of bone tissue engineering is reviewed and the traditional and novel scaffolding materials, their properties and scaffold fabrication techniques are explored. By acting as temporary synthetic extracellular matrices for cell accommodation, proliferation, and differentiation, scaffolds play a pivotal role in tissue engineering. This book does not only provide the comprehensive summary of the current trends in scaffolding design but also presents the new trends and directions for scaffold development for the ever expanding tissue engineering applications.

Both experimental and theoretical investigations make it clear that mesoscale materials, that is, materials at scales intermediate between atomic and bulk matter, do not always behave in ways predicted by conventional theories of shock compression. At these scales, shock waves interact with local material properties and microstructure to produce a hierarchy of dissipative structures such as inelastic deformation fields, randomly distributed lattice defects, and residual stresses. A macroscopically steady planar shock wave is neither plane nor steady at the mesoscale. The chapters in this book examine the assumptions underlying our understanding of shock phenomena and present new measurements, calculations, and theories that challenge these assumptions. They address such questions as: - What are the experimental data on mesoscale effects of shocks, and what are the implications? - Can one formulate new mesoscale theories of shock dynamics? - How would new mesoscale theories affect our understanding of shock-induced phase transitions or fracture? - What new computational models will be needed for investigating mesoscale shocks?

Powders have been studied extensively because they arise in a wide variety of fields, ranging from soil mechanics to manufacture of pharmaceuticals. Only recently, however, with the deepening understanding of fractals, chaos, 1/f noise, and self-organization, has it been useful to study the mechanical properties of powders from a fundamental physical perspective. This book collects articles by some of the foremost researchers in the field, including chapters on: the role of entropy in the specification of a powder, by S.F. Edwards (Cambridge); discrete mechanics, by P.K. Haff (Duke); computer simulations of granular materials, by G.C. Barker (Norwich); pattern formation and complexity in granular flow, by R.P. Behringer and G.W. Baxter (Duke); avalanches in real sand piles, by A. Mehta (Birmingham); micromechanical models of failure, by M.J. Adams (Unilever) and B.J. Briscoe (Imperial College); mixing and segregation in particle flows, by J. Bridgwater (Birmingham); and hard-sphere colloidal suspensions, by P. Bartlett (Bristol) and W. van Megen (Melbourne).

As any human activity needs goals, mathematical research needs problems -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the ben eficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a du ality gap between the two partners, and this gap is growing wider. Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications which fall into the two following complementary categories: 1. An annual book dedicated to the latest developments in mechanics and mathematics; 2. Monographs, advanced textbooks, handbooks, edited vol umes and selected conference proceedings. The AMMA annual book publishes invited and contributed compre hensive reviews, research and survey articles within the broad area of modern mechanics and applied mathematics. Mechanics is understood here in the most general sense of the word, and is taken to embrace relevant physical and biological phenomena involving electromagnetic, thermal and quantum effects and biomechanics, as well as general dy namical systems. Especially encouraged are articles on mathematical and computational models and methods based on mechanics and their interactions with other fields. All contributions will be reviewed so as to guarantee the highest possible scientific standards."

Bringing together contributions on a diverse range of topics, this text explores the relationship between discrete and continuum mechanics as a tool to model new and complex metamaterials. Providing a comprehensive bibliography and historical review of the field, it covers mechanical, acoustic and pantographic metamaterials, discusses Naive Model Theory and Lagrangian discrete models, and their applications, and presents methods for pantographic structures and variational methods for multidisciplinary modeling and computation. The relationship between discrete and continuous models is discussed from both mathematical and engineering viewpoints, making the text ideal for those interested in the foundation of mechanics and computational applications, and innovative viewpoints on the use of discrete systems to model metamaterials are presented for those who want to go deeper into the field. An ideal text for graduate students and researchers interested in continuum approaches to the study of modern materials, in mechanical engineering, civil engineering, applied mathematics, physics, and materials science.

This book has come into being as a result ofthe author's lectures on mathematical modelling rendered to the students, BS and MS degree holders specializing in applied mathematics and computer science and to post-graduate students in exact sciences of the Nizhny Novgorod State University after N. . Lobatchevsky. These lectures are adapted and presented as a single whole ab out mathematical models and modelling. This new course of lectures appeared because the contemporary Russian educational system in applied mathematics rested upon a combination of fundamental and applied mathematics training; this way of training oriented students upon solving only the exactly stated mathematical problems, and thus there was created a certain estrangement to the most essential stages and sides of real solutions for applied problems, such as thinking over and deeply piercing the essence of a specific problem and its mathematical statement. This statement embraces simplifications, adopted idealizations and creating a mathematical model, its correction and matching the results obtained against a real system. There also existed another main objective, namely to orient university graduates in their future research not only upon purely mathematical issues but also upon comprehending and widely applying mathematics as a universal language of contemporary exact science, and mathematical modelling as a powerful me ans for studying nature, engineering and human society.

A central problem in engineering is the deformation of structures. These may be structures made of metal, from concrete or other buildingmaterials, orfrom soilforexample. Generallyspeaking, the engineerrequiresthedeformationofastructuretoberelativelysmall, predictable, tolerable and non-damaging. Professor Jean Mandel devotedalargepartofhisprofessionalcareertostudiesofdeforma tionandhewassuccessfulinidentifyingprinciplesandproceduresof wideapplicability.Accordingly, itisveryappropriatetobringtogether as we dointhis volume papers by world authorities concerned with deformationinmemoryofProfessorMandel. The papers in this volume were all invited contributions to an international CNRS colloquium which was held at the Ecole Poly techniqueinParis, 30September-2October1985. Thevolumeconsidersthedeformationofmetals, rocks, composites, soils, sand and wood. The microscopic processes and theory of deformationaretreated, asarethegenerallawsrelatingdeformation with parameters such as stress system and temperature. A central problemwhichhasbeensystematicallyattackedinthecaseofmetalsis the relationship between the behaviour of crystal defects such as dislocations and the deformationofa large specimenorengineering component.Itshould be possible to produce accurate predictionsof macroscopic deformation from a microscopic model and substantial progresstowardsthisendhasbeenmadeinrecentyears.Thefirsttwo sectionsofthe bookare largelyconcerned with progress in this very importantarea. A parallel theme which was established in earlier days is the developmentofcontinuummodelsfordeformation.Suchmodelswere proposedatatimewhenmicroscopyhadnotdevelopedtoitspresent levelofsophisticationsothat, forexample, itwasnotestablishedthat v VI PREFACE crystalsactuallycontaineddislocations.Thecontinuumtheorieswhich datebackmorethanacenturysoughttoexplainmicroscopicdeforma tion in terms of abstract models involving mechanical elements of whichthespringand the dashpot wereprominentexamples. Froma strictly practical standpoint these continuum models still have great utilitytoday, particularlyinareaswhere the materialsaresocompli cated that the preferred route, linking microscopic behaviour with macroscopicbehaviour, is notyet available. Section3ofthe book is concernedthereforewiththecontinuumpointofviewformetals."

Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second varia tional formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Em phasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems."

This book covers the essential topics for a second-level course in strength of materials or mechanics of materials, with an emphasis on techniques that are useful for mechanical design. Design typically involves an initial conceptual stage during which many options are considered. At this stage, quick approximate analytical methods are crucial in determining which of the initial proposals are feasible. The ideal would be to get within 30% with a few lines of calculation. The designer also needs to develop experience as to the kinds of features in the geometry or the loading that are most likely to lead to critical conditions.

With this in mind, the author tries wherever possible to give a physical and even an intuitive interpretation to the problems under investigation. For example, students are encouraged to estimate the location of weak and strong bending axes and the resulting neutral axis of bending before performing calculations, and the author discusses ways of getting good accuracy with a simple one degree of freedom Rayleigh-Ritz approximation. Students are also encouraged to develop a feeling for structural deformation by performing simple experiments in their outside environment, such as estimating the radius to which an initially straight bar can be bent without producing permanent deformation, or convincing themselves of the dramatic difference between torsional and bending stiffness for a thin-walled open beam section by trying to bend and then twist a structural steel beam by hand-applied loads at one end.

In choosing dimensions for mechanical components, designers will expect to be guided by criteria of minimum weight, which with elementary calculations, generally leads to a thin-walled structure as an optimal solution. This consideration motivates the emphasis on thin-walled structures, but also demands that students be introduced to the limits imposed by structural instability. Emphasis is also placed on the effect of manufacturing errors on such highly-designed structures - for example, the effect of load misalignment on a beam with a large ratio between principal stiffness and the large magnification of initial alignment or loading errors in a strut below, but not too far below the buckling load.

Additional material can be found on http: //extras.springer.com/.
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Within the Solid Mechanics Program at the Office of Naval Research (ONR), our primary mission is to establish a basic research program which addresses the funda mental issues in solid mechanics where a clear scientific understanding is lacking. Our approach involves first identifying the various scales at which material and structural response and failure occur. Within each level of behavior we address the basic mechanical phenomena for which a clear physical description is not available. ONR's program emphasizes experimental research to identify and quantify the interacting behavior and response mechanisms. Theoretical and computational approaches are developed to explain the details of the physical processes and to establish the technology necessary to control the thermomechanical behavior of materials and structures. Within the Department of Defense, it is a natural evolution that all new systems must generally operate in more demanding environments than the systems they replace. Thus, structural designers are pushed towards lighter weight, precision structures utilizing new materials. In such an environment, structural design mar gins simultaneously shrink and become more critical. Such trends make it essential that a well founded scientific base for the nondestructive detection and assessment of subcritical flaws in structural materials and structures exist. Within the ONR Solid Mechanics Program we are interested in both the identification of flaws and assessment of their degree of criticality."

The IUT AM Symposium on "Micromechanics of Plasticity and Damage of Multiphase Materials" was held in Sevres, Paris, France, 29 August - 1 September 1995. The Symposium was attended by 83 persons from 18 countries. In addition 17 young French students attended the meeting. During the 4 day meeting, a total of 55 papers were presented, including 24 papers in the poster sessions. The meeting was divided into 7 oral and 3 poster sessions. The 7 oral sessions were the following: - Plasticity and Viscoplasticity I and II; - Phase transformations; - Damage I and II; - Statistical and geometrical aspects; - Cracks and interfaces. Each poster session was introduced by a Rapporteur, as follows: - Session I (Plasticity and Viscoplasticity): G. Cailletaud; - Session 2 (Damage): D. Franc;:ois; - Session 3 (Phase transformation; statistical and geometrical aspects): D. Jeulin. The main purpose of the Symposium was the discussion of the state of the art in the development of micromechanical models used to predict the macroscopic mechanical behaviour of mUltiphase solid materials. These materials consist of at least two chemically different phases, present either initially or formed during plastic deformation, when a strain-induced phase transformation takes place. One session was devoted to the latter case. Continuously strengthened composite materials, containing long fibers, were out of the scope of the Symposium.

In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be sides being quite spontaneous, allows us to consider a great many inter esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b], in order to obtain local existence and uniqueness for the traction problem in hyperelasticity under dead loads, inspired many of the ideas which led to this monograph. Chapter I aims to give a very brief introduction to some general concepts in the mathematical theory of elasticity, in order to show how the boundary value problems studied in the sequel arise. Chapter II is very technical; it supplies the framework for all sub sequent developments.

This is a consistent treatment of the material-independent fundamental equations of the theory of porous media, formulating constitutive equations for frictional materials in the elastic and plastic range, while tracing the historical development of the theory. Thus, for the first time, a unique treatment of fluid-saturated porous solids is presented, including an explanation of the corresponding theory by way of its historical progression, and a thorough description of its current state.