L. Cesari: Non-linear analysis.- J.K. Hale: Oscillations in neutral functional differential equations.- M. Jean: El ments de la th orie des quations diff rentielles avec commandes.- J. Mawhin: Un aper u des recherches belges en th orie des equations diff rentielles ordinaires dans le champ r el entre 1967 et 1972.- Yu A. Mitropol skii: Certains aspects des progr?'s de la methode de centrage.- Th. Vogel: Quelques probl mes non lin aires en physique math matique.

Substantialfundamental workhas been undertaken inthe different aspects of impact biomechanics over the past three decades. Much of this has been motivated and undertaken bythe automotive industry intheirefforts to improve transport safety. More recently, however, it has become app- ent that themultidisciplinary synergies which are realisedby interactions between engineers, scientists and clinical practitioners will ultimately lead to a greater understanding of the complex interacting phenomena withinthe human bodyafter it has sustained an impact. In turn, this greater depth of knowledge will provide more fundamentalinsights into the analysis, d- gnosis, treatment and prevention ofimpact injuries across a broader sp- trum of accident environments. Thescienti?c focus of this IUTAM symposium istoaddress those t- ics that are centrally important to the biomechanics ofimpact. These can be groupedinto those that are concerned with the different causes of - cidents (e. g. , transport, occupational and sports injuries), themechanics - volvedinaccident analysis (e. g. , accident investigation, computational m- elling techniques), the different types of resulting traumatic injuries (incl- ing musculoskeletal, organ, spinal and head injuries), methods of asse- ing the extent of injury (e. g. , injury assessment, injury criteria, constitutive laws for human tissue), and providing protection during an impact (e. g. , injury prevention, energy absorption materials, and safety devices).

The technology trends of Microelectronics and Microsystems are mainly characterized by miniaturization down to the nano-scale, increasing levels of system and function integration, and the introduction of new materials, while the business trends are mainly characterized by cost reduction, shorter-time-to market and outsourcing. Combination of these trends leads to increasing design complexity, dramatically decreasing design margins and process windows, reducing product development and qualification times, increasing risks of failures, and increasing difficulties to meet quality, robustness and reliability requirements. Consequentially, thermo-mechanical related failures, accounting for more than 65% of the total reliability failures, become the bottleneck for both current and future product and technology developments.

From a mechanical engineering point of view, Microelectronics and Microsystems are multi-scale in both geometric and time domains, multi-process, multi-functionality, multi-disciplinary, multi-material/interface, multi-damage and multi-failure mode. Their responses in manufacturing, assembling, qualification tests and application conditions are strongly nonlinear and stochastic. Mechanics of Microelectronics is extremely important and challenging, in terms of both industrial applications and academic research.

Written by the leading experts with both profound knowledge and rich practical experience in advanced mechanics and microelectronics industry, this book aims to provide the cutting edge knowledge and solutions for various mechanical related problems, in a systematic way. It contains essential and detailed information about the state-of-the-art theories, methodologies, the way of working and real case studies, covering the contents of:

• The trends in Microelectronics and Microsystems
• Reliability engineering and practices
• Thermal management
• Advanced mechanics
• Thermo-mechanics of integrated circuits and packages
• Characterization and modelling of moisture behaviour
• Characterization and modelling of solder joint reliability
• Virtual thermo-mechanical prototyping
• Challenges and future perspectives.

Modern computer simulations make stress analysis easy. As they continue to replace classical mathematical methods of analysis, these software programs require users to have a solid understanding of the fundamental principles on which they are based.

Develop Intuitive Ability to Identify and Avoid Physically Meaningless Predictions

Applied Mechanics of Solids is a powerful tool for understanding how to take advantage of these revolutionary computer advances in the field of solid mechanics. Beginning with a description of the physical and mathematical laws that govern deformation in solids, the text presents modern constitutive equations, as well as analytical and computational methods of stress analysis and fracture mechanics. It also addresses the nonlinear theory of deformable rods, membranes, plates, and shells, and solutions to important boundary and initial value problems in solid mechanics.

The author uses the step-by-step manner of a blackboard lecture to explain problem solving methods, often providing the solution to a problem before its derivation is presented. This format will be useful for practicing engineers and scientists who need a quick review of some aspect of solid mechanics, as well as for instructors and students.

Select and Combine Topics Using Self-Contained Modules and Subsections

Borrowing from the classical literature on linear elasticity, plasticity, and structural mechanics, this book:

• Introduces concepts, analytical techniques, and numerical methods used to analyze deformation, stress, and failure in materials or components
• Discusses the use of finite element software for stress analysis
• Assesses simple analytical solutions to explain how to set up properly posed boundary and initial-value problems
• Provides an understanding of algorithms implemented in software code

Complemented by the author s website, which features problem sets and sample code for self study, this book offers a crucial overview of problem solving for solid mechanics. It will help readers make optimal use of commercial finite element programs to achieve the most accurate prediction results possible."

Mechanics and model-based control are both rapidly expanding scientific fields and fundamental disciplines of mechatronics, sharing demanding mathematical and system-theoretic formulations and methods. The papers in this volume deal with smart materials, which allow the design and implementation of new types of actuator/sensor fields and networks. Main topics treated are fundamental studies on laminated, composite and functionally graded materials, thermal and piezoelectric actuation, active and passive damping, as well as vibrations and waves in smart structures. The book is based on the 1st Japanese-Austrian Workshop which took place in Linz in Fall 2008.

This book has grown out of lectures and courses given at Linkoeping University, Sweden, over a period of 15 years. It gives an introductory treatment of problems and methods of structural optimization. The three basic classes of geometrical - timization problems of mechanical structures, i. e. , size, shape and topology op- mization, are treated. The focus is on concrete numerical solution methods for d- crete and (?nite element) discretized linear elastic structures. The style is explicit and practical: mathematical proofs are provided when arguments can be kept e- mentary but are otherwise only cited, while implementation details are frequently provided. Moreover, since the text has an emphasis on geometrical design problems, where the design is represented by continuously varying-frequently very many- variables, so-called ?rst order methods are central to the treatment. These methods are based on sensitivity analysis, i. e. , on establishing ?rst order derivatives for - jectives and constraints. The classical ?rst order methods that we emphasize are CONLIN and MMA, which are based on explicit, convex and separable appro- mations. It should be remarked that the classical and frequently used so-called op- mality criteria method is also of this kind. It may also be noted in this context that zero order methods such as response surface methods, surrogate models, neural n- works, genetic algorithms, etc. , essentially apply to different types of problems than the ones treated here and should be presented elsewhere.

This book is motivated by stimulating problems in contact mechanics, emphasizing antiplane frictional contact with linearly elastic and viscoelastic materials. It focuses on the essentials with respect to the qualitative aspects of several classes of variational inequalities (VIs). Clearly presented, easy to follow, and well-referenced, this work treats almost entirely VIs of the second kind, with much of the material being state-of-the-art.

The notion dealt with in this volume of proceedings is often traced back to the late 19th-century writings of a rather obscure scientist, C. V. Burton. A probable reason for this is that the painstaking de ciphering of this author's paper in the Philosophical Magazine (Vol. 33, pp. 191-204, 1891) seems to reveal a notion that was introduced in math ematical form much later, that of local structural rearrangement. This notion obviously takes place on the material manifold of modern con tinuum mechanics. It is more or less clear that seemingly different phe nomena - phase transition, local destruction of matter in the form of the loss of local ordering (such as in the appearance of structural defects or of the loss of cohesion by the appearance of damage or the exten sion of cracks), plasticity, material growth in the bulk or at the surface by accretion, wear, and the production of debris - should enter a com mon framework where, by pure logic, the material manifold has to play a prominent role. Finding the mathematical formulation for this was one of the great achievements of J. D. Eshelby. He was led to consider the apparent but true motion or displacement of embedded material inhomogeneities, and thus he began to investigate the "driving force" causing this motion or displacement, something any good mechanician would naturally introduce through the duahty inherent in mechanics since J. L. d'Alembert."

Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.

Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.

Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems.

During the last decades completely new technologies for high speed railway vehicles have been developed. The primary goals have been to increase traction, axle load, and travelling speed, and to guarantee the safety of the passengers. However, new developments have revealed new limitations: settlement and destruction of the ballast and the subgrade lead to deterioration of the track; irregular wear of the wheels causes an increase in overall load and deterioration in passenger comfort; and damage of the running surfaces of the rail and the wheel is becoming more frequent. These problems have been investigated in the Priority Programme SPP 1015 supported by the Deutsche Forschungsgemeinschaft (DFG), with the goal of better understanding of the dynamic interaction of vehicle and track, and the long-term behavior of the components of the system. The book contains the scientific results of the programme as presented at the concluding colloquium held at University of Stuttgart, Germany, 2002.

This book can be viewed as a scientific investigation combined with methodological studies. For practical reasons each of the methods is described in the following general manner including: the uses and the scientific investigation tasks; methods of sampling; testing equipment; test preparation; tests; data processing; controversial issues and conclusions. Each of the 37 methods contains a range of 1 to 8 variants. As far as we know, the book is the first publication in the field.

Everyone involved with the mechanics of composite materials and structures must have come across the works of Dr. N.J. Pagano in their research. His research papers are among the most referenced of all existing literature in the field of mechanics of composite materials. This monograph makes available, in one volume, all Dr. Pagano's major technical papers. Most of the papers included in this volume have been published in the open literature, but there are a few exceptions -- a few key, unpublished reports have been included for continuity. The topics are: some basic studies of anisotropic behavior, exact solutions for elastic response, role of micromechanics, and some carbon--carbon spinoffs. The volume can be used as a reference book by researchers in academia, industry, and government laboratories, and it can be used as a reference text for a graduate course on the mechanics of composite materials.

From July 10th through July 13th, 1994, an informal workshop co-organized by RILEM committees 116-PCD and 123-MME was held at Saint-Remy-Ies Chevreuse, France, and attended by 38 delegates from 16 countries. Twenty-nine papers were presented, converging the general subjects of modelling micro structures and predicting durability of concrete and other cement-based materials. A short summary follows: G. M. Idom's paper entitled "Modelling Research for Concrete Engineering" serves as an introduction to the workshop, presenting an overview of modelling research with the conelusion that the broad practica1 objective is to produce high-quality concrete. This means that many characteristics, ranging from rheology to alkali-silica reaction, must be modelled. In other words, the system must be understood. Idom's paper sets the stage for papers in two general areas: 1) models and 2) transport properties. After this, abrief survey of the develop ment of microstructurally-based models is presented. A elose relationship between computer power and speed is suggested. The first group of papers on models covers the subjects of scale and resolution. Most models define and predict characteristics of the pore system, which range in scale from nanometer to millimeter. Various types ofnetworks are proposed in these papers. A good microstructural model must describe the pores and other phases at ascale appropriate to the properties that the model predicts. Also, a good model should be based on fundamental knowledge. In the case of cement-based materials, the important properties may depend on the microstructure, especially the porosity, at several scales."

Recent years have witnessed a rapid development of active control of various mechanical systems. With increasingly strict requirements for control speed and system performance, the unavoidable time delays in both controllers and actuators have become a serious problem. For instance, all digital controllers, analogue anti aliasing and reconstruction filters exhibit a certain time delay during operation, and the hydraulic actuators and human being interaction usually show even more significant time delays. These time delays, albeit very short in most cases, often deteriorate the control performance or even cause the instability of the system, be cause the actuators may feed energy at the moment when the system does not need it. Thus, the effect of time delays on the system performance has drawn much at tention in the design of robots, active vehicle suspensions, active tendons for tall buildings, as well as the controlled vibro-impact systems. On the other hand, the properly designed delay control may improve the performance of dynamic sys tems. For instance, the delayed state feedback has found its applications to the design of dynamic absorbers, the linearization of nonlinear systems, the control of chaotic oscillators, etc. Most controlled mechanical systems with time delays can be modeled as the dynamic systems described by a set of ordinary differential equations with time delays."

This monograph contains the results of my research in the area of asymmet- ric theory of elasticity, conducted from 1969 to 1986 under the direction of PROFESSOR WITOLD NOWACKI. I am indebted to PROFESSOR NOWACKI, thanks to whose invaluable and very kind research assistance I obtained the results which were the foundation of this monograph. Therefore, I would like to express my deepest gratitude to him and honour his memory. He will remain in my thoughts with due respect. During my research assistantship at the Institute of Mechanics at the Uni- versity of Warsaw in 1970-1973 I had the opportunity to participate in sem- inars and conferences, study critical reviews and carryon numerous discus- sions and conversations. All this resulted in many valuable remarks included in this monograph. In this connection, I would like to thank Professor J6zef Ignaczak and Professor Marek Sokolowski from the Institute of Fundamental Problems of Technology at the Polish Academy of Sciences, as well as Pro- fessor Zbigniew Olesiak and Professor Adam Piskorek from the Institute of Mechanics at the University of Warsaw.

The classical, phenomenological theory of plastically anisotropic materials has passed a long way: from the work of von Mises presented in 1928, and the HilI formulation given in 1948, to the latest papers on large elastic-plastic deformations of anisotropic metal sheets. A characteristic feature of this approach is a linear flow rule and a quadratic yield criterion. Mathematical simplicity of the theory is a reason of its numerous applications to the analysis of engineering structures during the onset of plastic deformations. However, such an approach is not sufficient for description of the metal forming processes, when a metal element undergoes very large plastic strains. If we take an initially isotropic piece of metal, it becomes plastically anisotropic during the forming process, and the induced anisotropy progressively increases. This fact strongly determines directions of plastic flow, and it leads to an unexpected strain localization in sheet elements. To explain the above, it is necessary to take into account a polycrystalline structure of the metal, plastic slips on slip systems of grains, crystallographic lattice rotations, and at last, a formation of textures and their evolution during the whole deformation process. In short, it is necessary to introduce the plasticity of crystals and polycrystals. The polycrystal analysis shows that, when the advanced plastic strains take place, some privileged crystallographic directions, called a crystallographic texture, occur in the material. The texture formation and evolution are a primary reason for the induced plastic anisotropy in pure metals.

Three subjects of major interest in one textbook: linear elasticity, mechanics of structures in linear isotropic elasticity, and nonlinear mechanics including computational algorithms. After the simplest possible, intuitive approach there follows the mathematical formulation and analysis, with computational methods occupying a good portion of the book. There are several worked-out problems in each chapter and additional exercises at the end of the book, plus mathematical expressions are bery often given in more than one notation. The book is intended primarily for students and practising engineers in mechanical and civil engineering, although students and experts from applied mathematics, materials science and other related fields will also find it useful.

Have you ever wondered where the safety factors come from? Why is it that deterministic analysis has reached a very sophisticated level, but in the end empirical factors are still needed? Is there a way to select them, rather than assigning them arbitrarily as is often done? This book clearly shows that safety factors are closely related with the reliability of structures, giving yet another demonstration of Albert Einstein's maxim that "It is incomprehensible that Nature is comprehensible." The book shows that the safety factors are much more comprehensible if they are seen in a probabilistic context. Several definitions of the safety factors are given, analytical results on insightful numbers are presented, nonprobabilistic safety factors are shown, as well as their estimates derived by the inequalities of Bienayme, Markov, Chebushev and Camp-Meidell. A special chapter is devoted to important contributions by Japanese experts. This volume will help to critically re-think the issue of safety factors, which can create a false feeling of security. The deterministic paradigm can be enhanced by incorporating probabilistic concepts wisely where they are needed without treating all variables as probabilistic ones. The book shows that there is a need of their integration rather than separation. This book is intended for engineers, graduate students, lecturers and researchers.

The field of composite materials has seen substantial development in the past decade, New composite systems are being continually developed for various applications. Among such systems are metal, intermetallic, and superalloy matrix composites, carbon-carbon composites as well as polymer matrix composites. At the same time, a new discipline has emerged of active or smart materials, which are often constructed as composite or heterogeneous media and structures. One unifying theme in these diverse systems is the influence that uncoupled and coupled eigenfields or transformation fields exert on the various types of overall response, as well as on the respective phase responses. Problems of this kind are currently considered by different groups which may not always appreciate the similarities of the problems involved. The purpose of the IUTAM Symposium on Transformation Problems in Composite and Active Materials held in Cairo, Egypt from March 10 to 12, 1997 was to bring together representatives of the different groups so that they may interact and explore common aspects of these seemingly different problem areas. New directions in micromechanics research in both composite and active materials were also explored in the symposium. Specifically, invited lectures in the areas of inelastic behavior of composite materials, shape memory effects, functionally graded materials, transformation problems in composite structures, and adaptive structures were delivered and discussed during the three-day meeting. This book contains the printed contributions to the IUTAM Symposium.

High-speed impact dynamics is of interest in the fundamental sciences, e.g., astrophysics and space sciences, and has a number of important applications in military technologies, homeland security and engineering. When compared with experiments or numerical simulations, analytical approaches in impact mechanics only seldom yield useful results. However, when successful, analytical approaches allow us to determine general laws that are not only important in themselves but also serve as benchmarks for subsequent numerical simulations and experiments. The main goal of this monograph is to demonstrate the potential and effectiveness of analytical methods in applied high-speed penetration mechanics for two classes of problem. The first class of problem is shape optimization of impactors penetrating into ductile, concrete and some composite media. The second class of problem comprises investigation of ballistic properties and optimization of multi-layered shields, including spaced and two-component ceramic shields. Despite the massive use of mathematical techniques, the obtained results have a clear engineering meaning and are presented in an easy-to-use form. One of the chapters is devoted solely to some common approximate models, and this is the first time that a comprehensive description of the localized impactor/medium interaction approach is given. In the monograph the authors present systematically their theoretical results in the field of high-speed impact dynamics obtained during the last decade which only partially appeared in scientific journals and conferences proceedings.

The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

This volume contains the edited versions of papers presented at the IUTAM-Symposium Topological design optimization of structures, machines and materials - status and perspectives, held at Rungstedgaard, near Copenhagen, Denmark, in October 2005. The Symposium was attended by scientists in mechanics, optics, and applied mathematics from 19 countries.

It is now more than 15 years ago that the so-called homogenization method was proposed as a basis for computational means to optimize the topology and shape of continuum structures. From initially being capable mainly of treating minimum compliance design we now see the basic material distribution idea of the methodology applied to a wide range of structural and mechanical problems as well as to problems that couple structural response to other physical responses. Also, the method has provided insight for micro-mechanical studies, meaning that the method has given feedback to the area which provided impetus to the field of topological design optimization in its creation. Finally, topological design is now an integral part of most FEM software systems and it has become a standard industrial tool in some fields.

The IUTAM Symposium provided a forum for the exchange of ideas for future developments in the area of topological design optimization. This encompassed the application to fluid-solid interaction problems, acoustics problems, and to problems in biomechanics, as well as to other multiphysics problems. New basic modelling paradigms, covering new geometry modelling such as level-set methods and topological derivatives, as well as developments in computational approaches were also focus areas.

This book describes the state of the art of our understanding of liquid-crystal interfaces on a molecular level. The interactions of liquid crystal molecules with a surface play an essential role in the operation of liquid crystal displays (LCD's) and other LC devices that are based on the controllable anchoring of LC molecules on polymer coated surfaces.

This book addresses the microscopic interaction between a macromolecule (liquid crystal, polymer) and a wall, using state of the art surface and interface-sensitive experimental techniques, such as Atomic Force Microscopy (AFM), Scanning Tunneling Microscopy (STM), Linear and Nonlinear Optical Microscopy and (Dynamic) Light Scattering (DLS). These experimental techniques were complemented with computer simulations and supra molecular chemistry methods to develop controllable polymeric surfaces.