In the pages of this present monograph readers will find virtually everything they need to know about the latest advanced materials. The authors have covered almost every angle, including composites, functionally graded materials, and materials for high temperature service. They also examine advanced approaches to local and non-local analysis of localized damage, and provide a new description of crack deactivation. This highly informative volume also tackles the material properties for high temperature applications.

This book provides a solid introduction to the foundation and the application of the finite element method in structural analysis. It offers new theoretical insight and practical advice. This second edition contains additional sections on sensitivity analysis, on retrofitting structures, on the Generalized FEM (X-FEM) and on model adaptivity. An additional chapter treats the boundary element method, and related software is available at www.winfem.de.

The last two decades have brought two important developments for aeroth- modynamics. One is that airbreathing hypersonic flight became the topic of technology programmes and extended system studies. The other is the emergence and maturing of the discrete numerical methods of aerodyn- ics/aerothermodynamics complementary to the ground-simulation facilities, with the parallel enormous growth of computer power. Airbreathing hypersonic flight vehicles are, in contrast to aeroassisted re-entry vehicles, drag sensitive. They have, further, highly integrated lift and propulsion systems. This means that viscous eflFects, like boundary-layer development, laminar-turbulent transition, to a certain degree also strong interaction phenomena, are much more important for such vehicles than for re-entry vehicles. This holds also for the thermal state of the surface and thermal surface effects, concerning viscous and thermo-chemical phenomena (more important for re-entry vehicles) at and near the wall. The discrete numerical methods of aerodynamics/aerothermodynamics permit now - what was twenty years ago not imaginable - the simulation of high speed flows past real flight vehicle configurations with thermo-chemical and viscous effects, the description of the latter being still handicapped by in sufficient flow-physics models. The benefits of numerical simulation for flight vehicle design are enormous: much improved aerodynamic shape definition and optimization, provision of accurate and reliable aerodynamic data, and highly accurate determination of thermal and mechanical loads. Truly mul- disciplinary design and optimization methods regarding the layout of thermal protection systems, all kinds of aero-servoelasticity problems of the airframe, et cetera, begin now to emerge."

Simplified fracture mechanics based assessment methods are widely used by the industry to determine the structural integrity significance of postulated cracks, manufacturing flaws, service-induced cracking or suspected degradation of engineering components under normal and abnormal service loads. In many cases, welded joints are the regions most likely to contain original fabrication defects or cracks initiating and growing during service operation. Various procedures provide upper bound residual stress profiles for various classes of welded joints that can be used in fracture assessments, but these often give very conservative results. Recently, the option to use more realistic profiles has been adopted, but only where such profiles are based on finite element residual stress simulations supported by detailed residual stress measurements. Rapid advances in the capability of residual stress measurement techniques, such as the contour and deep hole drilling techniques as well as the neutron and synchrotron X-ray diffraction methods, now readily allow residual stresses and strains to be mapped on defined planes within a structure. The contents of this book have been grouped into three topic areas covering theoretical /numerical and experimental analyses of residual stress and its effects on fatigue and fracture.

To predict loading limits for structures and structural elements is one of the oldest and most important tasks of engineers. Among the theoretical and numericalmethodsavailableforthispurpose, so-called"DirectMethods,"- bracing Limit- and Shakedown Analysis, play an eminent role due to the fact that they allow rapid access to the requested information in mathematically constructive manners. The collection of papers in this book is the outcome of a workshop held at Aachen University of Technology in November 2007. The individual c- tributions stem in particular from the areas of new numerical developments renderingthemethodsmoreattractive forindustrialdesign, extensionsofthe general methodology to new horizons of application, probabilistic approaches and concrete technological applications. The papers are arranged according to the order of the presentations in the workshop and give an excellent insight into state-of-the-art developments in this broad and growing ?eld of research. The editors warmly thank all the scientists, who have contributed by their outstanding papers to the quality of this edition. Special thanks go to Jaan Simon for his great help in putting together the manuscript to its ?nal shape.

Thisbookisacollectionof31paperspresentedattheInternationalWorkshop on Modern Trends in Geomechanics, held on 27-29 June 2005 in Vienna. This workshop was run under the motto to bring together di?erent schools of thought in geomechanics research. The workshop was attended by about 50 participants from 15 countries. Besides the presentations, the workshop also o?ered welcoming occasions for stimulating discussions. The contributions in this book cover a wide range of topics from applied mathematics to geoengineering applications, re?ecting the breadth and depth of geomechanics research. The articles are peer reviewed and arranged in six parts: general aspects, constitutive modelling, micromechanics, analytical and numerical methods, granular materials and engineering applications. Wewouldliketothankallcontributorsfortheirdiligencetoprovidetimely their contributions. The generous support received from the following orga- zations is gratefully acknowledged: - Alpine Mayreder Construction Ltd - Bank Austria - Credit Institute - Austrian Geomechanics Society Our thanks also go to the managing editors at Springer, in particular Ms. Heather King and Dr. Thomas Ditzinger, who have enabled the qu- ity publication of this book at reasonable price. Last but not least, we would like to express our thanks to our co-workers in Vienna and Nottingham for theirhelpduringtheworkshop.Inparticular, oursecretaries, AnkePriewasser (Vienna) and Caroline Dolby (Nottingham), deserve our heartfelt thanks for their e?ort in organising the workshop and compiling this boo

Linear elliptic equations arise in several models describing various phenomena in the applied sciences, the most famous being the second order stationary heat eq- tion or,equivalently,the membraneequation. Forthis intensivelywell-studiedlinear problem there are two main lines of results. The ?rst line consists of existence and regularity results. Usually the solution exists and "gains two orders of differen- ation" with respect to the source term. The second line contains comparison type results, namely the property that a positive source term implies that the solution is positive under suitable side constraints such as homogeneous Dirichlet bou- ary conditions. This property is often also called positivity preserving or, simply, maximum principle. These kinds of results hold for general second order elliptic problems, see the books by Gilbarg-Trudinger [198] and Protter-Weinberger [347]. For linear higher order elliptic problems the existence and regularitytype results - main, as one may say, in their full generality whereas comparison type results may fail. Here and in the sequel "higher order" means order at least four. Most interesting models, however, are nonlinear. By now, the theory of second order elliptic problems is quite well developed for semilinear, quasilinear and even for some fully nonlinear problems. If one looks closely at the tools being used in the proofs, then one ?nds that many results bene?t in some way from the positivity preserving property. Techniques based on Harnack's inequality, De Giorgi-Nash- Moser's iteration, viscosity solutions etc.

Thisbookdealswith theclassicalkinetictheoryofgases.Itsaimisto present the basic principles of this theory within an elementary framework and from a more rigorous approach based on the Boltzmann equation. The subjects are presented in a self-contained manner such that the readers can und- stand and learn some methods used in the kinetic theory of gases in order to investigate the Boltzmann equation. In Chapter 1, a sketch on the evolution of the ideas of the kinetic theory is presented. Afterwards, the basic principles of an elementary kinetic theory areintroduced,which arebasedonthe concepts ofmean freepath, molecular mean velocity and mean free time. The Maxwellian distribution function is determinedfromstatisticalarguments,andthetransportcoe?cients ofshear viscosity, thermal conductivity and self-di?usion are obtained from the e- mentary theory. The most common interaction potentials used in the kinetic theory of gases are also introduced in this chapter, and the dynamics of a binary collision is analyzed. Chapter 2 is dedicated to the study of the Boltzmann equation. First, the BoltzmannequationisderivedandtheequationsoftheBBGKYhierarchyare determined.Fromtheknowledgeofthetransferequation-whichfollowsfrom theBoltzmannequation-themacroscopicbalanceequationsforthemoments ofthedistributionfunctionarederived. Theequilibriumdistributionfunction is determined from the Boltzmann equation and the equilibrium states of a rare?ed gas are also analyzed. In this chapter, theH-theorem and the paradoxes of Loschmidt and Zermelo are discussed. The chapter ends with an analysis of the di?erent forms of the entropy which are used in statistical mechanics to describe the canonical and microcanonical ensembles.

First published in 1987, this text offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton 's laws through Lagrange 's equations and Hamilton 's principle, to Hamilton 's equations and canonical transformations.

This new edition has been extensively revised and updated to include:

• A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations.
• A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles.
• A greater emphasis on the links to special relativity and quantum theory showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics.

A wealth of examples show the subject in action and a range of exercises with solutions are provided to help test understanding.

Polymer chains that interact with themselves and/or with their environment are fascinating objects, displaying a range of interesting physical and chemical phenomena. The focus in this monograph is on the mathematical description of some of these phenomena, with particular emphasis on phase transitions as a function of interaction parameters, associated critical behavior and space-time scaling. Topics include: self-repellent polymers, self-attracting polymers, polymers interacting with interfaces, charged polymers, copolymers near linear or random selective interfaces, polymers interacting with random substrate and directed polymers in random environment. Different techniques are exposed, including the method of local times, large deviations, the lace expansion, generating functions, the method of excursions, ergodic theory, partial annealing estimates, coarse-graining techniques and martingales. Thus, this monograph offers a mathematical panorama of polymer chains, which even today holds plenty of challenges.

The main motivation for this book lies in the breadth of applications in which a statistical model is used to represent small departures from, for example, a Poisson process. Our approach uses information geometry to provide a c- mon context but we need only rather elementary material from di?erential geometry, information theory and mathematical statistics. Introductory s- tions serve together to help those interested from the applications side in making use of our methods and results. We have available Mathematica no- books to perform many of the computations for those who wish to pursue their own calculations or developments. Some 44 years ago, the second author ?rst encountered, at about the same time, di?erential geometry via relativity from Weyl's book [209] during - dergraduate studies and information theory from Tribus [200, 201] via spatial statistical processes while working on research projects at Wiggins Teape - searchandDevelopmentLtd-cf. theForewordin[196]and[170,47,58]. H- ing started work there as a student laboratory assistant in 1959, this research environment engendered a recognition of the importance of international c- laboration, and a lifelong research interest in randomness and near-Poisson statistical geometric processes, persisting at various rates through a career mainly involved with global di?erential geometry. From correspondence in the 1960s with Gabriel Kron [4, 124, 125] on his Diakoptics, and with Kazuo Kondo who in?uenced the post-war Japanese schools of di?erential geometry and supervised Shun-ichi Amari's doctorate [6], it was clear that both had a much wider remit than traditionally pursued elsewhere.

There are a lot of textbooks for mechanics - why another one?
Because reading this book should be fun - but as a side effect the reader should also learn the basics of mechanics without suffering to much Or to say it more officially: The scope of the textbook is to teach mechanics by means of simple examples from everyday life instead of sophisticated scientific approaches. The examples, supported by a lot of cartoons, should help to learn by associations and practical experiences. Many exercises with solutions garanty to pass exams successfully. A similar book has not existed before - the terms "mechanics" and "fun" have always been contradictious. Besides students from the disciplines of mechanical or electrical engineering, civil engineering, physics, and chemistry also practitioners will enjoy reading this book.

Liquid crystals are fluids with a directionality defined. Polymers are long molecules with a shape that can be changed. As a network, polymers form rubber - a soft solid that is locally liquid-like and capable of huge extension. Liquid crystal elastomers are a combination of all these curious aspects, but with additional, revolutionary new phenomena - for example, spontaneous shape changes of several hundred percent induced by temperature change, with equally large opto-mechanical responses, shape change without energy cost ("soft elasticity"), colour change with strain, lasing and photonics, sensitivity to molecular handedness and soft solid ferroelectricity. This book is a primer for liquid crystals, polymers, rubber, and elasticity. It then describes the theory and experiment of these remarkable materials for the first time as a monograph. Worked examples are solved so that the reader can become proficient in the field himself. The book is directed at physicists, chemists, material scientists, engineers and applied mathematicians at the graduate student level and beyond

This book collects 42 peer-reviewed papers presented in the NATO Advanced Research Workshop on Nanostructured Materials by High-Pressure Severe Plastic Deformation, held in Donetsk, Ukraine, September 22-24, 2004.

Recently, it was reported that nanostructured materials processed under high pressure by HPT and ECAP have an extraordinary combination of both high strength and high ductility, which are two desirable, but rarely co-existing properties. These findings indicate that high-pressure is a critical factor that can be employed to process nanostructured materials with superior mechanical, and possibly also physical, properties. It is the objective of this workshop to review our current knowledge, identify issues for future research, and discuss future directions on the processing and properties of nanostructured materials via SPD techniques, with a special emphasis on high-pressure effects.

During the 3-day workshop, about 60 scientists from 12 countries presented 60 papers. Over 20 keynote presentations were given by distinguished scientists in this field. Papers in this book cover areas of high pressure effect on the nanostructure and properties of SPD-processed materials, fundamentals of nanostructured materials, development of high-pressure SPD technologies for commercializations, recent advances of SPD technologies as well as applications and future markets of SPD-processed nanostructured materials

Thebookoffersaselectionofpapersmostofwhicharerevisedandenrichedversions of the contributions presented at the 12th Symposium on Trends of Applications of Mathematics to Mechanics (STAMM) which was sponsored by the International - ciety for the Interaction between Mathematics and Mechanics (ISIMM) and held in Maiori (Salerno), Italy, from September 29th to October 4th, 2002. The Symposium attracted leading researchers from around the world who are working at the interface between mathematics and mechanics. The importance of a close link between these two disciplines has long been recognized; each bene?ts from and is stimulated by open problems, methods and results emerging from the other. The book comp- ses 22 papers which report specialized investigations and which contribute broader presentations of linear and nonlinear problems. It is with the deepest gratitude to the authors who have contributed to the volume and to the publisher, for its highly professional assistance, that the editors submit this book to the international mathematics and mechanics communities. The editors gratefully acknowledge the ?nancial support of the following institutions: Gruppo NazionalediFisicaMatematica(GNFM)oftheIstitutoNazionalediAltaMatematica (INDAM), Universita ' degli Studi di Napoli Federico II and Regione Campania.

This book presents the most recents developments in the modelling of degradations (of thermo-chemo-mechanical origin) and of bifurcations and instabilities (leading to localized or diffuse failure modes) taking place in geomaterials (soils, rocks, concrete). Applications (landslides, rockfalls, debris flows, concrete and rock ageing, etc.) are discussed in detail.

Although several books and conference proceedings have already appeared dealing with either the mathematical aspects or applications of homogenization theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at the NATO Advanced Workshop on Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials. The list of thirty one contributed papers is also appended.

The key lectures cover both fundamental, mathematical aspects of homogenization, including nonconvex and stochastic problems, as well as several applications in micromechanics, thin films, smart materials, and structural and topology optimization. One lecture deals with a topic important for nanomaterials: the passage from discrete to continuum problems by using nonlinear homogenization methods. Some papers reveal the role of parameterized or Young measures in description of microstructures and in optimal design. Other papers deal with recently developed methods-both analytical and computational-for estimating the effective behavior and field fluctuations in composites and polycrystals with nonlinear constitutive behavior.

All in all, the volume offers a cross-section of current activity in nonlinear homogenization including a broad range of physical and engineering applications. The careful reader will be able to identify challenging open problems in this still evolving field. For instance, there is the need to improve bounding techniques fornonconvex problems, as well as for solving geometrically nonlinear optimum shape-design problems, using relaxation and homogenization methods.

* Comprehensive textbook/reference applies mathematical methods and modern symbolic computational tools to anisotropic elasticity

* Presents unified approach to a vast diversity of structural models

* State-of-the-art solutions are provided for a wide range of composite material configurations, including: 3-D anisotropic bodies, 2-D anisotropic plates, laminated and thin-walled structures

This book focuses on the mechanical response in viscoelastic media under isothermal and nonisothermal conditions. The viscoelastic response covered in this book is observed in a wide variety of common materials: polymers and plastics, metals and alloys at elevated temperatures, concrete, soils, road construction and building materials, biological tissues, and foodstuffs. Emphasizing the mechanical behavior of solid polymers subjected to physical aging, the book analyzes constitutive equations in thermoviscoelasticity and compares the results of numerical simulation with experimental data. After covering linear viscoelastic media at small strains, a clear approach to nonlinear constitutive equations in viscoelasticity at small strains and at finite strains is developed. The book concludes with coverage of constitutive relations in thermoviscoelasticity which account for thermally-induced changes both in elastic moduli and relaxation spectra. Written for specialists in mechanical and chemical engineering in the fields of manufacturing polymer and polymer-composite articles, this book will also appeal to specialists in applied and industrial mathematics, mechanics of continua and polymer physics who study the response of solid polymers to thermomechanical stimuli.

The significant increase in the use of composite materials in all phases of structures, from spacecraft to marine vessels, from bridges and domes on civil buildings to sporting goods, has called for the development of rigorous mathematical methods capable of modelling, designing and optimizing composites under any given set of conditions. This book provides solutions to many problems in the analysis of the effective and local properties of composite structures, as well as to problems of their design and optimization on account of strength, stiffness and weight minimization requirements. The numerous results are presented in the form of analytical formulas or numerical algorithms. Programs providing numerical solutions to many engineering analysis, design and optimization problems for the composite and reinforced structures, including fibre-reinforced materials, laminated and angle-ply shells and plates, ribbed, wafer and honeycomb-like composite shells and plates, are available on the Internet

Stochastic Processes and Random Vibrations Theory and Practice JAlA-us SA3lnes University of Iceland, ReykjavA-k, Iceland This book covers the fundamental theory of stochastic processes for analysing mechanical and structural systems subject to random excitation, and also for treating random signals of a general nature with special emphasis on earthquakes and turbulent winds. Starting with basic probability calculus and the fundamental theory of stochastic processes, the author progresses onto engineering applications: systems analysis and treatment of random signals. The random excitation and response of simple mechanical systems and complex structural systems is discussed in some detail. Extreme conditions such as distribution of large vibration peaks, random excursions above certain limits and mechanical failure due to fatigue are then addressed. The text also offers a discussion of some well-known stochastic models and an introduction to signal processing and digital filters. Numerous worked examples are included: distribution of extreme wind speeds, analysis of structural reliability, earthquake response of a tall multi-storey structure, wind loading of tall towers, generation of random earthquake signals and earthquake risk analysis.

Corrosion affects every industry in which metal is involved, from manufacturing machinery to transport pipelines, and it is estimated to cost the global economy trillions of dollars per year. Many of the traditional methods for inhibiting corrosion are highly toxic (such as hexavalent chromium) or do not degrade readily in the environment (such as Benzotriazole) meaning they pose a risk to human and environmental health. Much recent work in the area has gone into searching for greener alternatives that will be both safe and effective. Beginning with a look at the fundamentals of corrosion inhibition and an explanation of the concepts of green chemistry, this book discusses various types of chemical that have been tested for their potential as greener corrosion inhibitors with reference to industrial applications. Green Corrosion Inhibition is a valuable reference for chemists and chemical engineers working in both research and design and academia who want to learn more about green corrosion inhibitors, their synthesis, design, and industrial scale applications.

This text provides the fundamental background in mechanics, materials, and numerical analysis necessary to understand the principles of metal forming and its analysis. Using a unified approach, the authors bridge traditional gaps between forming practitioners, manufacturing engineers, materials scientists, and mechanicians, to give readers a complete picture of the dynamic field of modern metal forming.

In this new edition, the fundamental material on classical linear aeroelasticity has been revised. Also new material has been added describing recent results on the research frontiers dealing with nonlinear aeroelasticity as well as major advances in the modelling of unsteady aerodynamic flows using the methods of computational fluid dynamics and reduced order modeling techniques. New chapters on aeroelasticity in turbomachinery and aeroelasticity and the latter chapters for a more advanced course, a graduate seminar or as a reference source for an entr e to the research literature.

This book deals with the safety assessment of structures and structural components, possibly operating beyond the elastic limits under variable repeated thermo-mechanical loads. Examples of such situations can be found both in mechanical and civil engineering (e.g. transportation technologies, pressure vessels, pipelines, offshore platforms, dams, pavements and buildings in seismic zones). So-called "direct" methods are focused, based on the shakedown theorems and their specialisation to limit theorems. These methods are receiving increased attention for the prediction of structural failure because they provide the information that is essential in practice (e.g. safety factor and collapse mechanisms) by more economical procedures than step-by-step inelastic analysis; also, they only need a minimum of information on the evolution of loads as functions of time. The addressed audience are primarily engineers and scientists active in Structural Engineering and Safety and Reliability Analysis.