This book presents new ideas in the framework of novel, finite element discretization schemes for solids and structure, focusing on the mechanical as well as the mathematical background. It also explores the implementation and automation aspects of these technologies. Furthermore, the authors highlight recent developments in mixed finite element formulations in solid mechanics as well as novel techniques for flexible structures at finite deformations. The book also describes automation processes and the application of automatic differentiation technique, including characteristic problems, automatic code generation and code optimization. The combination of these approaches leads to highly efficient numerical codes, which are fundamental for reliable simulations of complicated engineering problems. These techniques are used in a wide range of applications from elasticity, viscoelasticity, plasticity, and viscoplasticity in classical engineering disciplines, such as civil and mechanical engineering, as well as in modern branches like biomechanics and multiphysics.

High resolution upwind and centered methods are a mature generation of computational techniques. They are applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. For its third edition the book has been thoroughly revised to contain new material.

Differential equations are often used in mathematical models for technological processes or devices. However, the design of a differential mathematical model is crucial and difficult in engineering. As a hands-on approach to learn how to pose a differential mathematical model the authors have selected 9 examples with important practical application and treat them as following: - Problem-setting and physical model formulation - Designing the differential mathematical model - Integration of the differential equations - Visualization of results Each step of the development of a differential model is enriched by respective Mathcad 11 commands, todays necessary linkage of engineering significance and high computing complexity. To support readers of the book with respect to changes that might occur in future versions of Mathcad (Mathcad 12 for example), updates of examples, codes etc. can be downloaded from the following web page www.thermal.ru. Readers can work with Mathcad-sheets of the book without any Mathcad by help Mathcad Application Server Technology.

Offers an eye-opening and revealing look into an interpersonal/scientific conflict involving the 'Father of Modern Soil Mechanics' Karl von Terzaghi.

Exemplifies the 'human side' of science in which, sometimes, the prominence of a theorist and the inertia of the 'accepted wisdom' can inhibit progress and rational discussion of the facts.

More than 100 illustrations combine with historical details in the text to evoke a vivid picture of the lost era of pre-WWII Vienna.

The book focuses on the fluid dynamics of cavitation with special reference to high power density turbopumps, where it represents the major source of performance and life degradation. While covering the more fundamental aspects of cavitation and the main kinds of cavitating flows, there is focus on the hydrodynamics and instabilities of cavitating turbopumps. The book also illustrates the alternative approaches for modeling and engineering simulation of cavitating flows.

Microscale Diagnostic Techniques highlights the most innovative and powerful developments in microscale diagnostics. It provides a resource for scientists and researchers interested in learning about the techniques themselves, including their capabilities and limitations. The fields of Micro- and Nanotechnology have emerged over the past decade as a major focus of modern scientific and engineering research and technology. Driven by advances in microfabrication, the investigation, manipulation and engineering of systems characterized by micrometer and, more recently, nanometer scales have become commonplace throughout all technical disciplines. With these developments, an entirely new collection of experimental techniques has been developed to explore and characterize such systems.

The articles in this book describe new developments in the area of structural testing, particularly those based upon the principle of fusing numerical and experimental methods such as real-time dynamic substructuring and hardware-in-the loop testing. In addition to the hybrid methods, chapters on the latest develoments in more established techniques, such as shaking table testing, provide a completely up-to-date survey of structural testing methods.

The book is characterized by a multidisciplinary nature of the work that integrates cutting-edge research from the fields of non-linear dynamics, automatic control, numerical analysis, system modelling and mechatronics.

Shock waves in multiphase flows refers to a rich variety of phenomena of interest to physicists, chemists, and fluid dynamicists, as well as mechanical, biomedical and aeronautical engineers. This volume treats shock and expansion waves in: - complex, bubbly liquids (L. van Wijngaarden, Y. Tomita, V. Kedrinskii) and - cryogenic liquids (M. Murakami) and examines the relationship of shock waves with - phase transitions (A. Guha, C.F. Delale, G. Schnerr, M.E.H. van Dongen) - induced phase transitions (G.E.A. Meier) as well as their interaction with - solid foams, textiles, porous and granular media (B. Skews, D.M.J. Smeulders, M.E.H. van Dongen, V. Golub, O. Mirova).

All chapters are self-contained, so they can be read independently, although they are of course thematically interrelated. Taken together, they offer a timely reference on shock waves in multiphase flows, including new viewpoints and burgeoning developments. The book will appeal to beginners as well as professional scientists and engineers.

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.

This book presents a unified hierarchical formulation of theories for three-dimensional continua, two-dimensional shells, one-dimensional rods, and zero-dimensional points. It allows readers with varying backgrounds easy access to fundamental understanding of these powerful Cosserat theories.

Written by one of the world's leading authorities on plate behavior, this study gives a clear physical insight into elastic plate behavior. Small-deflection theory is treated in Part 1 in chapters dealing with basic equations: including thermal effects and multi-layered anisotropic plates, rectangular plates, circular and other shaped plates, plates whose boundaries are amenable to conformal transformation, plates with variable thickness, and approximate methods. Large-deflection theory is treated in Part 2 in chapters dealing with basic equations and exact solutions; approximate methods, including post-buckling behavior; and asymptotic theories for very thin plates, including tension field theory and inextensional theory. The mathematical content is necessarily high, making the style of the book appropriate to engineers and applied mathematicians. E.H. Mansfield is a Fellow of the Royal Society, a founder member of the Fellowship of Engineering, and the author of over 100 publications.

Inelastic Analysis of Solids and Structures presents in a unified manner the physical and theoretical background of inelastic material models and computational methods, and illustrates the behavior of the models in typical engineering conditions. The book describes experimental observations and principles of mechanics, and efficient computational algorithms for stress calculations as typically performed in finite element analysis. The theoretical background is given to an extent necessary to describe the commonly employed material models in metal isotropic and orthotropic plasticity, thermoplasticity and viscoplasticity, and the plasticity of geological materials. The computational algorithms are developed in a unified manner with some detailed derivations of the algorithmic relations. Many solved examples are presented, which are designed to give insight into the material behavior in various engineering conditions, and to demonstrate the application of the computational algorithms.

This book offers an easy to read, all-embracing history of thermodynamics. It describes the long development of thermodynamics, from the misunderstood and misinterpreted to the conceptually simple and extremely useful theory that we know today. Coverage identifies not only the famous physicists who developed the field, but also engineers and scientists from other disciplines who helped in the development and spread of thermodynamics as well.

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.

Providing a basic foundation for advanced graduate study and research in the mechanics of solids, this 2004 treatise contains a systematic development of the fundamentals of finite inelastic deformations of heterogeneous materials. The book combines the mathematical rigour of solid mechanics with the physics-based micro-structural understanding of the material science, to present a coherent picture of finite inelastic deformation of single and polycrystalline metals, over broad ranges of strain rates and temperatures. It also includes a similarly rigourous and experimentally based development of the quasi-static deformation of cohesionless granular materials that support the applied loads through contact friction. Every effort has been made to provide a thorough treatment of the subject, rendering the book accessible to students in solid mechanics and in the mechanics of materials. This book integrates rigourous mathematical description of finite deformations seamlessly with mechanisms based on micromechanics in order to produce useful results with relevance to practical problems.

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.

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.

The reciprocity theorem has been used for over 100 years to establish interesting and useful relationships and to formulate problems. Internationally distinguished for his contributions to mechanics, Jan Achenbach presents a novel method of solving wave fields. The material presented here is relevant to applications in engineering and applied physics such as ultrasonics for medical imaging and non-destructive evaluation, acoustic microscopy, seismology, exploratory geophysics, and structural acoustics.

This book covers statics and dynamics to provide the student with everything needed to complete typical first-year undergraduate courses. Although students often find it difficult to visualize problems and grasp the mathematics, Adrian Roberts' approach tackles concepts with many examples, exercises and helpful diagrams. A key section on background mathematics allows students to review the prerequisite mathematics needed to progress through both topics.