This technical book considers the application side of LDA techniques. Starting from the basic theories that are crucial for each LDA user, the main subject of the book is focused on diverse application methods. In details, it deals with universal methodical techniques that have been mostly developed in the last 15 years. The book thus gives for the first time an application reference for LDA users in improving the optical conditions and enhancing the measurement accuracies. It also provides the guidelines for simplifying the measurements and correcting measurement errors as well as for clarifying the application limits and extending the application areas of LDA techniques. Beside the treatments of some traditional optical and flow mechanical features influencing the measurement accuracies, the book shows a broad spectrum of LDA application methods in the manner of measuring the flow turbulence, resolving the secondary flow structures, and quantifying the optical aberrations at measurements of internal flows etc.. Thus, it also supports the further developments of both the hard- and software of LDA instrumentations.

As the shift from the Metal Age progresses, materials engineers and materials scientists seek new analytical and design methods to create stronger and more reliable materials. Based on extensive research and developmental work done at the author s multi-disciplinary material laboratory, this graduate-level and professional reference addresses the relationship between fracture mechanisms (macroscale) and the microscopic, with the goal of explaining macroscopic fracture behavior based on a microscopic fracture mechanism. A careful fusion of mechanics and materials science, this text and monograph systematically considers an array of materials, from metals through ceramics and polymers, and demonstrates lab-tested strategies to develop desirable high-temperature materials for technological applications."

The aim of the book is to present, in a novel and unified fashion, the elements of Mechanics in Material Space or Configurational Mechanics, with applications to fracture and defect mechanics. This mechanics, in contrast to Newtonian mechanics in physical space, is concerned with defects such as cracks and dislocations, which are embedded in the material and might move in it. The level is kept accessible to any engineer, scientist or graduate student possessing some knowledge of calculus and partial differential equations, and working in the various areas where rational use of materials is essential.

PREFACE The theory of differential-operator equations has been described in various monographs, but the initial physical problem which leads to these equations is often hidden. When the physical problem is studied, the mathematical proofs are either not given or are quickly explained. In this book, we give a systematic treatment of the partial differential equations which arise in elastostatic problems. In particular, we study problems which are obtained from asymptotic expansion with two scales. Here the methods of operator pencils and differential-operator equations are used. This book is intended for scientists and graduate students in Functional Analy sis, Differential Equations, Equations of Mathematical Physics, and related topics. It would undoubtedly be very useful for mechanics and theoretical physicists. We would like to thank Professors S. Yakubov and S. Kamin for helpfull dis cussions of some parts of the book. The work on the book was also partially supported by the European Community Program RTN-HPRN-CT-2002-00274. xiii INTRODUCTION In first two sections of the introduction, a classical mathematical problem will be exposed: the Laplace problem. The domain of definition will be, on the first time, an infinite strip and on the second time, a sector. To solve this problem, a well known separation of variables method will be used. In this way, the structure of the solution can be explicitly found. For more details about the separation of variables method exposed in this part, the reader can refer to, for example, the book by D. Leguillon and E. Sanchez-Palencia LS]."

Over the past decades, the Boundary Element Method has emerged as a ver satile and powerful tool for the solution of engineering problems, presenting in many cases an alternative to the more widely used Finite Element Method. As with any numerical method, the engineer or scientist who applies it to a practical problem needs to be acquainted with, and understand, its basic principles to be able to apply it correctly and be aware of its limitations. It is with this intention that we have endeavoured to write this book: to give the student or practitioner an easy-to-understand introductory course to the method so as to enable him or her to apply it judiciously. As the title suggests, this book not only serves as an introductory course, but also cov ers some advanced topics that we consider important for the researcher who needs to be up-to-date with new developments. This book is the result of our teaching experiences with the Boundary Element Method, along with research and consulting activities carried out in the field. Its roots lie in a graduate course on the Boundary Element Method given by the authors at the university of Stuttgart. The experiences gained from teaching and the remarks and questions of the students have contributed to shaping the 'Introductory course' (Chapters 1-8) to the needs of the stu dents without assuming a background in numerical methods in general or the Boundary Element Method in particular."

This book introduces spectral analysis as a means of investigating wave propagation and transient oscillations in structures. After developing the foundations of spectral analysis and the fast Fourier transform algorithm, the book provides a thorough treatment of waves in rods, beams, and plates, and introduces a novel matrix method for analysing complex structures as a collection of waveguides. The presentation includes an introduction to higher-order structural theories, the results of many experimental studies, practical applications, and source-code listings for many programs. An extensive bibliography provides an entry to the research literature. Intended as a textbook for graduate students of aerospace or mechanical engineering, the book will also be of interest to practising engineers in these and related disciplines.

In an area as vast and important as rheology, it is essential that the experimentalist understands the underlying theories and shortcomings of the measurement technique used, that they are aware of the likely microstructure of the fluid under study and that from this they can appreciate how the fluid and the measuring system interact with each other. This major handbook, written by an international group of experts in the range of rheological techniques, presents the state of the art in rheological measurement, and concentrates on the techniques and underlying physical principles. The second edition, fully revised and updated to include new techniques is invaluable to polymer and materials scientists, engineers and technologists, and anyone else making rheological measurements on materials whether they be polymeric, biological, slurries, food or other complex fluids.

Historically, black body radiation in the tungsten filament lamp was our primary industrial means for producing 'artificial' light, as it replaced gas lamps. Solid state luminescent devices for applications ranging from lamps to displays have proliferated since then, particularly owing to the develop ment of semiconductors and phosphors. Our lighting products are now mostly phosphor based and this 'cold light' is replacing an increasing fraction of tungsten filament lamps. Even light emitting diodes now chal lenge such lamps for automotive brake lights. In the area of information displays, cathode ray tube phosphors have proved themselves to be outstandingly efficient light emitters with excellent colour capability. The current push for flat panel displays is quite intense, and much confusion exists as to where development and commercialization will occur most rapidly, but with the need for colour, it is now apparent that solid state luminescence will play a primary role, as gas phase plasma displays do not conveniently permit colour at the high resolution needed today. The long term challenge to develop electroluminescent displays continues, and high performance fluorescent lamps currently illuminate liquid crystal monochrome and colour displays. The development of tri component rare earth phosphors is of particular importance."

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.

Provides a rigorous derivation of surface properties such as temperature and deformation using continuum mechanics; Discussion is animated by the authors' decades of experience in experimental mechanics; Includes many techniologically motivated problems, solutions and computer solutions

Inverse problems occur in a wide variey of fields. In general, the inverse problem can be defined as one where one should estimate the cause from the result, while the direct problem is concerned with how to obtain the result from the cause. The aim of this symposium was to gather scientists and researchers in engineering mechanics concerned with inverse problems in order to exchange research result and develop computational and experimentalapproaches to solve inverse problems. The contributions in this volume cover the following subjects: mathematical and computational aspects of inverse problems, parameter or system identification, shape determination, sensitivity analysis, optimization, material property characterization, ultrasonic nondestructive testing, elastodynamic inverse problems, thermal inverse problems, and other miscellaneous engineering applications.

My wife Tatyana, daughter Mariya, son Alexandr It is well known that the mixed-mode conditions appear when the direction of the applied loading does not coincide with the orthogonal K, -Kn-Km space. In general, in the industrial practice the mixed-mode fracture and the mixed-mode crack growth are more likely to be considered the rule than the exception. Miller et al. considers that cracks can grow due to a mixture of processes (ductile and brittle), mechanisms (static, fatigue, creep) and loading modes (tension, torsion, biax ial/multiaxial). Additionally mixed-mode crack-extension can be affected by many other considerations such as artifact geometry (thin plates, thick shells, and the size, shape and orientation of the defect), environmental effects (temperature, gaseous and liquid surroundings), material state (crystallographic structure, heat treatment and route of manufacture) and stress conditions (out-of-phase and ran dom loading effects). The main feature of the mixed-mode fracture is that the crack growth would no longer take place in a self-similar manner and does not follow a universal trajec tory that is it will grow on a curvilinear path. There are various fracture criteria, which predict the behavior of cracks in brittle and ductile materials loaded in combined modes. Linear elastic fracture mechanics (LEFM) criteria predict basi cally the same direction for crack propagation. Cracks in brittle materials have been shown to propagate normal to the maximum tangential stress. In ductile ma terials yielding occurs at the crack tip and LEFM is no longer applicable."

The volume is devoted to mechanics of rods, which is a branch of mechanics of deformable bodies. The main goal of the book is to present systematically theoretical fundamentals of mechanics of rods as well as numerical methods used for practical purposes. The monograph is concerned with the most general statements of the problems in mechanics of rods. Various types of external loads that a rod may be subject to are discussed. Advanced technique that includes vector is used in the derivation of linear analysis, linear algebra, and distributions and nonlinear equilibrium equations. The use of this technique helps us to make transformations and rearrangement of equations more transparent and compact. Theoretical basics of rods interacting with external and internal flows of fluid and the derivation of the formulas for the hydrodynamic and aerody namic forces are presented. The book consists of six chapters and appendices and may be convention ally divided into two parts. That is, Chapters 1 to 3 contain, in the main, theoretical material, whereas Chapters 4 to6 illustrate the application of the theoretical results to problems of practical interest. Problems for self-study are found in Chapters 1, 3, 4, and 5. The solutions to most of the problems are given in Appendix B. The monograph is addressed to scientists, institutional and industrial re searchers, lecturers, and graduate students."

In this book a systematic discussion of crack problems in elastic-plastic materials is presented. The state of the art in fracture mechanics research and assessment of cracks is documented, with the help of analytic, asymptotic methods as well as finite element computations. After a brief introduction to fracture mechanics, the two-parameter concept for stationary cracks is studied in addition to the issues in three-dimensional crack fields under coupling with strong out-of-plane effects. Cracks along interfaces and crack growth problems under mixed mode conditions are also treated. A systematic study of stress singularities for different notches is accompanied by detailed finite element computations.

This book presents a rational scheme of analysis for the periodic and quasi-periodic solution of a broad class of problems within technical and celestial mechanics. It develops steps for the determination of sufficiently general averaged equations of motion, which have a clear physical interpretation and are valid for a broad class of weak-interaction problems in mechanics. The criteria of stability regarding stationary solutions of these equations are derived explicitly and correspond to the extremum of a special "potential" function. Much consideration is given to applications in vibrational technology, electrical engineering and quantum mechanics, and a number of results are presented that are immediately useful in engineering practice. The book is intended for mechanical engineers, physicists, as well as applied mathematicians specializing in the field of ordinary differential equations.

As one of the oldest natural sciences, mechanics occupies a certain pioneering role in determining the development of exact sciences through its interaction with mathematics. As a matter of fact, there is hardly an area in mathematics that hasn't found an application of some form in mechanics. It is thus almost inevitable that theoretical methods in mechanics are highly developed and laid out on different levels of abstraction. With the spread of digital processors this goes as far as the implementation in commercial computer codes, where the user is merely con fronted on the surface with the processes that run in the background, i. e. mechan ics as such: in teaching and research, as well as in the context of industry, me chanics is much more, and must remain much more than the mere production of data with the help of a processor. Mechanics, as it is talked about here, tradition ally includes a wide spectrum, ranging from applied mechanics, analytical and technical mechanics to modeling. and experimental mechanics, as well as technical realization. It also includes the subdisciplines of rigid body mechanics, continuum mechanics, or fluid mechanics, to mention only a few. One of the fundamental and most important concepts used by nearly all natural sciences is the concept of linearization, which assumes the differentiability of mappings. As a matter of fact, all of classical mechanics is based on the avail ability of this quality."

The monograph text is based on lectures delivered by author during many years for students of Applied Iechanics Department of Bauman Ioscow State Technical University. The monograph includes also analitical results of scientific research obtained in collaboration with industry. Progress in developing new equipment has called for a better understand ing of the physical peculiarities pertaining to the action of designed structures in real conditions. This is necessary for increasing the accuracy of the analysis and making these structures more reliable. It has been found that classical determined perturbations are not principal and that determinism-based methods of classical mechanics prove insufficient for understanding and explaining physical effects that arise at the operation of instruments located on moving objects, the vibration of rocket engines, the motion of a vehicle, and the action of wind and seismic loads. Therefore the necessity arose for devising a new physical model to analyze these dynamic processes and, in particular, for creating a new mathematical apparatus that would allow us to take into account non-deterministic external excitations. The theory of random processes that had been developed well enough as applied to problems of radio engineering and automatic control, where the effect produced by random excitations appeared to be commensurable with that of deterministic excitations and where the ignoring of the random ex citations would bring about incorrect results, became such an apparatus."

Computational mechanics, as a science employed for the numerical model ing of processes in nature and engineering, has over the last few decades developed two strands. The first concerns the putting of more and more powerful software packages into computational practice, using increas ingly high-performance computers with increasingly large memory. The traditional finite element and finite difference approaches are still preva lent. Over the years however, researchers have met with new problems; their solutions on the basis of traditional methods are at best difficult and at worst impossible to obtain. Such problems provided a powerful impetus in the development of the second strand, resulting in the development of es sentially new approaches for numerical modeling, for example meshless methods, "molecular" dynamics, neuron networks. The current state of the art formed the basis of many papers presented at the Fifth World Congress on Computational Mechanics, Vienna 2002. It is within the framework of the second strand that this book has been written."

At the VIIth International Congress on Rheology, which was held in Goteborg in 1976, Proceedings were for the first time printed in advance and distributed to all participants at the time of the Congress. Although of course we Italians would be foolish to even try to emulate our Swedish friends as far as efficiency of organization is concerned, we decided at the very beginning that, as far as the Proceedings were concerned, the VIIIth International Congress on Rheology in Naples would follow the standards of time liness set by the Swedish Society of Rheology. This book is the result we have obtained. We wish to acknowledge the cooperation of Plenum Press in producing it within the very tight time schedule available. Every four years, the International Congress on Rheology represents the focal point where all rheologists meet, and the state of the art is brought up to date for everybody interested; the Proceedings represent the written record of these milestones of scientific progress in rheology. We have tried to make use of the traditions of having invited lectures, and of leaving to the organizing committee the freedom to choose the lecturers as they see fit, in order to collect a group of invited lectures which gives as broad as possible a landscape of the state of the art in every relevant area of rheology. The seventeen invited lectures are collected in the first volume of the proceedings."

Micromechanisms of Fracture and Fatigue forms the culmination of 20 years of research in the field of fatigue and fracture. It discusses a range of topics and comments on the state of the art for each. The first part is devoted to models of deformation and fracture of perfect crystals. Using various atomistic methods, the theoretical strength of solids under simple and complex loading is calculated for a wide range of elements and compounds, and compared with experimental data. The connection between the onset of local plasticity in nanoindentation tests and the ideal shear strength is analysed using a multi-scale approach. Moreover, the nature of intrinsic brittleness or ductility of perfect crystal lattices is demonstrated by the coupling of atomistic and mesoscopic approaches, and compared with brittle/ductile behaviour of engineering materials. The second part addresses extrinsic sources of fracture toughness of engineering materials, related to their microstructure and microstructurally-induced crack tortuosity. Micromechanisms of ductile fracture are also described, in relation to the fracture strain of materials. Results of multilevel modelling, including statistical aspects of microstructure, are used to explain remarkable phenomena discovered in experiments. In the third part of the book, basic micromechanisms of fatigue cracks propagation under uniaxial and multiaxial loading are discussed on the basis of the unified mesoscopic model of crack tip shielding and closure, taking both microstructure and statistical effects into account. Applications to failure analysis are also outlined, and an attempt is made to distinguish intrinsic and extrinsic sources of materials resistance to fracture. Micromechanisms of Fracture and Fatigue provides scientists, researchers and postgraduate students with not only a deep insight into basic micromechanisms of fracture behaviour of materials, but also a number of engineering applications.

Phenomena occurring during a contact of two bodies are encountered in everyday life. In reality almost every type of motion is related to frictional contact between a moving body and a ground. Moreover, modeling of simple and more complex processes as nailing, cutting, vacuum pressing, movement of machines and their elements, rolling or, finally, a numerical simulation of car crash tests, requires taking contact into account. Therefore, its analysis has been a subject of many research efforts for a long time now. However, it is author's opinion that there are relatively few efforts related to contact between structural elements, like beams, plates or shells. The purpose of this work is to fill this gap. It concerns the beam-to-beam contact as a specific case of the 3D solids contact. A numerical formulation of frictional contact for beams with two shapes of cross-section is derived. Further, a couple of effective methods for modeling of smooth curves representing beam axes are presented. A part of the book is also devoted to analyze some aspects of thermo-electro-mechanical coupling in contact of thermal and electric conductors. Analyses in every chapter are illustrated with numerical examples showing the performance of derived contact finite elements.

Although realistic soil and rock foundations reveal noticeable deviations in their properties from homogeneity and isotropy, the model of the homogeneous isotropie elastic half-space is widely used when studying static and dynamie interactions between a defonnable foundation and structures. This is explained by significant mathematieal difficulties inherent in problems conceming mechanies of anisotropie and heterogeneous elastic bodies. Solving the basic static and dynamie problems for heterogeneous and anisotropic half-spaces, such as different contact problems and problems of constructing Green's functions, has become possible in the last few decades due to the development of computer engineering techniques and numerical methods. This book contains the results of investigations in the area of statics and dynamies of heterogeneous and anisotropic foundations, carried out by the author in the last five years while working in the Faculty of Civil Engineering at Technion - Israel Institute of Technology. The book is directed at engineers and scientists in the areas of soil mechanics, soil-structures interaction, seismology and geophysics. Some characteristic features of the book are: i) Constructing (Chap.l) solutions in a general fonn for the heterogeneous (in the depth direction) transversely isotropic elastic half-space subjected to different loadings, hannonic in time. Characteristics of the given half-space have an influence on functions (of depth z and parameter k of Hankel's transfonns), which are detennined from a system of ordinary differential equations.

The last decades have witnessed the development of methods for solving struc tural reliability problems, which emerged from the efforts of numerous re searchers all over the world. For the specific and most common problem of determining the probability of failure of a structural system in which the limit state function g( x) = 0 is only implicitly known, the proposed methods can be grouped into two main categories: * Methods based on the Taylor expansion of the performance function g(x) about the most likely failure point (the design point), which is determined in the solution process. These methods are known as FORM and SORM (First- and Second Order Reliability Methods, respectively). * Monte Carlo methods, which require repeated calls of the numerical (nor mally finite element) solver of the structural model using a random real ization of the basic variable set x each time. In the first category of methods only SORM can be considered of a wide applicability. However, it requires the knowledge of the first and second deriva tives of the performance function, whose calculation in several dimensions either implies a high computational effort when faced with finite difference techniques or special programs when using perturbation techniques, which nevertheless require the use of large matrices in their computations. In or der to simplify this task, use has been proposed of techniques that can be regarded as variants of the Response Surface Method.

In 1975 we and four of our former colleagues wrote the textbook Principles of Tribology. That book was very successful both in the United Kingdom and overseas and it is still being sold today. However, 13 years after the first publication of the book, the publishers suggested that we should consider revising the text, to include the more important developments which had taken place in the meantime. Although we have remained active in tribological research, it was only when we started work on this revision that we realised that the developments which have taken place have been so extensive that they could not be accommodated simply by revision of our existing text. As a result, although we have reused some of our original material, the present book has resulted from a complete reappraisal of our ideas on the necessary content of a modern introductory textbook on tribology. As the title of the book implies, it has been our intention to write a book which will provide a thorough grounding in the principles of our subject for undergraduates and new research workers and will also act as a basic reference book for practising designers. In the areas of friction and wear, although there has been a great deal of high-quality research on the underlying physical and mechanical processes, there are no current, or indeed foreseeable, models which will allow quantitative predictions of friction coefficients or wear rates from basic physical, chemical and mechanical properties.

The objective of this book is to provide a comprehensive introduction to ?nite rotation shells and to non-linear shell ?nite elements. It is divided into 5 parts: I. Preliminaries (20 pages), II. Shell equations (104 pages), III. Finite rotations for shells (103 pages), IV. Four-node shell elements (189 pages), and V. Numerical examples (41 pages). Additional numerical examples are presented in Parts III and IV. The bibliography includes 270 entries. The book is intended for both teaching and self-study, and emphasizes fundamental aspects and techniques of the subject. Some familiarity with non-linear mechanics and the ?nite element method is assumed. Shell elements are a subject of active research which results in many publications every year and several conferences and sessions are held r- ularly, among them, two large international conferences: \Computation of Shell and Spatial Structures" and \Shell Structures. Theory and - plications" (SSTA). The literature is voluminous, not easy to follow and evaluate, and the subject is di-cult to comprehend. I hope that this will be facilitated by the book. I would like to express my gratitude to several persons who helped me in my professional life, in this way contributing to the book. I thank Prof. R.L. Taylor from the University of California at Berkeley, Prof. B. Schre er from the University of Padua, and Prof. J.T. Santos from the Instituto Superior Tecnico at Lisbon, for hosting and supporting me when I was a post-doctoral researcher.