Solid Mechanics and Its Applications - Böcker

This book is intended for mechanicians, engineering mathematicians, and, generally for theoretically inclined mechanical engineers. It has its origin in my Master's Thesis (J 957), which I wrote under the supervision of Professor Dr. R. Timman of the Delft TH and Dr. Ir. A. D. de Pater of Netherlands Railways. I did not think that the surface of the problem had even been scratched, so I joined de Pater, who had by then become Professor in the Engineering Mechanics Lab. of the Delft TH, to write my Ph. D. Thesis on it. This thesis (1967) was weil received in railway circles, which is due more to de Pater's untiring promotion than to its merits. Still not satisfied, I feit that I needed more mathe­ matics, and I joined Professor Timman's group as an Associate Professor. This led to the present work. Many thanks are due to G. M. L. Gladwell, who thoroughly polished style and contents of the manuscript. Thanks are also due to my wife, herself an engineering mathematician, who read the manuscript through critically, and made many helpful comments, to G. F. M. Braat, who also read an criticised, and, in addition, drew the figures together with J. Schonewille, to Ms. A. V. M. de Wit, Ms. M. den Boef, and Ms. P. c. Wilting, who typed the manuscript, and to the Publishers, who waited patiently. Delft-Rotterdam, 17 July 1990. J. J.

This book has been written with two purposes, as a textbook for engineering courses and as a reference book for engineers and scientists. The book is an outcome of several lecture courses. These include lectures given to graduate students at the Asian Institute of Technology for several years, a course on elasticity for University of Tokyo graduate students in the spring of 1979, and courses on elasticity, viscoelasticity and ftnite deformation at the National University of Singapore from May to November 1985. In preparing this book, I kept three objectives in mind: ftrst, to provide sound fundamental knowledge of solid mechanics in the simplest language possible; second, to introduce effective analytical and numerical solution methods; and third, to impress on readers that the subject is beautiful, and is accessible to those with only a standard mathematical background. In order to meet those objectives, the ftrst chapter of the book is a review of mathematical foundations intended for anyone whose background is an elementary knowledge of differential calculus, scalars and vectors, and Newton's laws of motion. Cartesian tensors are introduced carefully. From then on, only Cartesian tensors in the indicial notation, with subscript as indices, are used to derive and represent all theories.

This book is concerned with the static and dynamic analysis of structures. Specifi­ cally, it uses the stiffness formulated matrix methods for use on computers to tackle some of the fundamental problems facing engineers in structural mechanics. This is done by covering the Mechanics of Structures, its rephrasing in terms of the Matrix Methods, and then their Computational implementation, all within a cohesivesetting. Although this book is designed primarily as a text for use at the upper-undergraduate and beginning graduate level, many practicing structural engineers will find it useful as a reference and self-study guide. Several dozen books on structural mechanics and as many on matrix methods are currently available. A natural question to ask is why another text? An odd devel­ opment has occurred in engineering in recent years that can serve as a backdrop to why this book was written. With the widespread availability and use of comput­ ers, today's engineers have on their desk tops an analysis capability undreamt of by previous generations. However, the ever increasing quality and range of capabilities of commercially available software packages has divided the engineering profession into two groups: a small group of specialist program writers that know the ins and outs of the coding, algorithms, and solution strategies; and a much larger group of practicing engineers who use the programs. It is possible for this latter group to use this enormous power without really knowing anything of its source.

Composite materials are increasingly used in aerospace, underwater, and automotive structures. To take advantage of the full potential of composite materials, structural analysts and designers must have accurate mathematical models and design methods at their disposal. The objective of this monograph is to present the laminated plate theories and their finite element models to study the deformation, strength and failure of composite structures. Emphasis is placed on engineering aspects, such as the analytical descriptions, effective analysis tools, modeling of physical features, and evaluation of approaches used to formulate and predict the response of composite structures. The first chapter presents an overview of the text. Chapter 2 is devoted to the introduction of the definitions and terminology used in composite materials and structures. Anisotropic constitutive relations and laminate plate theories are also reviewed. Finite element models of laminated composite plates are presented in chapter 3. Numerical evaluation of element coefficient matrices, post-computation of strains and stresses and sample examples of laminated plates in bending and vibration are discussed.Chapter 4 introduces damage and failure criteria in composite laminates. Finally, Chapter 5 is dedicated to case studies involving various aspects and types of composite structures. Joints, cutouts, woven composites, environmental effects, postbuckling response and failure of composite laminates are discussed by considering specific examples.

The purpose of this book is to present, describe and demonstrate the use of numerical methods in solving crack problems in fracture mechanics. The text concentrates, to a large extent, on the application of the Boundary Element Method (BEM) to fracture mechanics, although an up-to-date account of recent advances in other numerical methods such as the Finite Element Method is also presented. The book is an integrated presentation of modem numerical fracture mechanics, it contains a compilation of the work of many researchers as well as accounting for some of authors' most recent work on the subject. It is hoped that this book will bridge the gap that exists between specialist books on theoretical fracture mechanics on one hand, and texts on numerical methods on the other. Although most of the methods presented are the latest developments in the field of numerical fracture mechanics, the authors have also included some simple techniques which are essential for understanding the physical principles that govern crack problems in general. Different numerical techniques are described in detail and where possible simple examples are included, as well as test results for more complicated problems. The book consists of six chapters. The first chapter initially describes the historical development of theoretical fracture mechanics, before proceeding to present the basic concepts such as energy balance, stress intensity factors, residual strength and fatigue crack growth as well as briefly describing the importance of stress intensity factors in corrosion and residual stress cracking.

This book is concerned with the static and dynamic analysis of structures. Specifi­ cally, it uses the stiffness formulated matrix methods for use on computers to tackle some of the fundamental problems facing engineers in structural mechanics. This is done by covering the Mechanics of Structures, its rephrasing in terms of the Matrix Methods, and then their Computational implementation, all within a cohesivesetting. Although this book is designed primarily as a text for use at the upper-undergraduate and beginning graduate level, many practicing structural engineers will find it useful as a reference and self-study guide. Several dozen books on structural mechanics and as many on matrix methods are currently available. A natural question to ask is why another text? An odd devel­ opment has occurred in engineering in recent years that can serve as a backdrop to why this book was written. With the widespread availability and use of comput­ ers, today's engineers have on their desk tops an analysis capability undreamt of by previous generations. However, the ever increasing quality and range of capabilities of commercially available software packages has divided the engineering profession into two groups: a small group of specialist program writers that know the ins and outs of the coding, algorithms, and solution strategies; and a much larger group of practicing engineers who use the programs. It is possible for this latter group to use this enormous power without really knowing anything of its source.

1. 1 Preliminary Concepts A cam mechanism is a mechanical system consisting of three basic components: a driving element, called the cam; a driven element, termed the follower; and a fixed frame. Sometimes, an intermediate element is introduced between the cam and the follower with the purpose of improving the mechanism performance. This element is called the roller because function is to produce a pure-rolling relative motion be­ tween the cam and the follower. The purpose ofa cam mechanism is the transmission of power or information. In applications concerning power transmission, the main good to be transmitted is force or torque; in applications ofinformation transmission, the main good transmitted takes the form of motion signals. Most modern appli­ cations of cam mechanisms, to be described shortly, are of the former type. Cam mechanisms used for information transmission were traditionally found in measuring instruments. With the advent ofmodern microprocessor-based hardware, this typeof application is becoming less common. Nevertheless, cam mechanisms are still used in a wide spectrum of applications, especially in automatic machines and instruments, textile machinery, computers, printing presses, food-processing equipment, internal combustion engines, control systems, and photographic equipment (Prenzel, 1989). In the design of cam mechanisms, the engineer performs several activities, namely, task definition, synthesis, analysis, optimization, and dynamic simulation. These tasks do not always follow this order. In fact, some loops may appear in the foregoing tasks, such as those illustrated in Fig. 1. 1. 1.

The field of structural optimization is still a relatively new field undergoing rapid changes in methods and focus. Until recently there was a severe imbalance between the enormous amount of literature on the subject, and the paucity of applications to practical design problems. This imbalance is being gradually redressed. There is still no shortage of new publications, but there are also exciting applications of the methods of structural optimizations in the automotive, aerospace, civil engineering, machine design and other engineering fields. As a result of the growing pace of applications, research into structural optimization methods is increasingly driven by real-life problems. t-.Jost engineers who design structures employ complex general-purpose software packages for structural analysis. Often they do not have any access to the source program, and even more frequently they have only scant knowledge of the details of the structural analysis algorithms used in this software packages. Therefore the major challenge faced by researchers in structural optimization is to develop methods that are suitable for use with such software packages. Another major challenge is the high computational cost associated with the analysis of many complex real-life problems. In many cases the engineer who has the task of designing a structure cannot afford to analyze it more than a handful of times.

The field of structural optimization is still a relatively new field undergoing rapid changes in methods and focus. Until recently there was a severe imbalance between the enormous amount of literature on the subject, and the paucity of applications to practical design problems. This imbalance is being gradually redressed. There is still no shortage of new publications, but there are also exciting applications of the methods of structural optimizations in the automotive, aerospace, civil engineering, machine design and other engineering fields. As a result of the growing pace of applications, research into structural optimization methods is increasingly driven by real-life problems. t-.Jost engineers who design structures employ complex general-purpose software packages for structural analysis. Often they do not have any access to the source program, and even more frequently they have only scant knowledge of the details of the structural analysis algorithms used in this software packages. Therefore the major challenge faced by researchers in structural optimization is to develop methods that are suitable for use with such software packages. Another major challenge is the high computational cost associated with the analysis of many complex real-life problems. In many cases the engineer who has the task of designing a structure cannot afford to analyze it more than a handful of times.

This is a first-year graduate textbook on linear elasticity, based on a one-semester course taught by the author at the University of Michigan. It is written with the practical engineering reader in mind, with dependence on previous knowledge of solid mechanics, continuum mechanics or mathematics being minimized. Most of the text should be readily intelligible to a reader with an undergraduate background of one or two courses in elementary strength of materials and a rudimentary knowledge of partial differentiation. Throughout, emphasis is placed on engineering applications of elasticity and examples are generally worked through to final expressions for the stress and displacement fields in order to explore the engineering consequences of the results. The topics covered are chosen with a view to modern research applications in fracture mechanics, composite materials, tribology and numerical methods. Thus, significant attention is given to crack and contact problems, problems involving interfaces between dissimilar media, thermoelasticity, singular asymptotic stress fields and three-dimensional problems.Problems suitable for class use are included at the end of most of the chapters. These are expressed wherever possible in the form in which they would arise in engineering - ie as a body of a given geometry subjected to prescribed loading - instead of inviting the student to "verify" that a given candidate stress function is appropriate to the problem. The text is therefore written in such a way as to enable the student to approach such problems deductively.

This is a first-year graduate textbook on linear elasticity, based on a one-semester course taught by the author at the University of Michigan. It is written with the practical engineering reader in mind, with dependence on previous knowledge of solid mechanics, continuum mechanics or mathematics being minimized. Most of the text should be readily intelligible to a reader with an undergraduate background of one or two courses in elementary strength of materials and a rudimentary knowledge of partial differentiation. Throughout, emphasis is placed on engineering applications of elasticity and examples are generally worked through to final expressions for the stress and displacement fields in order to explore the engineering consequences of the results. The topics covered are chosen with a view to modern research applications in fracture mechanics, composite materials, tribology and numerical methods. Thus, significant attention is given to crack and contact problems, problems involving interfaces between dissimilar media, thermoelasticity, singular asymptotic stress fields and three-dimensional problems.Problems suitable for class use are included at the end of most of the chapters. These are expressed wherever possible in the form in which they would arise in engineering - ie as a body of a given geometry subjected to prescribed loading - instead of inviting the student to "verify" that a given candidate stress function is appropriate to the problem. The text is therefore written in such a way as to enable the student to approach such problems deductively.

The study of intelligent (smart) structures and systems is emerging as a new research area that is multi-disciplinary in nature, requiring technical expertise from mechanical engineering, structural enginering, electrical engineering, applied mechanics, engineering mathematics, material science, computer science, biological science etc. This technololgy is quite likely to contribute significantly to advances in the design of high-performance structures, adaptive structures, high-precision systems, microsystems, etc. This volume contains specially invited contributions to state-of-the-art research in the evolution of intelligent (smart) structures and systems. Topics include: current intelligent (smart) structures research activities, peizoelectric structures, shape memory alloy reinforced composites, applications of electrorheological fluids, intelligent sensor systems, adaptive precision trusses, damage detection, model reinforcement, control of axial moving continua, distributed transducers etc.

This book is a concise and readable introductory text on solid mechanics suitable for engineers, scientists and applied mathematicians. It presents the foundations of stress, strain and elasticity theory and consistently employs the use of vectors and (particularly) Cartesian tensor notation. The first chapter introduces vectors with particular emphasis being paid to applications which arise in later chapters. Chapter 2 introduces Cartesian tensors and describes some of their important applications. In particular, finite and infinitessimal rotations are examined as are isotropic tensors and second order symmetric tensors. The last topic of this chapter includes a full discussion on eigenvalues and eigenvectors. There are separate introductions, in Chapters 3 and 4, to stress and strain and to their practical measurement using, respectively, photoelastic methods and strain gauges. In Chapter 5 the concepts of stress and strain are brought together and, in conjunction with Newton's equilibrium equations, used to deduce the basic equations of linear elasticity theory.These fundamental equations are then examined and analyzed by obtaining simple exact solutions, including solutions which describe twisting, bending and stretching of beams. Chapter 6 introduces the fundamental concept of strain energy and uses this concept to derive the Kirchoff uniqueness theorem, Rayleigh's reciprocal theorem and the important Castigliano relations. The chapter concludes with a thorough treatment of the theorem of minimum potential energy and examines some of its applications. The final three chapters examine the application of the fundamental equations to the theory of torsion, to structural analysis and to the treatment of two dimensional elastostatics by analytical and approximate (finite element) methods.

Shell structures are widely used in the fields of civil, mechanical, architectural, aeronautical, and marine engineering. Shell technology has been enhanced by the development of new materials and prefabrication schemes. Despite the mechanical advantages and aesthetic value offered by shell structures, many engineers and architects are relatively unacquainted with shell behaviour and design. This book familiarizes the engineering and architectural student, as well as the practicing engineer and architect, with the behaviour and design aspects of shell structures. Three aspects are presented: the physical behaviour, the structural analysis, and the design of shells in a simple, integrated, and yet concise fashion. Thus, the book contains three major aspects of shell engineering - (1) physical understanding of shell behaviour; (2) use of applied shell theories; and (3) development of design methodologies together with shell design examples.The theoretical tools required for rational analysis of shells are kept at a modest level to give a sound grasp of the fundamentals of shell behaviour and, at the same time, an understanding of the related theory, allowing it to be applied to actual design problems. To achieve a physical understanding of complex shell behaviour, quantitative presentations are supplemented by qualitative discussions so that the reader can grasp the "physical feeling" of shell behaviour. A number of analysis and detailed design examples are also worked out in various chapters, making the book a useful reference manual. This book can be used as a textbook and/or a reference book in undergraduate as well as graduate university courses in the fields of civil, mechanical, architectural, aeronautical, and materials engineering. It can also be used as a reference and design-analysis manual for the practicing engineers and architects. The text is supplemented by a number of appendices containing tables of shell analysis and design charts and tables.

Research into and development of high-precision systems, micro-electromechanical syustems, distributed sensors/actuators, smart structural systems, high-precision controls, etc, have drawn much attention in recent years. These new devices and systems will bring about a new technological revolution in modern industries and impact future human life. This book presents an overview of these technologies such as silicon based sensors/actuators and control piezoelectric micro sensors/actuators, micro actuation and control, micro sensor applications in robot control, optical fibre sensors/systems, and more. There are four main subjects emphasized in the book: (current) research and development; fundamental theories and tools; practical applications; and future research and development.

Shell structures are used in all phases of structures, from space vehicles to deep submergence hulls, from nuclear reactors to domes on sport arenas and civic buildings. With new materials and manufacturing methods, curved thin walled structures are being used increasingly. This text is a graduate course in the theory of shells. It covers shells of isotropic materials, such as metal alloys and plastics, and shells of composite materials, such as fibre reinforced polymer, metal or ceramic matrix materials. It provides the essential information for an understanding of the underlying theory, and solution of some of the basic problems. It also provides a basis to study the voluminous shell literature. Beyond being primarily a textbook, it is intended also for self study by practising engineers who would like to learn more about the behaviour of shells. The book has two parts: Part I deals with shells of isotropic materials. In this part the mathematical formulations are introduced involving curvilinear coordinates. The techniques of solutions and resulting behavior is compared to planar thin walled isotropic structures such as plates and beams.Part II then treats the behavior of shells, involving anisotropic composite materials, so widely used today. The analysis involves the complications due to the many elastic constants, effects of transverse shear deformation, thermal thickening and offer effects arising from the properties of composite materials.

This volume presents a collection of contributions describing the latest developments in the field of multibody system dynamics. It includes the results of a nationwide five-year research project by the German Research Council to determine: research on fundamental methods of multibody systems; concepts for new formalisms of dynamical analysis; development of efficient numerical algorithms; realization of a powerful software package of multibody systems. Contributions are of an interdisciplinary nature with research from the fields of mathematics, computer science, mechanics and control theory, and the volume should be invaluable to engineers and scientists working in these areas.

Concerning the topic of rotor dynamics, this book examines rotor problems through vibration analysis and emphasizes the analytical aspects. The book is therefore very useful as an advanced course/self-study book on rotor dynamics for readers with a good knowledge of vibration analysis. The text introduces simple rotor systems and gradually progresses to the complex systems, with a description of all analytical solutions for discrete and continuous rotor systems. A chapter is devoted to the introduction of lambda matrices, which allow a unified approach to the rotor vibration problems examined later in the book. The book should be of interest to graduate-level mechanical engineers, either on rotor dynamic courses or who need a reference text.

to Continuum Mechanics - after Truesdell and Noll by DONALD R. SMITH University of California -San Diego, Department of Mathematics, La Jolla, U. S. A. SPRINGER-SCIENCE+BUSINESS MEDIA, B. V. Library ofCongress Cataloging-in-Publication Data Smlth. Dona ld R. An introductlon to continuum mechanlcs ! by Donald R. Smlth. p. cm. -- . 24 0. 4 Gradients of Principal Invariants ...32 38 0. 5 Chain Rules of Differentiation ...41 0. 6 Gradient of a Field ...45 0.

Inverse Problems in Scattering exposes some of the mathematics which has been developed in attempts to solve the one-dimensional inverse scattering problem. Layered media are treated in Chapters 1--6 and quantum mechanical models in Chapters 7--10. Thus, Chapters 2 and 6 show the connections between matrix theory, Schur's lemma in complex analysis, the Levinson--Durbin algorithm, filter theory, moment problems and orthogonal polynomials. The chapters devoted to the simplest inverse scattering problems in quantum mechanics show how the Gel'fand--Levitan and Marchenko equations arose. The introduction to this problem is an excursion through the inverse problem related to a finite difference version of Schrodinger's equation. One of the basic problems in inverse quantum scattering is to determine what conditions must be imposed on the scattering data to ensure that they correspond to a regular potential, which involves Lebesque integrable functions, which are introduced in Chapter 9.

This work is a treatise on the design of robust and accurate elements for applications in structural mechanics. It describes the epistemological conflict between the principles in finite element technology that can be described as Art and those that have a scientific basis. The main emphasis of the book establishes the process by which continuum structural behaviour is replaced by a discretized description so that this can be coded as mechanics algorithms. Early efforts to do this were founded on engineering principles proceeding mostly from heuristic judgement (Art). However, considerable critical and analytical study in recent years has shown that it is possible to establish these methods on a more scientific basis. This book therefore sets this aspect of the use of the finite element method against such principles. It is an account of the state-of-the-art of the theory of finite element development and its critical assessment.

This text presents the techniques for a wide set of applications, ranging from the problems of size and shape optimization (historically the first to be studied) to topology and material optimization. Structural models are considered that use both discrete and finite elements. Structural materials can be classical or new. Emerging methods are also addressed, such as automatic differentiation, intelligent structures optimization, integration of structural optimization in concurrent engineering environments, and multidisciplinary optimization. This text should be of interest to researchers and designers in industries such as aerospace, automotive, mechanical, civil, nuclear, naval and offshore. It provides a reference for advanced undergraduate or graduate courses on structural optimization and optimum design.

This work sets out a simple, efficient and cost-effective computational technique which provides numerical solutions, for objects of any shape, to a wide range of scientific and engineering problems. It provides a complete approach to formulating boundary integral equations for scientific and engineering problems and solving them numerically using an element approximation. Only a knowledge of elementary calculus is required, since the text begins by relating familiar differential equations to integral equations and then moves on to the simple solution of integral equations. From this starting point, the mathematics of formulation and numerical approximation are developed progressively with every mathematical step being provided. Particular attention is paid to the problem of accurate evaluation of singular integrands and to the use of increasing levels of accuracy provided by constant, linear and quadratic approximations. This enables a full solution to be given for both two-dimensional and three-dimensional potential problems and finally, for the two-dimensional elastostatics problem."The Boundary Element Method" develops the mathematics of the text progressively both within chapters and from chapter to chapter. It is a self-contained, step-by-step exposition of the boundary element method, leading to its application to the key problem of elastostatics. The text may be used as a standard introductory reference text for the mathematics of this method and is suitable for final year undergraduate study as well as for postgraduates, scientists and engineers new to the subject. Worked examples and exercises are provided throughout the text.

This volume provides an account of developments in computational kinematics. Included are both numerical computations and symbolic manipulations. The volume reports on trends and progress in a broad class of problems, and the information is collated into six parts describing the main themes: (i) kinematic algorithms, whereby general kinematic problems are discussed in light of their solution algorithms; (ii) redundant manipulators; (iii) kinematic and dynamic control, in which the link between kinematics and the disciplines of dynamics and control is highlighted; (iv) parallel manipulators; (v) motion planning, touching on computational geometry; and (vi) kinematics of mechanisms, describing the closed kinematic chains. The volume contains a representative sample of current techniques available for kinematics problems. It should be of interest to researchers, graduate students and practising engineers engaged in work relating to kinematics, robotics, machine design and computer science.

Summary This bookis an introdU(;tion to the three numerical methodsmost commonly used for the mechanical analysisof deformable solids, namely: * the finite element method(FEM), a particularcaseofGalerkin's method, for the spatial discretisationofsolids; * the linear iteration method(LIM), a generalizationofNewton's method, for solving geometricandmaterial nonlinearities; * the finite difference method (FDM), in fact Newmark's method, for the temporal discretisation oftheproblem. The main reason for this selection is the degree of generality reached by the computerprograms basedon the combinationofthese methods. The originalityofthepresentation lies in the comparable emphasisputon the spatial, temporal and nonlinear dimensions of problem solving. For each dimension, there corresponds one method whose basic principle is exposed. It is then shown how they can be combined in a compact and flexible fonn. Thisjoint investigationofthe three methods leads to a particularly neat global algorithm. It is with this double objectiveof simplicity and unity in mind that this book has been designed. An outline of the book follows.A one-dimensional bar model problem, including all the ingredients necessary for acompletepresentationofthe addressed methods, isdefined in Chapter1. Emphasis is placedon the virtual work principle as an alternative to the.differentialequation ofmotion. Chapters 2, 3 and 4 present the three numerical methods: FEM, LIM and FDM, respectively. Although the presentation relies on a one-dimensional model problem, the fonnalism used is general and directly extendible to two- and three-dimensional situations. The compact combination of the three methods is discussed in detail in Chapter 5, which also contains several sections concerning their computer implementation.

Aeroelasticity is the study of flexible structures situated in a flowing fluid. Its modern origins are in the field of aerospace engineering, but it has now expanded to include phenomena arising in other fields such as bioengineering, civil engineering, mechanical engineering and nuclear engineering. The present volume is a teaching text for a first, and possibly second, course in aeroelasticity. It should also be useful as a reference source on the fundamentals of the subject for practitioners. In this third edition, several chapters have been revised and three new chapters added. The latter include a brief introduction to experimental aeroelasticity an overview of a frontier of research nonlinear aeroelasticity and an account of aeroelastic control. The authors are drawn from a range of fields including aerospace engineering, civil engineering, mechanical engineering, rotorcraft and turbomachinery. Each author is a leading expert in the subject of his chapter and has many years of experience in consulting, research and teaching.

Aeroelasticity is the study of flexible structures situated in a flowing fluid. Its modern origins are in the field of aerospace engineering, but it has now expanded to include phenomena arising in other fields such as bio-engineering, civil engineering, mechanical engineering and nuclear engineering. The present volume is a teaching text for a first, and possibly second, course in aeroelasticity. It should also be useful as a reference source on the fundamentals of the subject for practitioners. In this third edition, several chapters have been revised and three new chapters added. The latter include a brief introduction to experimental aeroelasticity, an overview of a frontier of research - nonlinear aeroelasticity and an account of aeroelastic control. The authors are drawn from a range of fields including aerospace engineering, civil engineering, mechanical engineering, rotorcraft and turbomachinery. Each author is a leading expert in the subject of his chapter and has many years of experience in consulting, research and teaching.

The field of fretting fatigue is extremely important in many areas of mechanical engineering. Fatigue cracks frequently initiate not from free surfaces, but from clamped or bolted components suffering vibration or other forms of minor oscillatory loading. This produces surface degradation, and conditions ripe for the initiation and early propulsion of cracks, constituting the phenomenon of fretting fatigue. This volume presents a summary of the current state of knowledge of fretting fatigue, with particular reference to the influence of mechanical variables, such as the applied forces, coefficient of friction and surface finish. It includes elements of the theories of contact mechanics and fracture mechanics in order to establish a rigorous framework for the understanding of the phenomenon. It goes on to describe fretting fatigue experiments and to describe the influence of the variables cited on fretting fatigue performances. The treatment is largely independent of the materials studied. The book does not require specialized mathematical knowledge.It should be of interest to mechanical engineers and materials scientists in research and development, but could also be used as a supplementary text for graduate students.

Variational methods provide a versatile framework for several branches of theoretical mechanics. For problems in dynamics, variational formulations provide a powerful alternative to vector methods. This approach has a legacy of ideas advanced by numerous researchers including such celebrated mathematicians as d'Alembert, Lagrange, Hamilton, Jacobi, Gauss and Euler. In this volume, the subject matter is developed systematically with worked-out problems. Initially, differential variational formulations are described followed by the integral formulations. An account of the essentials of the calculus of variations is provided. While classical formulations in dynamics have a long history, the complementary formulations are relatively new. This book aims to provide a detailed development of complementary formulations and highlight certain dualities that are revealed as a consequence of the two formulations. The chapter on special applications studies problems of small amplitude oscillations about equilibrium and steady state configurations, and the problem of impulsive or spike loads.The book ends with historical sketches of the personalities associated with variational methods in dynamics. Designed for structural, mechanical and aeronautical engineers, this volume should also be useful as a graduate text in analytic dynamics.