This volume contains thirteen articles on advances in applied mathematics and computing methods for engineering problems. Six papers are on optimization methods and algorithms with emphasis on problems with multiple criteria; four articles are on numerical methods for applied problems modeled with nonlinear PDEs; two contributions are on abstract estimates for error analysis; finally one paper deals with rare events in the context of uncertainty quantification. Applications include aerospace, glaciology and nonlinear elasticity.

Hereinis a selection of contributions from speakers at two conferences on applied mathematics held in June 2012 at the University of Jyvaskyla, Finland. The first conference, Optimization and PDEs with Industrial Applications celebrated the seventieth birthday of Professor Jacques Periaux of theUniversity of Jyvaskyla and Polytechnic University of Catalonia (Barcelona Tech) and the second conference, Optimization and PDEs with Applications celebrated the seventy-fifth birthday of Professor Roland Glowinski of the University of Houston.

This work should be of interest to researchers and practitioners as well as advanced students or engineers in computational and applied mathematics or mechanics."

This book examines pedestrian shoe-floor slip resistance from an engineering standpoint in order to better understand friction and wear behavior. This analysis includes an extensive investigation into the surface properties of shoes and flow, and the measurement of dynamic friction and other mechanical and physical aspects of shoe-floor tribology. Lastly, the book proposes a measurement concept for the identification and classification of operational floor surfaces under a range of different conditions. Novel techniques and methods are proposed that can improve the reliability of slip resistance assessments. The current state of knowledge is critically examined and discussed from a tribological perspective, including aspects like friction, wear, lubrication and the mechanical behavior of shoes, floors and their wider environment. Further, the book reports on extensive experimental investigations into the topographical characteristics of shoe and floor surfaces and how they affect slip resistance. Slips resulting in pedestrian falls are a major cause of injuries and deaths for all age groups. This important book provides essential insights for researchers, practicing engineers and public safety officials wishing to learn about how the risk of pedestrian slips can be assessed and understood.

This comprehensive treatise covers in detail practical methods of analysis as well as advanced mathematical models for structures highly sensitive to creep and shrinkage. Effective computational algorithms for century-long creep effects in structures, moisture diffusion and high temperature effects are presented. The main design codes and recommendations (including RILEM B3 and B4) are critically compared. Statistical uncertainty of century-long predictions is analyzed and its reduction by extrapolation is discussed, with emphasis on updating based on short-time tests and on long-term measurements on existing structures. Testing methods and the statistics of large randomly collected databases are critically appraised and improvements of predictions of multi-decade relaxation of prestressing steel, cyclic creep in bridges, cracking damage, etc., are demonstrated. Important research directions, such as nanomechanical and probabilistic modeling, are identified, and the need for separating the long-lasting autogenous shrinkage of modern concretes from the creep and drying shrinkage data and introducing it into practical prediction models is emphasized. All the results are derived mathematically and justified as much as possible by extensive test data. The theoretical background in linear viscoelasticity with aging is covered in detail. The didactic style makes the book suitable as a textbook. Everything is properly explained, step by step, with a wealth of application examples as well as simple illustrations of the basic phenomena which could alternate as homeworks or exams. The book is of interest to practicing engineers, researchers, educators and graduate students.

Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). Among the special applications addressed in this second volume are: stability of motion, nonlinear oscillations, dynamics and statics of the Stewart platform, mechanics under random forces, elements of control theory, relations between nonholonomic mechanics and the control theory, vibration and autobalancing of rotor systems, physical theory of impact, statics and dynamics of a thin rod. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.

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

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

The essential aim of the present book is to consider a wide set of problems arising in the mathematical modelling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities, and the transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems. Important new results concern contact problems with friction. The Coulomb friction law and some others are considered, in which relative sliding velocities appear.

This book is the authors' crowning achievement. In particular, it comprises the problems contained in the three books, together with detailed solutions and explanations. Thus, Part I (Chapters 1--12) is related to the book "The Mathematical Theory of Elasticity," Part II (Chapters 13--21) covers the problems in the book "Thermal Stresses," and Part III (Chapters 22--26) covers problems in the book "Thermal Stresses - Advanced Theory and Applications." The three parts are augmented by Part IV (Chapters 27--29), Numerical Methods, that covers three important topics: Method of Characteristics, Finite Element Method for Coupled Thermoelasticity, and Boundary Element Method for Coupled Thermoelasticity. As Part IV is independent of the earlier parts, it may be studied separately. The book is an indispensable companion to all who study any of the three books listed above, and should also be of importance to those interested in the topics covered in Part IV. It contains not only the problems and their careful and often extensive solutions, but also explanations in the form of introductions that appear at the beginning of chapters in Parts I, II and III. Therefore, this book links the three listed books into one comprehensive entity consisting of four publications.

The volume is devoted to the dynamics of rods, which is a branch of mech- ics of deformable bodies. The main goal of the book is to present systema- cally theoretical fundamentals of the mechanics of rods as well as numerical methods used for practical purposes. Linear and nonlinear equations governing a rod's oscillations are p- sented. Methods of determining eigenvalues and eigenfunctions in conser- tive and non-conservative problems along with numerical methods dealing with forced, parametric, and random oscillations of rods are given. Some - sues of interaction of rods with air (liquid) flows and the dynamics of spa- curved rods containing flows of liquid are considered. The book consists of nine chapters and appendices and may be conv- tionally divided into two parts. That is, Chapters 1 to 6 contain, in the main, theoretical material, whereas Chapters 7 to 9 illustrate the application of the theoretical results to problems of practical interest. Problems for self-study are found in Chapters 3, 5, and 7. The solutions to most of the problems are given in Appendix B. The monograph is addressed to undergraduate and postgraduate students and teaching staff of technical universities. It may also be useful for scientists and mechanical engineers working in a wide range of industries. I wish to express my deep appreciation to my colleagues, Dr. S.A. Voronov and C.B. Danilenko, for their help in preparing the manuscript.

This book presents an introduction to viscoelasticity; in particular, to the theories of dilute polymer solutions and dilute suspensions of rigid particles in viscous and incompressible fluids. These theories are important, not just because they apply to practical problems of industrial interest, but because they form a solid theoretical base upon which mathematical techniques can be built, from which more complex theories can be constructed, to better mimic material behaviour. The emphasis is not on the voluminous current topical research, but on the necessary tools to understand viscoelasticity at a first year graduate level. The main aim is to provide a still compact book, sufficient at the level of first year graduate course for those who wish to understand viscoelasticity and to embark in modeling of viscoelastic multiphase fluids. To this end, a new chapter on Dissipative Particle Dynamics (DPD) was introduced which is relevant to model complex-structured fluids. All the basic ideas in DPD are reviewed, with some sample problems to illustrate the methodology.

Despite the apparent activity in the field, the ever increasing rate of development of new engineering materials required to meet advanced technological needs poses fresh challenges in the field of constitutive modelling. The complex behaviour of such materials demands a closer interaction between numerical analysts and material scientists in order to produce thermodynamically consistent models which provide a response in keeping with fundamental micromechanical principles and experimental observations. This necessity for collaboration is further highlighted by the continuing remarkable developments in computer hardware which makes the numerical simulation of complex deformation responses increasingly possible.

This book contains 14 invited contributions written by distinguished authors who participated in the VIII International Conference on Computational Plasticity held at CIMNE/UPC (www.cimne.com) from 5-8 September 2005, Barcelona, Spain. The meeting was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS, www.eccomas.org).

The different chapters of this book present recent progress and future research directions in the field of computational plasticity. A common line of many contributions is that a stronger interaction between the phenomenological and micromechanical modelling of plasticity behaviour is apparent and the use of inverse identification techniques is also more prominent. The development of adaptive strategies for plasticity problems continues to be a challenging goal, while it is interesting to note the permanence of element modelling as a research issue. Industrial forming processes, geomechanics, steel and concrete structures form the core of the applications of the different numerical methods presented in the book.

This second edition of the textbook presents a systematic introduction to the structural mechanics of composite components. The book focusses on modeling and calculation of sandwiches and laminated composites i.e. anisotropic material. The new edition includes an additional chapter covering the latest advances in both research and applications, which are highly relevant for readers. The textbook is written for use not only in engineering curricula of aerospace, civil and mechanical engineering, but also for materials science and applied mechanics. Furthermore, it addresses practicing engineers and researchers. No prior knowledge of composite materials and structures is required for the understanding of its content. The book is close to classical courses of "Strength of Materials" and "Theory of Beams, Plates and Shells" but it extends the classic content on two topics: the linear elastic material behavior of isotropic and non-isotropic structural elements, and inhomogeneous material properties in the thickness direction. The Finite Element Analysis of laminate and sandwich structures is briefly presented. Many solved examples illustrate the application of the techniques learned.

This volume is dedicated to Jacob Aboudi, a ?ne scientist who has made seminal c- tributions in applied mechanics. The papers presented here re?ect the appreciation of many of Jacob's colleagues. A publication list f- lowing this introduction provides an indi- tion of his distinguished academic career, c- rently in its ?fth decade, and the breadth of hisknowledge. His papersconsistentlydem- strate originality, innovation and diligence. This list uncovers the methodical work of a dedicated researcher whose achievements established him as a leading authority in the area of mathematical modeling of the beh- ior of heterogeneous materials, the area which became known as homogenization theory. Starting in 1981, Jacob established a micromechanical model known as the Method of Cells (MOC) which evolved into the Generalized Method of Cells (GMC) that predicts the macroscopic response of composite materials as a function of the pr- erties, volume fractions, shapes, and constitutive behavior of its constituents. The versatility of the model has been demonstrated to effectively incorporate various types of constituent material behavior (i. e. , both coupled and uncoupled mecha- cal, thermal, electrical and magnetic effects). As a result of its potential in providing an ef?cient tool for the emerging ?eld of multiscale analysis, the method gained increasing attention and became a subject for further research.

The articles in this book present advanced soft methods related to genetic and evolutionary algorithms, immune systems, formulation of deterministic neural networks and Bayesian NN. Many attention is paid to hybrid systems for inverse analysis fusing soft methods and the finite element method. Numerical efficiency of these soft methods is illustrated on the analysis and design of complex engineering structures.

This book describes thermoelastic and inelastic deformation processes in crystalline solids undergoing loading by shock compression. Constitutive models with a basis in geometrically nonlinear continuum mechanics supply these descriptions. Large deformations such as finite strains and rotations, are addressed. The book covers dominant mechanisms of nonlinear thermoelasticity, dislocation plasticity, deformation twinning, fracture, flow, and other structure changes. Rigorous derivations of theoretical results are provided, with approximately 1300 numbered equations and an extensive bibliography of over 500 historical and modern references spanning from the 1920s to the present day. Case studies contain property data, as well as analytical, and numerical solutions to shock compression problems for different materials. Such materials are metals, ceramics, and minerals, single crystalline and polycrystalline. The intended audience of this book is practicing scientists (physicists, engineers, materials scientists, and applied mathematicians) involved in advanced research on shock compression of solid materials.

This book is devoted to two primary objectives. The first is to present the errors, inadaptability and mistakes arising when the current theory on concrete is applied to explaining practical construction of concrete; the second is to put forward viewpoints in modern concrete science. Taking a number of engineering cases as examples, we experimentally studied and theoretically analyzed the errors, inadaptability, and mistakes when the current theory on concrete is applied to explaining practical construction of concrete. Moreover, we investigated the use of mixing ratios, aggregates, cement, high-performance concrete and fibers, as well as the frost resistance, cracking behavior, durability, dry shrinkage and autogenous healing to address and remedy the shortcomings in today's concrete science, put forward new proposals and make a number of innovative achievements in the field, particularly in modern theory on concrete science. The results and topics which will be of particular interest to engineers and researchers include: corrections to several one-sided, even mistaken views on concrete construction in the field and a new theory that can be adopted to improve the durability of concrete projects, to control and improve the implementation quality of concrete projects and to guide teaching in universities. Wenke Yang is a distinguished senior engineer at China Airport Construction Group Corporation, General Administration of Civil Aviation of China (CAAC).

Micromechanisms of Fracture and Fatigue forms the culmination of 20 years of research in the field of fatigue and fracture. It discusses a range of topics and comments on the state of the art for each. The first part is devoted to models of deformation and fracture of perfect crystals. Using various atomistic methods, the theoretical strength of solids under simple and complex loading is calculated for a wide range of elements and compounds, and compared with experimental data. The connection between the onset of local plasticity in nanoindentation tests and the ideal shear strength is analysed using a multi-scale approach. Moreover, the nature of intrinsic brittleness or ductility of perfect crystal lattices is demonstrated by the coupling of atomistic and mesoscopic approaches, and compared with brittle/ductile behaviour of engineering materials. The second part addresses extrinsic sources of fracture toughness of engineering materials, related to their microstructure and microstructurally-induced crack tortuosity. Micromechanisms of ductile fracture are also described, in relation to the fracture strain of materials. Results of multilevel modelling, including statistical aspects of microstructure, are used to explain remarkable phenomena discovered in experiments. In the third part of the book, basic micromechanisms of fatigue cracks propagation under uniaxial and multiaxial loading are discussed on the basis of the unified mesoscopic model of crack tip shielding and closure, taking both microstructure and statistical effects into account. Applications to failure analysis are also outlined, and an attempt is made to distinguish intrinsic and extrinsic sources of materials resistance to fracture. Micromechanisms of Fracture and Fatigue provides scientists, researchers and postgraduate students with not only a deep insight into basic micromechanisms of fracture behaviour of materials, but also a number of engineering applications.

A systematic treatment of the thermal and elastic deformation of bearings, seals, and other machine elements under a wide variety of conditions, with particular emphasis on failure mechanisms when high speeds or loads cause significant frictional heating and on methods for predicting and avoiding such failures. Intended for designers and mechanical engineers responsible for high-performance machinery, the book is unique in discussing instabilities driven by frictional heating and thermal expansion and in developing a theoretical approach to engineering design in those cases in which the thermal problems are pivotal. It thus provides a guide as to what is important in the development of high-performance engineering systems. References to recent publications, new material that fill gaps in the literature, a consistent nomenclature, and a large number of worked examples make this a useful text and reference for both researchers and practising engineers.

Masonry constructions are the great majority of the buildings in Europe's historic centres and the most important monuments of its architectural heritage. Given the age of these constructions, the demand for safety assessments and restoration projects is pressing and constant; still within the broad studies in the subject it is not yet recognised, in particular within the seismic area, a unitary approach to deal with Masonry structures. This successful book contributes to clarify the issues with a rigorous approach offering a comprehensive new Statics of Masonry Constructions. This third edition has been driven by some recent developments of the research in the field, and it gives the fundamentals of Statics with an original and rigorous mathematical formulation, further in-depth inquired in this new version. With many refinements and improvements, the book investigates the static behaviour of many historic monuments, such as the Gothic Cathedrals, the Mycenaean Tholoi, the Pantheon, the Colosseum, the domes of Santa Maria del Fiore in Florence and St Peter's in Rome, as well as the Leaning Tower of Pisa. The last chapter - the 11th - regarding the behaviour of masonry buildings under seismic actions, has been modified and integrated in order to take into account the numerous recent achievements of the research in the dynamic and seismic analysis. The focal point is that there's no dissipation of energy during the deformation of masonry structures, even if accompanied by cracks. If properly reinforced, masonry constructions have the sole resource to escape the seismic action developing the rocking without failure, under alternate seismic action. In this context, the rocking of pier walls, the main resistant components of the masonry structure, has been here thoroughly examined. Furthermore, the out of plane and the in-plane seismic strengths of masonry walls with openings has been investigated within the framework of Limit Analysis. Through an interdisciplinary approach, involving Mathematics, Engineering and Architecture, this book highlights the tight connection existing between the Statics of Masonry constructions and the principles that ruled the history of constructions, since the beginnings as far as the Seventeenth century.

Computational Mechanics in solids, structures and coupled problems in engineering is today a mature science with applications to major industrial designs. This book reflects the state of art and it is written by some of the world leading authorities in this field, addressing such topics as: design and topology optimisation, inverse engineering, multibody dynamics, non-linear and railway dynamics, non-linear and textile composites, sandwich structures, uncertainty and reliability of structures, micromechanics of biological materials, computational geometry, multiscale strategies, discrete and mesh free elements, hybrid crack element, adaptive mesh generation, neural networks, structural model validation, vibro-acoustics, active aeroelastic structures, shells with incompressible flows, fluid-structure interaction, aeroelasticity, fluid-saturated and damage porous media and ceramics, high porosity solids, multiphase viscous porous material and masonry.

This is the first book on the subject of the periodic unfolding method (originally called "eclatement periodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the solution of some open problems. Written by the three mathematicians who developed the method, the book presents both the theory as well as numerous examples of applications for partial differential problems with rapidly oscillating coefficients: in fixed domains (Part I), in periodically perforated domains (Part II), and in domains with small holes generating a strange term (Part IV). The method applies to the case of multiple microscopic scales (with finitely many distinct scales) which is connected to partial unfolding (also useful for evolution problems). This is discussed in the framework of oscillating boundaries (Part III). A detailed example of its application to linear elasticity is presented in the case of thin elastic plates (Part V). Lastly, a complete determination of correctors for the model problem in Part I is obtained (Part VI). This book can be used as a graduate textbook to introduce the theory of homogenization of partial differential problems, and is also a must for researchers interested in this field.

This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is devoted to the detailed study of illuminating specific problems of nonlinear elasticity, directed toward the scientist, engineer, and mathematician who wish to see careful treatments of precisely formulated problems. Special emphasis is placed on role of nonlinear material response. The mathematical tools from nonlinear analysis are given self-contained presentations where they are needed. This book begins with chapters on (geometrically exact theories of) strings, rods, and shells, and on the applications of bifurcation theory and the calculus of variations to problems for these bodies. The book continues with chapters on tensors, three-dimensional continuum mechanics, three-dimensional elasticity, large-strain plasticity, general theories of rods and shells, and dynamical problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.

This book gives a brief but thorough introduction to the fascinating subject of non-Newtonian fluids, their behavior and mechanical properties. After a brief introduction of what characterizes non-Newtonian fluids in Chapter 1 some phenomena characteristic of non-Newtonian fluids are presented in Chapter 2. The basic equations in fluid mechanics are discussed in Chapter 3. Deformation kinematics, the kinematics of shear flows, viscometric flows, and extensional flows are the topics in Chapter 4. Material functions characterizing the behavior of fluids in special flows are defined in Chapter 5. Generalized Newtonian fluids are the most common types of non-Newtonian fluids and are the subject in Chapter 6. Some linearly viscoelastic fluid models are presented in Chapter 7. In Chapter 8 the concept of tensors is utilized and advanced fluid models are introduced. The book is concluded with a variety of 26 problems. Solutions to the problems are ready for instructors

This book provides an insight into the welding techniques with a cross-disciplinary treatment to address the shortcomings of contemporary learning of welding terminology. Various topics covered include introduction to welding processes, design requirements, prominence of design, case studies presenting structural defacements due to inappropriate design, comprehensive surveys on welding processes selected from various process categories, design calculations to be adopted for specific applications and sample calculations. This book is useful for researchers, engineers and professionals working on welding equipment and technologies.

This book provides a general introduction to the topic of buildings for resistance to the effects of abnormal loadings. The structural design requirements for nuclear facilities are very unique. In no other structural system are extreme loads such as tornadoes, missile and loud interaction, earthquake effects typical in excess of any recorded historical data at a site, and postulated system accident at very low probability range explicitly, considered in design. It covers the whole spectrum of extreme load which has to be considered in the structural design of nuclear facilities and reactor buildings, the safety criteria, the structural design, the analysis of containment. Test case studies are given in a comprehensive treatment. Each major section contains a full explanation which allows the book to be used by students and practicing engineers, particularly those facing formidable task of having to design complicated building structures with unusual boundary conditions.