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Books > Professional & Technical > Mechanical engineering & materials > Mechanical engineering

Computational Geomechanics and Hydraulic Structures (Hardcover, 1st ed. 2019): Sheng-Hong Chen Computational Geomechanics and Hydraulic Structures (Hardcover, 1st ed. 2019)
Sheng-Hong Chen
R6,361 Discovery Miles 63 610 Ships in 10 - 15 working days

This book presents recent research into developing and applying computational tools to estimate the performance and safety of hydraulic structures from the planning and construction stage to the service period. Based on the results of a close collaboration between the author and his colleagues, friends, students and field engineers, it shows how to achieve a good correlation between numerical computation and the actual in situ behavior of hydraulic structures. The book's heuristic and visualized style disseminates the philosophy and road map as well as the findings of the research. The chapters reflect the various aspects of the three typical and practical methods (the finite element method, the block element method, the composite element method) that the author has been working on and made essential contributions to since the 1980s. This book is an advanced continuation of Hydraulic Structures by the same author, published by Springer in 2015.

Mechanics of Microstructured Solids 2 - Cellular Materials, Fibre Reinforced Solids and Soft Tissues (Hardcover, 2010 ed.):... Mechanics of Microstructured Solids 2 - Cellular Materials, Fibre Reinforced Solids and Soft Tissues (Hardcover, 2010 ed.)
J.-F. Ganghoffer, Franco Pastrone
R2,843 Discovery Miles 28 430 Ships in 10 - 15 working days

This second volume of the series Lecture Notes in Applied and Computational Mechanics is the second part of the compendium of reviewed articles presented at the 11th EUROMECH-MECAMAT conference entitled "Mechanics of microstructured solids: cellular materials, fibre reinforced solids and soft tissues," which took place in Torino (Italy) in March 10-14, 2008, at the Museo Regional delle Scienze. This EUROMECH-MECAMAT conference was jointly organized by the Dipartimento di Matematica dell'Universita di Torino, Italy and the INPL Institute (LEMTA, Nancy-Universite, France). Prof. Franco Pastrone and Prof. Jean-Francois Ganghoffer were the co-chairmen.

Proceedings of International Conference on Advances in Tribology and Engineering Systems - ICATES 2013 (Hardcover, 2014 ed.):... Proceedings of International Conference on Advances in Tribology and Engineering Systems - ICATES 2013 (Hardcover, 2014 ed.)
Himanshu C. Patel, Gunamani Deheri, Harshvadan S. Patel, Shreya M. Mehta
R6,520 Discovery Miles 65 200 Ships in 12 - 17 working days

This book contains advanced-level research material in the area of lubrication theory and related aspects, presented by eminent researchers during the International Conference on Advances in Tribology and Engineering Systems (ICATES 2013) held at Gujarat Technological University, Ahmedabad, India during October 15 17, 2013. The material in this book represents the advanced field of tribology and reflects the work of many eminent researchers from both India and abroad. The treatment of the presentations is the result of the contributions of several professionals working in the industry and academia. This book will be useful for students, researchers, academicians, and professionals working in the area of tribology, in general, and bearing performance characteristics, in particular, especially from the point-of-view of design. This book will also appeal to researchers and professionals working in fluid-film lubrication and other practical applications of tribology. A wide range of topics has been included despite space and time constraints. Basic concepts and fundamentals techniques have been emphasized upon, while also including highly specialized topics and methods (such as nanotribology, bio-nanotribology). Care has been taken to generate interest for a wide range of readers, considering the interdisciplinary nature of the subject."

Microwave Heating Handbook (Hardcover): Doreen Rowe Microwave Heating Handbook (Hardcover)
Doreen Rowe
R2,057 Discovery Miles 20 570 Ships in 12 - 17 working days
Russian Models from the Mechanisms Collection of Bauman University (Hardcover, 2008 ed.): A. Golovin, V. Tarabarin Russian Models from the Mechanisms Collection of Bauman University (Hardcover, 2008 ed.)
A. Golovin, V. Tarabarin
R2,808 Discovery Miles 28 080 Ships in 10 - 15 working days

In 1998 the chairman of the Russian National Committee of TMM Professor Arcady Bessonov, recommended one of authors of this book to be come a member of the IFToMM Permanent Commission on the History of Mechanisms and Machines Sciences (PC HMMS). Willy-nilly from this time the history of technique, as hobby passed on to a serious the employment in the history of engineering science. Interest history of a subject is natural for Professor, a leading a course of Theory of Mechanisms and Machines in Bauman University. This interest is supported by the fact that Bauman University is one of the oldest technical universities in Russia, and the course "Applied Mechanics" - later "Theory of Mechanisms and Machines" was the first systematic course in Russia. The second author supervises a cycle of laboratory works on TMM. Models of mechanisms are placed in laboratory in show-windows of ancient cases quite possibly coevals of the first course. He became interested in contents of these cases: firstly in models, and then in their origin. Later he occupied himself with the creation of a web-site "The Collection of mechanisms in department TMM in Bauman University". Gradually both authors had the idea of cooperation, although several years previously, we could not imagine this happening. We took an active part in the work of PC HMMS from 2000. It was promoted by of chairman of the commission Professor Marco Ceccarelli.

IUTAM Symposium on Multiscale Problems in Multibody System Contacts - Proceedings of the IUTAM Symposium held in Stuttgart,... IUTAM Symposium on Multiscale Problems in Multibody System Contacts - Proceedings of the IUTAM Symposium held in Stuttgart, Germany, February 20-23, 2006 (Hardcover)
Peter Eberhard
R4,844 R4,276 Discovery Miles 42 760 Save R568 (12%) Ships in 12 - 17 working days

The investigation of multiscale problems in multibody system contacts is a most interesting and timely topic which has been the subject of intensive research for more than one decade. While many questions have been answered and the mechanically sound description and simulation is increasingly applied in practical engineering problems, this IUTAM Symposium facilitated discussions between researchers active in the field and enabled us to review the state-of-the-art and to identify for the years to come the hot topics which require further efforts.

It was especially useful to bring together scientists from closely related but traditionally distinct fields such as multibody system contact, molecular dynamics, finite element contact, collision detection or the mathematics of unilateral contact. It is observed that the once clear boundaries between these fields are blurring and an exchange of ideas will accelerate the development with mutual benefits.

Multiscale problems occur very naturally in contact mechanics. Typically the contact forces and stresses are very high and they are transmitted within a very short period of time. This leads to questions, e.g. how the slow rigid body motion and the fast motion changes can be considered simultaneously or how interface effects couple to wave propagation and the large-scale motion.

The purpose of the symposium was be to provide a basis for discussion and exchange of new concepts and ideas to scientists from all over Europe and the world. This proceedings volume summarizes contributions of many authors active in the field and gives insight in very different areas of this fascinating research.

Analog Circuit Design - Sensor and Actuator Interface Electronics, Integrated High-Voltage Electronics and Power Management,... Analog Circuit Design - Sensor and Actuator Interface Electronics, Integrated High-Voltage Electronics and Power Management, Low-Power and High-Resolution ADC's (Hardcover, 2004 ed.)
Johan Huijsing, Michiel Steyaert, Arthur H. M. van Roermund
R5,764 R4,351 Discovery Miles 43 510 Save R1,413 (25%) Ships in 12 - 17 working days

Analog Circuit Design contains the contribution of 18 experts from the 13th International Workshop on Advances in Analog Circuit Design. It is number 13 in the successful series of Analog Circuit Design.

It provides 18 excellent overviews of analog circuit design in: Sensor and Actuator Interfaces, Integrated High-Voltage Electronics and Power Management, and Low-Power and High-Resolution ADC s.

Analog Circuit Design is an essential reference source for analog circuits designers and researchers wishing to keep abreast with the latest developments in the field. The tutorial coverage also makes it suitable for use in an advanced design course.

Nanocoatings - Size Effect in Nanostructured Films (Hardcover, 2011 ed.): Mahmood Aliofkhazraei Nanocoatings - Size Effect in Nanostructured Films (Hardcover, 2011 ed.)
Mahmood Aliofkhazraei
R2,810 Discovery Miles 28 100 Ships in 10 - 15 working days

Size effect in structures has been taken into consideration over the last years. In comparison with coatings with micrometer-ranged thickness, nanostructured coatings usually enjoy better and appropriate properties, such as strength and resistance. These coatings enjoy unique magnetic properties and are used with the aim of producing surfaces resistant against erosion, lubricant system, cutting tools, manufacturing hardened sporadic alloys, being resistant against oxidation and corrosion.

This book reviews researches on fabrication and classification of nanostructured coatings with focus on size effect in nanometric scale. Size effect on electrochemical, mechanical and physical properties of nanocoatings are presented.

IUTAM Symposium on Nonlinear Singularities in Deformation and Flow - Proceedings of the IUTAM Symposium Held in Haifa, Israel,... IUTAM Symposium on Nonlinear Singularities in Deformation and Flow - Proceedings of the IUTAM Symposium Held in Haifa, Israel, 17-21 March 1997 (Hardcover)
D. Durban, J.R.A. Pearson
R2,421 Discovery Miles 24 210 Ships in 12 - 17 working days

This volume is a collection of the main lectures over a broad spectrum of rheological models with singularities as the "Leitmotiv", with 30 papers on the most recent developments in the analysis and understanding of non-linear singularities. Singularity-dominated local fields are frequently encountered in various branches of continuum mechanics, such as elasticity, plasticity, Newtonian fluids and more complex rheological models. Examples are provided by near tip fields of cracks, notches and wedges; interfacial phenomena; flow around corners, wedges and cones; moving contact lines in multiphase systems; cusps in fluid interfaces and shocks and localizations. The volume should be of interest to researchers and engineers in virtually all branches of continuum mechanics.

The Essentials of Finite Element Modeling and Adaptive Refinement: For Beginning Analysts to Advanced Researchers in Solid... The Essentials of Finite Element Modeling and Adaptive Refinement: For Beginning Analysts to Advanced Researchers in Solid Mechanics (Hardcover)
John O. Dow
R2,332 Discovery Miles 23 320 Ships in 12 - 17 working days

Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a "mesh". The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same time advancing adaptive refinement procedures. The book presents: A more simplified approach to finite element analysis based on computational continuum mechanics Physically interpretable notation that identifies a common basis for the finite element and the finite difference methods New point-wise error estimators that identify errors in terms of quantities of direct interest in solid mechanics

Tandem Cold Metal Rolling Mill Control - Using Practical Advanced Methods (Hardcover, 2011): John Pittner, Marwan A. Simaan Tandem Cold Metal Rolling Mill Control - Using Practical Advanced Methods (Hardcover, 2011)
John Pittner, Marwan A. Simaan
R4,947 Discovery Miles 49 470 Ships in 12 - 17 working days

This book deals with a novel and practical advanced method for control of tandem cold metal rolling processes based on the emerging state-dependent Riccati equation technique. After a short history of tandem cold rolling, various types of cold rolling processes are described. A basic mathematical model of the process is discussed, and the diverse conventional control methods are compared. A detailed treatment of the theoretical and practical aspects of the state-dependent algebraic Riccati equation technique is given, with specific details of the new procedure described and results of simulations performed to verify the control model and overall system performance with the new controller coupled to the process model included. These results and data derived from actual operating mills are compared showing the improvements in performance using the new method. Material is included which shows how the new technique can be extended to the control of a broad range of large-scale complex nonlinear processes.

Publishing Opportunities for Energy Research - A Descriptive Guide to Selective Serials in the Social and Technical Sciences... Publishing Opportunities for Energy Research - A Descriptive Guide to Selective Serials in the Social and Technical Sciences (Hardcover)
Roberta A Scull
R2,423 Discovery Miles 24 230 Ships in 10 - 15 working days
Mechanical Engineering (Hardcover): Rene Sava Mechanical Engineering (Hardcover)
Rene Sava
R2,768 Discovery Miles 27 680 Ships in 12 - 17 working days
Viscosity of Liquids - Theory, Estimation, Experiment, and Data (Hardcover, 2007 ed.): Dabir S. Viswanath, Tushar K. Ghosh,... Viscosity of Liquids - Theory, Estimation, Experiment, and Data (Hardcover, 2007 ed.)
Dabir S. Viswanath, Tushar K. Ghosh, Dasika. H. L. Prasad, Nidamarty V. K. Dutt, Kalipatnapu Y Rani
R5,563 Discovery Miles 55 630 Ships in 10 - 15 working days

The need for properties is ever increasing to make processes more economical. A good survey of the viscosity data, its critical evaluation and correlation would help design engineers, scientists and technologists in their areas of interest. This type of work assumes more importance as the amount of experimental work in collection and correlation of properties such as viscosity, thermal conductivity, heat capacities, etc has reduced drastically both at the industry, universities, and national laboratories. One of the c o-authors, Professor Viswanath, co-authored a book jointly with Dr. Natarajan Data Book on the Viscosity of Liquids in 1989 which mainly presented collected and evaluated liquid viscosity data from the literature. Although it is one of its kinds in the field, Prof. Viswanath recognized that the design engineers, scientists and technologists should have a better understanding of theories, experimental procedures, and operational aspects of viscometers. Also, rarely the data are readily available at the conditions that are necessary for design of the equipment or for other calculations. Therefore, the data must be interpolated or extrapolated using the existing literature data and using appropriate correlations or models. We have tried to address these issues in this book."

Advanced Numerical Simulations in Mechanical Engineering (Hardcover): Ashwani Kumar, Pravin P. Patil, Yogesh Kr. Prajapati Advanced Numerical Simulations in Mechanical Engineering (Hardcover)
Ashwani Kumar, Pravin P. Patil, Yogesh Kr. Prajapati
R4,300 Discovery Miles 43 000 Ships in 10 - 15 working days

Recent developments in information processing systems have driven the advancement of numerical simulations in engineering. New models and simulations enable better solutions for problem-solving and overall process improvement. Advanced Numerical Simulations in Mechanical Engineering is a pivotal reference source for the latest research findings on advanced modelling and simulation method adopted in mechanical and mechatronics engineering. Featuring extensive coverage on relevant areas such as fuzzy logic controllers, finite element analysis, and analytical models, this publication is an ideal resource for students, professional engineers, and researchers interested in the application of numerical simulations in mechanical engineering.

Modeling, Control and Coordination of Helicopter Systems (Hardcover, 2012): Beibei Ren, Shuzhi Sam Ge, Chang Chen, Cheng-Heng... Modeling, Control and Coordination of Helicopter Systems (Hardcover, 2012)
Beibei Ren, Shuzhi Sam Ge, Chang Chen, Cheng-Heng Fua, Tong Heng Lee
R2,806 Discovery Miles 28 060 Ships in 10 - 15 working days

"Modeling, Control and Coordination of Helicopter Systems" provides a comprehensive treatment of helicopter systems, ranging from related nonlinear flight dynamic modeling and stability analysis to advanced control design for single helicopter systems, and also covers issues related to the coordination and formation control of multiple helicopter systems to achieve high performance tasks. Ensuring stability in helicopter flight is a challenging problem for nonlinear control design and development. This book is a valuable reference on modeling, control and coordination of helicopter systems, providing readers with practical solutions for the problems that still plague helicopter system design and implementation. Readers will gain a complete picture of helicopters at the systems level, as well as a better understanding of the technical intricacies involved.

Phase Change Materials - Science and Applications (Hardcover, 2009 ed.): Simone Raoux, Matthias Wuttig Phase Change Materials - Science and Applications (Hardcover, 2009 ed.)
Simone Raoux, Matthias Wuttig
R5,247 Discovery Miles 52 470 Ships in 12 - 17 working days

"Phase Change Materials: Science and Applications" provides a unique introduction of this rapidly developing field. Clearly written and well-structured, this volume describes the material science of these fascinating materials from a theoretical and experimental perspective. Readers will find an in-depth description of their existing and potential applications in optical and solid state storage devices as well as reconfigurable logic applications.

Researchers, graduate students and scientists with an interest in this field will find "Phase Change Materials" to be a valuable reference.

Error Analysis with Applications in Engineering (Hardcover, 2010 ed.): Zbigniew A. Kotulski, Wojciech Szczepi nski Error Analysis with Applications in Engineering (Hardcover, 2010 ed.)
Zbigniew A. Kotulski, Wojciech Szczepi nski
R4,605 R4,319 Discovery Miles 43 190 Save R286 (6%) Ships in 12 - 17 working days

Our intention in preparing this book was to present in as simple a manner as possible those branches of error analysis which ?nd direct applications in solving various problems in engineering practice. The main reason for writing this text was the lack of such an approach in existing books dealing with the error calculus. Most of books are devoted to mathematical statistics and to probability theory. The range of applications is usually limited to the problems of general statistics and to the analysis of errors in various measuring techniques. Much less attention is paid in these books to two-dimensional and three-dim- sional distributions, and almost no attention is given to problems connected with the two-dimensional and three-dimensional vectorial functions of independent random variables. The theory of such vectorial functions ?nds new applications connected, for example, with analysis of the positioning accuracy of various mechanisms, among them of robot manipulators and automatically controlled earth-moving and loading machines, such as excavators.

Basics of Cutting and Abrasive Processes (Hardcover, 1st ed. 2012): Hans Kurt Toenshoff, Berend Denkena Basics of Cutting and Abrasive Processes (Hardcover, 1st ed. 2012)
Hans Kurt Toenshoff, Berend Denkena
R5,695 R4,282 Discovery Miles 42 820 Save R1,413 (25%) Ships in 12 - 17 working days

Manufacturing is the basic industrial activity generating real value. Cutting and abrasive technologies are the backbone of precision production in machine, automotive and aircraft building as well as of production of consumer goods. We present the knowledge of modern manufacturing in these technologies on the basis of scientific research. The theory of cutting and abrasive processes and the knowledge about their application in industrial practice are a prerequisite for the studies of manufacturing science and an important part of the curriculum of the master study in German mechanical engineering. The basis of this book is our lecture "Basics of cutting and abrasive processes" (4 semester hours/3 credit hours) at the Leibniz University Hannover, which we offer to the diploma and master students specializing in manufacturing science.

Modeling and Simulation for RF System Design (Hardcover, 2005): Ronny Frevert, Joachim Haase, Roland Jancke, Uwe Knochel, Peter... Modeling and Simulation for RF System Design (Hardcover, 2005)
Ronny Frevert, Joachim Haase, Roland Jancke, Uwe Knochel, Peter Schwarz, …
R4,609 R4,324 Discovery Miles 43 240 Save R285 (6%) Ships in 12 - 17 working days

Modern telecommunication systems are highly complex from an algorithmic point of view. The complexity continues to increase due to advanced modulation schemes, multiple protocols and standards, as well as additional functionality such as personal organizers or navigation aids.

To have short and reliable design cycles, efficient verification methods and tools are necessary. Modeling and simulation need to accompany the design steps from the specification to the overall system verification in order to bridge the gaps between system specification, system simulation, and circuit level simulation. Very high carrier frequencies together with long observation periods result in extremely large computation times and requires, therefore, specialized modeling methods and simulation tools on all design levels.

The focus of Modeling and Simulation for RF System Design lies on RF specific modeling and simulation methods and the consideration of system and circuit level descriptions. It contains application-oriented training material for RF designers which combines the presentation of a mixed-signal design flow, an introduction into the powerful standardized hardware description languages VHDL-AMS and Verilog-A, and the application of commercially available simulators.

Models are provided on a CD-ROM included with the book because models are necessary to reproduce, understand and explore the real world behavior on a simulation platform. Modeling and Simulation for RF System Design is addressed to graduate students and industrial professionals who are engaged in communication system design and want to gain insight into the system structure by own simulation experiences.

The authors areexperts in design, modeling and simulation of communication systems engaged at the Nokia Research Center (Bochum, Germany) and the Fraunhofer Institute for Integrated Circuits, Branch Lab Design Automation (Dresden, Germany).

Epicyclic Drive Trains (Hardcover): Herbert W Muller Epicyclic Drive Trains (Hardcover)
Herbert W Muller
R2,602 Discovery Miles 26 020 Ships in 10 - 15 working days

This first English-language edition is a completely revised and expanded version of Die Umlaufgetriebe, published by the Springer-Verlag in 1971. It will be extremely useful to American engineers since it stresses the efficiencies of new and existing transmission designs and provides concise guide rules as well as worksheets. A thorough understanding of the sometimes difficult material is facilitated through the use of both schematic and symbolic diagrams. The book is profusely illustrated and analyzes many applications. These drives receive an unusually clear treatment because at Dr. Muller's discovery of their perfect analogy to the simple epicyclic drive trains. Unified methods of analysis and synthesis of complex drives are employed throughout, suggesting that further simplifications may be possible through the use of a multivalued logic system which is analogous to the bivalent logic system of digital electronics. This book presents a clear and concise description of a multitude of revolving gear trains in terms common to all, whereas previous publications have been limited to treatment on interesting subproblems. Its well-reasoned definitions and classifications will aid engineers in the selection and design of the best drives for any given application.

Hot Cracking Phenomena in Welds III (Hardcover, Edition.): John Lippold, Thomas Boellinghaus, Carl E Cross Hot Cracking Phenomena in Welds III (Hardcover, Edition.)
John Lippold, Thomas Boellinghaus, Carl E Cross
R5,137 R4,287 Discovery Miles 42 870 Save R850 (17%) Ships in 12 - 17 working days

This is the third in a series of compendiums devoted to the subject of weld hot cracking. It contains 22 papers presented at the 3rd International Hot Cracking Workshop in Columbus, Ohio USA in March 2010. In the context of this workshop, the term "hot cracking" refers to elevated temperature cracking associated with either the weld metal or heat-affected zone. These hot cracking phenomena include weld solidification cracking, HAZ and weld metal liquation cracking, and ductility-dip cracking. The book is divided into three major sections based on material type; specifically aluminum alloys, steels, and nickel-base alloys. Each of these sections begins with a keynote paper from prominent researchers in the field: Dr. Sindo Kou from the University of Wisconsin, Dr. Thomas Bollinghaus from BAM and the University of Magdeburg, and Dr. John DuPont from Lehigh University. The papers contained within include the latest insight into the mechanisms associated with hot cracking in these materials and methods to prevent cracking through material selection, process modification, or other means. The three "Hot Cracking Phenomena in Welds" compendiums combined contain a total of 64 papers and represent the best collection of papers on the topic of hot cracking ever assembled.

Recent Studies in Sustainable Energy Harvesting (Hardcover): Ted Weyland Recent Studies in Sustainable Energy Harvesting (Hardcover)
Ted Weyland
R2,089 Discovery Miles 20 890 Ships in 12 - 17 working days
Topology Optimization of Compliant Mechanisms (Hardcover, 1st ed. 2018): Xianmin Zhang, Benliang Zhu Topology Optimization of Compliant Mechanisms (Hardcover, 1st ed. 2018)
Xianmin Zhang, Benliang Zhu
R3,619 Discovery Miles 36 190 Ships in 12 - 17 working days

This book covers various topics regarding the design of compliant mechanisms using topology optimization that have attracted a great deal of attention in recent decades. After comprehensively describing state-of-the-art methods for designing compliant mechanisms, it provides a new topology optimization method for finding new flexure hinges. It then presents several attempts to obtain distributed compliant mechanisms using the topology optimization method. Further, it discusses a Jacobian-based topology optimization method for compliant parallel mechanisms, and introduces readers to the topology optimization of compliant mechanisms, taking into account geometrical nonlinearity and reliability. Providing a systematic method for topology optimization of flexure hinges, which are essential for designing compliant mechanisms, the book offers a valuable resource for all readers who are interested in designing compliant mechanism-based positioning stages. In addition, the methods for solving the de facto hinges in topology optimized compliant mechanisms will benefit all engineers seeking to design micro-electro-mechanical system (MEMS) structures.

Composite Materials - Properties as Influenced by Phase Geometry (Hardcover, 2005 ed.): Lauge Fuglsang Nielsen Composite Materials - Properties as Influenced by Phase Geometry (Hardcover, 2005 ed.)
Lauge Fuglsang Nielsen
R2,945 Discovery Miles 29 450 Ships in 10 - 15 working days

In the past ?ve decades considerable attention has been devoted to comp- ite materials. A number of expressions have been suggested by which mac- scopic properties can be predicted when the properties, geometry, and volume concentrations of the constituent components are known. Many expressions are purely empirical or semi-theoretical. Others, however, are theoretically well founded such as the exact results from the following classical boundary studies: Bounds for the elastic moduli of composites made of perfectly coherent homogeneous, isotropic linear elastic phases have been developed by Paul [1] and Hansen [2] for unrestricted phase geometry and by Hashin and Shtrikman [3] for phase geometries, which cause macroscopic homogeneity and isotropy. The composites dealt with in this book are of the latter type. For two speci?c situations (later referred to), Hashin [4] and Hill [5] derived exact - lutionsforthebulkmodulusofsuchmaterials.Hashinconsideredtheso-called Composite Spheres Assemblage (CSA) consisting of tightly packed congruent composite elements made of spherical particles embedded in concentric - trix shells. Hill considered materials in which both phases have identical shear moduli. In the ?eld of predicting the elastic moduli of homogeneous isotropic c- posite materials in general the exact Hashin and Hill solutions are of th- retical interest mainly. Only a few real composites have the geometry de?ned by Hashin or the sti?ness distribution assumed by Hill. The enormous sign- icance, however, of the Hashin/Hill solutions is that they represent bounds which must not be violated by sti?ness predicted by any new theory claiming to consider geometries in general.

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