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 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.

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.

This book addresses problems in structural dynamics and control encountered in applications such as robotics, aerospace structures, earthquake-damage prevention, and active noise suppression. The rapid developments of new technologies and computational power have made it possible to formulate and solve engineering problems that seemed unapproachable only a few years ago. This presentation combines concepts from control engineering (such as system norms and controllability) and structural engineering (such as modal properties and models), thereby revealing new structural properties as well as giving new insight into well-known laws. This book will assist engineers in designing control systems and dealing with the complexities of structural dynamics.

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."

Nanoindentation, Third Edition gives a detailed account of the most up-to-date research in this important field of materials testing. As in previous editions, extensive theoretical treatments are provided and explained in a clear and consistent manner that will satisfy both experienced and novice scientists and engineers. Additionally, numerous examples of the applications of the technique are provided directly from manufacturers of nanoindentation instruments. A helpful series of appendices provides essential reference information that includes a list of frequently asked questions. The new edition has been restructured to provide results of the latest research and developments in the field of mechanical testing while retaining the essential background and introductory, but authoritative nature, of the previous editions. The new edition also expands on the instrumentation and applications chapters by including material sourced direct from the instrument manufacturers in this field. Aimed at graduate student level, this book is designed to fill a need associated with the use of nanoindentation as a quantitative test method for mechanical properties of small volumes of materials.

According to a proposal made in 1974 by the Gesell- schaft fUr Angewandte Mathematik und Mechanik (GAMM) the General Assembly of the International Union of Theoretical and Applied Mechanics (IUTAM) decided in 1975 to sponsor an international symposium on "Dynamics of Multibody Systems". A Scientific Committee has been appointed consisting of J.D.C. Crisp, Australia, T.R. Kane, USA, D.M. Klimov, USSR, A.D. De Pater, Netherlands, K. Magnus, Germany (chairman). This committee selected the participants to be invited and the papers to be presented at the symposium. As a result of this process 82 active scientific partici- pants from 15 countries followed the invitation and 29 papers were presented. They are collected in this volume. At the symposium an additional presentation was delivered: Mrs. E. Gottzein introduced and ex- plained a recently completed scientific movie on mag- netic levitated vehicles. The aim of the symposium was the exchange of ideas and the discussion of methods and results in the field of Multibody Dynamics. This has been achieved by a really efficient scientific and social progr~m, organ- ized for the six symposium days by a Local Organizing Committee. Members of this Committee were: S. Ballout, M. Lippmann, P.C. MUller, W.O. Schiehlen, G. Schweitzer, E. Truckenbrodt, K. Magnus (chair- man) and members of the staff of the Institute of Mechanics.

The main focus of the book is to convey modern techniques applied within the range of computational mechanics of beams, plates and shells. The topics of interest are wide ranging and include computational aspects of nonlinear theories of shells and beams including dynamics, advanced discretization methods for thin shells and membranes, shear-deformable shell finite elements for SMA composite devices, optimization and design of shells and membranes, fluid-structure interaction with thin-walled structures, contact mechanics with application to thin structures and edge effects in laminated shells.

The International Conference on Fracture Mechanics Technology Applied to Material Evaluation and Structure Design was held in Melbourne, Australia, from August 10 to 13, 1982. It was sponsored jointly by the Australian Fracture Group and Institute of Fracture and Solid Mechanics at Lehigh University. Pro fessor G. C. Sih of Lehigh University, Drs. N. E. Ryan and R. Jones of Aeronau tical Research Laboratories served as Co-Chairmen. They initiated the organiza tion of this international event to provide an opportunity for the practitioners, engineers and interested individuals to present and discuss recent advances in the evaluation of material and structure damage originating from defects or cracks. Particular emphases were placed on applying the fracture mechanics tech nology for assessing interactions between material properties, design and opera tional requirements. It is timely to hold such a Conference in Australia as she embarks on technology extensive industries where safeguarding structures from pre mature and unexpected failure is essential from both the technical and economical points. view The application of system-type approach to failure control owes much of its success to fracture mechanics. It is now generally accepted that the discipline, when properly implemented, provides a sound engineering basis for accounting in teractions between material properties, design, fabrication, inspection and op erational requirements. The approach offers effective solutions for design and maintenance of large-scale energy generation plants, mining machineries, oil ex ploration and retrieval equipments, land, sea and air transport vehicles."

Everything flows, so rheology is a universal science. Even if we set aside claims of such width, there can be no doubt of its importance in polymers. It joins with chemistry in the polymerisation step but polymer engineering is supreme in all the succeeding steps. This is the area concerned with the fabrication of the polymer into articles or components, with their design to meet the needs in service, and with the long and short term performance of the article or component. This is a typical area of professional engineering activity, but one as yet without its proper complement of professional engineers. An understanding of polymer rheology is the key to effective design and material plus process selection, to efficient fabrication, and to satisfactory service, yet few engineers make adequate use of what is known and understood in polymer rheology. Its importance in the flow processes of fabrication is obvious. Less obvious, but equally important, are the rheological phenomena which determine the in-service performance. There is a gap between the polymer rheologist and the polymer engineer which is damaging to both parties and which contributes to a less than satisfactory use of polymers in our society. It is important that this gap be filled and this book makes an attempt to do so. It presents an outline of what is known in a concise and logical fashion. It does this starting from first principles and with the minimum use of complex mathematics.

This volume is dedicated to Jacob Aboudi, a ?ne scientist who has made seminal c- tributions in applied mechanics. The papers presented here re?ect the appreciation of many of Jacob s colleagues. A publication list f- lowing this introduction provides an indi- tion of his distinguished academic career, c- rently in its ?fth decade, and the breadth of hisknowledge. His papersconsistentlydem- strate originality, innovation and diligence. This list uncovers the methodical work of a dedicated researcher whose achievements established him as a leading authority in the area of mathematical modeling of the beh- ior of heterogeneous materials, the area which became known as homogenization theory. Starting in 1981, Jacob established a micromechanical model known as the Method of Cells (MOC) which evolved into the Generalized Method of Cells (GMC) that predicts the macroscopic response of composite materials as a function of the pr- erties, volume fractions, shapes, and constitutive behavior of its constituents. The versatility of the model has been demonstrated to effectively incorporate various types of constituent material behavior (i. e., both coupled and uncoupled mecha- cal, thermal, electrical and magnetic effects). As a result of its potential in providing an ef?cient tool for the emerging ?eld of multiscale analysis, the method gained increasing attention and became a subject for further research."

The editors have published a select group of full length papers on boundary element analysis (BEA) photographed from camera ready manuscripts. The articles have been prepared by some of the most distinguished and prolific individuals in this field. More than half of these articles have been submitted by authors that participated in an International Forum on Boundary Element Methods, in Melbourne Australia, in the Summer of 1991. However, this volume is not a conference proceedings, as these authors have expanded their accounts to chapter length, and/or have tailored their expositions more toward the style employed in archival journal publications. The authors that did not participate in the International Forum have also adhered to the above mentioned philosophy. This work contains a definitive representation of the significant capabilities and applications currently available or under investigation that fall under the general category of advanced boundary element analysis. With treatments of mechanical, thermal, fluid, and electromagnetic phenomena, this book should thus be of value to graduate students, practitioners, and researchers in engineering, mathematics, and the physical sciences wishing to obtain a broader perspective or remain current in these important areas of computational simulation.

Included is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture.

Rapid Tooling Guidelines for Sand Casting describes the guidelines for the sand casting industry in using rapid tooling processes. Topics in the seven chapters include sand casting processes, tool design and construction, fast freeform fabrication processes, rapid tooling processes, sand casting dimension control, rapid tooling evaluation methods and decision making processes. Twelve case studies will also be examined in the book.

This volume contains the proceedings of the symposium held on Friday 6 July 1990 at the University Pierre et Marie Curie (Paris VI), France, in honor of Professor Henri Cabannes on the occasion of his retirement. There were about one hundred participants from nine countries: Canada, France, Germany, Italy, Japan, Norway, Portugal, the Netherlands, and the USA. Many of his past students or his colleagues were among the participants. The twenty-six papers in this volume are written versions submitted by the authors and cover almost all the fields in which Professor Cabannes has actively worked for more than forty-five years. The papers are presented in four chapters: classical kinetic theory and fluid dynamics, discrete kinetic theory, applied fluid mechanics, and continuum mechanics. The editors would like to take this opportunity to thank the generous spon sors of the symposium: the University Pierre et Marie Curie, Commissariat a l'Energie Atomique (especially Academician R. Dautray and Dr. N. Camarcat) and Direction des Recherches et Etudes Techniques (especially Professor P. Lallemand). Many thanks are also due to all the participants for making the symposium a success. Finally, we thank Professor W. Beiglbock and his team at Springer-Verlag for producing this volume.

This volume contains the written texts of the papers presented at a Symposium on Buckling of Structures held at Harvard University in June 1974. This symposium, one of several on various topics sponsored annually by the International Union of Theoretical and Applied Me chanics (IUTAM), was organized by a Scientific Committee consisting of B. Budiansky (Chairman), A. H. Chilver, W. T. Koiter, and A. S. Vol' mir. Participation was by invitation of the Scientific Committee, and specific lecturers were invited to speak in the areas of experimental research, buckling and post-buckling calculations, post-buckling mode interaction, plasticity and creep effects, dynamic buckling, stochastic problems, and design. A total of 29 lectures were delivered, including a general opening lecture by Professor Koiter, and there were 93 reg istered participants from 16 different countries. Financial support for the symposium was provided by IUTAM, in the form of partial travel support for a number of participants, and also by the National Science Foundation, the National Aeronautics and Space Administration, and the Air Force Office of Scientific Re search, for additional travel support and administrative expenses. Meeting facilities and services were efficiently provided by the Science Center of Harvard University, and administrative support was gen erously provided by the Division of Engineering and Applied Physics of Harvard University. The scientific chairman enjoyed the invaluable assistance of his colleagues Professors J. W. Hutchinson and J. L."

Auf einer Sitzung des :Biiros der Internationalen Union fiir Theore- tische und Angewandte Mechanik (IUTAM) in :Briissel am 21. Septem- ber 1953 wurde beschlossen, ein Kolloquium iiber Festkorpermechanik (vorlaufiger Titel) fiir die letzte Septemberwoche 1955 zu pla.nen, und zwa.r in Madrid, entsprechend einer EinIadung, welche die Vertreter der zugehorigen spanischen Organisation Instituto Naciona.l de Tecnica Aeronautica "Esteban Terradas" (INTA) , die Herren A. NUNEz und A. PEREZ-MARiN personIich iiberbrachten. Das vom :Biiro der IUTAM hierfiir eingesetzte Wissenschaftliche Komitee bestand aus R. GRAMMEL als Vorsitzendem und den Herren TH. VON K.ARMiN, M. Roy und G. I. TAYLOR, das spanische Organisa- tions-Komitee aus den Herren A. NUNEz und A. PEREZ-MARiN samt einem Stab technischer und administrativer Mitarbeiter. In drei :Beratungen des Wissenschaftlichen Komitees (:Briissel, 27. Juli 1954; Farnborough, to. September 1954; Paris, 23. Mai 1955) wurde das Programm des Kolloquiums mit dem endgiiltigen Titel "Verformung und FlieBen des Festkorpers" festgelegt und dann in den Tagen vom 26. bis 30. September 1955 gemaB dem Plan von Seite IX verwirklicht. Jedes der drei Themen (Versetzungen und Plastizitat; Nichtlineare Elastizitat; Viskoelastizita.t und Relaxation) und insbesondere jede Sitzung wurde durch einen AIIgemeinen V ortrag eingeleitet. Die Titel aller V ortrage gibt das Inhaltsverzeichnis Seite XI und XII an. Die Vortrage wurden am 26., 27. und 29. September im Consejo Superior de Investigaciones Cientificas in Madrid gehalten, am 28. Sep- tember in Torrej6n de Ardoz, verbunden mit einer :Besichtigung der Laboratorien des INTA daselbst.

The objective of this monograph is to provide a concise introduction to the dynamics of systems comprised of charged small-scale particles. Flowing, small-scale, particles ("particulates'') are ubiquitous in industrial processes and in the natural sciences. Applications include electrostatic copiers, inkjet printers, powder coating machines, etc., and a variety of manufacturing processes. Due to their small-scale size, external electromagnetic fields can be utilized to manipulate and control charged particulates in industrial processes in order to achieve results that are not possible by purely mechanical means alone. A unique feature of small-scale particulate flows is that they exhibit a strong sensitivity to interparticle near-field forces, leading to nonstandard particulate dynamics, agglomeration and cluster formation, which can strongly affect manufactured product quality. This monograph also provides an introduction to the mathematically-related topic of the dynamics of swarms of interacting objects, which has gained the attention of a number of scientific communities. In summary, the following topics are discussed in detail: (1) Dynamics of an individual charged particle, (2) Dynamics of rigid clusters of charged particles, (3) Dynamics of flowing charged particles, (4) Dynamics of charged particle impact with electrified surfaces and (5) An introduction to the mechanistic modeling of swarms. The text can be viewed as a research monograph suitable for use in an upper division undergraduate or first year graduate course geared towards students in the applied sciences, mechanics and mathematics that have an interest in the analysis of particulate materials.

This volume contains selected presentations of the IUTAM Symposium on Combustion in Supersonic Flows' held in Poitiers at the Ecole Nationale Superieure de Mecanique et d'Aerotechnique (ENSMA) from 2 to 6 October 1995. The presentations focus on four main topics related to combustion in supersonic streams and practical issues relevant to the development of new propulsion systems: fundamental studies of premixed and unpremixed combustion, fluid dynamics aspects of supersonic combustion, practical systems including Scramjet, Ramaccelerators and Pulsed Detonation Engines, and the application of detonation to propulsion. Important progress has been made in the understanding of local mechanisms which allow combustion to be stabilized in a supersonic flow; in particular, various mechanisms controlled by mixing, chemical kinetics, viscous heating and shock waves are now well identified. Despite the difficulty of developing experimental work on supersonic combustion, a good set of experimental data is now available, allowing validation of theoretical analysis and models. The main aspects of modelling of turbulent combustion in high speed flows were discussed, including the influence of turbulent fluctuations on the chemistry-controlled phase of combustion and the applicability of flamelet models to high speed flows. The full range of numerical approaches is covered including Direct Numerical Simulation, Large Eddy Simulation, k-epsilon and shock tracking methods. A considerable effort has been made to generalize these methods to the treatment of supersonic reactive flows and to develop new numerical methods taking into account the most recent theoretical work and a better understanding of the underlying physics."

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."

This textbook fits courses on mechanical behavior of materials in mechanical engineering and materials science and includes numerous examples and problems. It emphasizes quantitative problem solving. This text differs from others because the treatment of plasticity emphasizes the interrelationship of the flow, effective strain, and effective stress and their use in conjunction with yield criteria to solve problems. The treatment of defects is new, as is the analysis of particulate composites. Schmid's law is generalized for complex stress states. Its use with strains allows for prediction of R-values for textures. Of note is the treatment of lattice rotations related to deformation textures. The chapter on fracture mechanics includes coverage of Gurney's approach. Among the highlights in this new edition are the treatment of the effects of texture on properties and microstructure in Chapter 7, a new chapter (12) on discontinuous and inhomogeneous deformation, and the treatment of foams in Chapter 21.

Lamb waves are guided waves that propagate in thin plate or shell structures. There has been a clear increase of interest in using Lamb waves for identifying structural damage, entailing intensive research and development in this field over the past two decades. Now on the verge of maturity for diverse engineering applications, this emerging technique serves as an encouraging candidate for facilitating continuous and automated surveillance of the integrity of engineering structures in a cost-effective manner. In comparison with conventional nondestructive evaluation techniques such as ultrasonic scanning and radiography which have been well developed over half a century, damage identification using Lamb waves is in a stage of burgeoning development, presenting a number of technical challenges in application that need to be addressed and circumvented. It is these two aspects that have encouraged us to write this book, with the intention of consolidating the knowledge and know-how in the field of Lamb-wave-based damage identification, and of promoting widespread attention to mature application of this technique in the practical engineering sphere. This book provides a comprehensive description of key facets of damage identification technique using Lamb waves, based on the authors' knowledge, comprehension and experience, ranging from fundamental theory through case studies to engineering applications.

Porous Semiconductors: Optical Properties and Applications provides an examination of porous semiconductor materials. Beginning with a description of the basic electrochemistry of porous semiconductors and the different kinds of porous semiconductor materials that can be fabricated, the book moves on to describe the fabrication processes used in the production of porous semiconductor optical components. Concluding the text, a number of optical components based on porous semiconductor materials are discussed in depth.

Porous Semiconductors: Optical Properties and Applications provides a thorough grounding in the design, fabrication and theory behind the optical applications of porous semiconductor materials for graduate and undergraduate students interested in optics, photonics, MEMS, and material science. The book is also a valuable reference for scientists, researchers, and engineers in the field of optics and materials science.

An International Symposium on Defects and Fracture was held in Tuczno, Poland, 13-17 October 1980 under the sponsorship of the Polish Academy of Sci ences and Institute of Fracture and Solid Mechanics, Lehigh University. Profes sor H. Zorski of the Academy and Professor G. C. Sih of Lehigh University were Co-Chairmen. The idea for the Symposium was initiated by the members of the Organizing Committee: G. C. Sih (Co-Chairman), H. Zorski (Co-Chairman), M. Matczynski (Secretary), D. R. Axelrad, R. Bullough, J. W. Provan and R. deWit. With the rapid development of high performance materials and their increasing use in vital structural applications, there is a need for a more in-depth under standing of the fundamentals associated with material behavior and failure. Al though this topic encompasses a wide range of disciplines, it is appropriate to narrow the discussion to material failures initiating from inherent, unavoidable defects or cracks. A balanced coverage of analysis and physics was achieved by inviting speakers with backgrounds in applied mechanics and solid state physics. The input was limited to a small group of specialists who had the opportunity to discuss not only past progress but also ideas for future research."

Con?gurational mechanics has attracted quite a bit of attention from various - search ?elds over the recent years/decades. Having been regarded in its infancy of the early years as a somewhat obscureand almost mystic ?eld of researchthat could only be understood by a happy few of insiders with a pronounced theoretical inc- nation, con?gurational mechanics has developed by now into a versatile tool that can be applied to a variety of problems. Since the seminal works of Eshelby a general notion of con?gurational - chanics has been developed and has successfully been applied to many pr- lems involving various types of defects in continuous media. The most pro- nent application is certainly the use of con?gurational forces in fracture - chanics. However, as con?gurational mechanics is related to arbitrary mat- ial inhomogeneities it has also very successfully been applied to many ma- rials science and engineering problems such as phase transitions and inelastic deformations. Also the modeling of materials with micro-structure evolution is an important ?eld, in which con?gurational mechanics can provide a better understanding of processes going on within the material. Besides these mechanically, physically, and chemically motivated applications, ideas from con?gurational mechanics are now increasingly applied within computational mechanics.