This book summarizes the actual state of the art and future trends of surface effects in solid mechanics. Surface effects are more and more important in the precise description of the behavior of advanced materials. One of the reasons for this is the well-known from the experiments fact that the mechanical properties are significantly influenced if the structural size is very small like, for example, nanostructures. In this book, various authors study the influence of surface effects in the elasticity, plasticity, viscoelasticity. In addition, the authors discuss all important different approaches to model such effects. These are based on various theoretical frameworks such as continuum theories or molecular modeling. The book also presents applications of the modeling approaches.

These are the proceedings of the International Conference on Design, Fabrication and Economy of Metal Structures held on 24-26 April 2013 in Miskolc, Hungary which contain 99 papers covering: Structural optimization Thin-walled structures Stability Fatigue Frames Fire Fabrication Welding technology Applications Steel-concrete composite Special problems The authors are from 23 different countries, ensuring that the themes covered are of worldwide interest and importance. The International Institute of Welding (IIW), the International Society of Structural and Multidisciplinary Optimization (ISSMO), the TAMOP 4.2.1.B-10/2/KONV-2010-0001 project entitled "Increasing the quality of higher education through the development of research - development and innovation program at the University of Miskolc supported by the European Union, co-financed by the European Social Fund" and many other sponsors helped organizers to collect these valuable studies, the results of which will provoke discussion, and provide an important reference for civil and mechanical engineers, architects, researchers and structural designers and fabricators, as well as managers in a range of industries including building, transport, shipbuilding, aircraft, chemical and offshore engineering.

This SpringerBrief presents information on a wide variety of hazards and the damage potential caused by installation of a photovoltaic (PV) system. The current installation practices for PV systems on roofs create electrical, fire, structural, and weather-related hazards that do not comply to current codes, standards and guidance documents. Potential dangers include structural loading, wind loads, hail, snow, debris accumulation, seismic hazards, firefighting hazards, and electrical hazards. Despite the increased popularity of PV systems after the environmental movement, research shows that the costs of installing PV systems outweigh the benefits. Hazards of PV systems on roofs have caused several incidents in the United States; the most notable in Bakersfield, California, and Mount Holly, North Carolina. Designed for fire engineers and professionals, Best Practices for Commercial Roof-Mounted Photovoltaic System Installation offers recommendations to set up PV systems safely and sustainably.

Andreas Hazir is investigating the door seal contribution to the interior noise level of production vehicles. These investigations contain experimental contribution analyses of real production vehicles and of academic test cases as well as the development of a simulation methodology for noise transmission through sealing systems and side windows. The simulations are realized by coupling transient computational aeroacoustics of the exterior flow to nonlinear finite element simulations of the structural transmission. By introducing a linear transmission model, the setup and computational costs of the seal noise transmission are significantly reduced, resulting in the feasibility of numerical contribution analyses of real production vehicles.

This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einstein's theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

In this second edition a new chapter has been added covering the buffeting theory in a finite element format. The motivation for this has been that a finite element format is becoming more and more dominant in all areas of structural mechanics. It is streamlined for computer programming, and it facilitates the use of general purpose routines that are applicable in several types of structural engineering problems. In this book the finite element formulation of the problem of dynamic response calculations follows the general principle of virtual work, a general principle which may be found in many other text books. While the buffeting wind load itself has with no trouble been included in a finite element format, the main challenge has been to obtain a consistent formulation that includes all the relevant motion induced forces. This has been important, because, while many structures (e.g. long-span suspension bridges) may suffer greatly and become unstable at high wind velocities, the same structures may also benefit from these effects at the design wind velocity. It is well known that motion induced forces will change the stiffness and damping properties of the combined structure and flow system. If calculations are performed for a suitably close set of increasing mean wind velocities and the changing mechanical properties (stiffness and damping) are updated from one velocity to the next, then the response of the system may be followed up to wind velocities close to the stability limit, i.e. up to response values that are perceived as unduly large. Finite element calculations may be performed in time domain, in frequency domain or converted into a modal format. All these options have been included. Pursuing a time domain solution strategy requires the use of the so-called indicial functions. The theory behind such a formulation is also covered, and the determination of these functions from aerodynamic derivatives has been included in a separate appendix.

A molecular view on the fundamental issues in polymer physics is provided with an aim at students in chemistry, chemical engineering, condensed matter physics and material science courses. An updated translation by the author, a renowned Chinese chemist, it has been proven to be an effective source of learning for many years. Up-to-date developments are reflected throughout the work in this concise presentation of the topic. The author aims at presenting the subject in an efficient manner, which makes this particularly suitable for teaching polymer physics in settings where time is limited, without having to sacrifice the extensive scope that this topic demands.

This book focuses on the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis. It is divided into three parts, with the first part providing a detailed introduction to plasticity, the second part covering the mathematical analysis of the elasticity problem, and the third part devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. This revised and expanded edition includes material on single-crystal and strain-gradient plasticity. In addition, the entire book has been revised to make it more accessible to readers who are actively involved in computations but less so in numerical analysis. Reviews of earlier edition: "The authors have written an excellent book which can be recommended for specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory." (ZAMM, 2002) "In summary, the book represents an impressive comprehensive overview of the mathematical approach to the theory and numerics of plasticity. Scientists as well as lecturers and graduate students will find the book very useful as a reference for research or for preparing courses in this field." (Technische Mechanik) "The book is professionally written and will be a useful reference to researchers and students interested in mathematical and numerical problems of plasticity. It represents a major contribution in the area of continuum mechanics and numerical analysis." (Math Reviews)

Die Casting: An Analytical Approach will refresh knowledge of the governing laws of the fluid dynamics that have an effect on die cast die and die cast process design. It will be bought by product designers that design die cast parts and die cast die and process engineers and designers.

In the last few years, a significant increase in applications of MMCs has taken place, particularly in the areas of automotive, aerospace, electronics, and recreation. These include continuous fiber reinforced MMCs for cables in power transmission, high temperature superconducting wires, particulate MMCs in civilian aircraft and automotive applications, and high volume fraction, high thermal conductivity substrates for electronic packaging. Nevertheless, as with any novel material systems, there is a lack of fundamental understanding on the part of practicing engineers and designers. This book would seek to address these issues, in a thorough and cohesive manner, as well as to provide students and scientists with a basic understanding of MMCs. This book will emphasize the synergistic relationships among processing, structure, and properties of metal matrix composites.

This is a book for people who love mechanics of composite materials and ? MATLAB . We will use the popular computer package MATLAB as a matrix calculator for doing the numerical calculations needed in mechanics of c- posite materials. In particular, the steps of the mechanical calculations will be emphasized in this book. The reader will not ?nd ready-made MATLAB programs for use as black boxes. Instead step-by-step solutions of composite material mechanics problems are examined in detail using MATLAB. All the problems in the book assume linear elastic behavior in structural mechanics. The emphasis is not on mass computations or programming, but rather on learning the composite material mechanics computations and understanding of the underlying concepts. The basic aspects of the mechanics of ?ber-reinforced composite materials are covered in this book. This includes lamina analysis in both the local and global coordinate systems, laminate analysis, and failure theories of a lamina.

st The21 InternationalCongressofTheoreticalandAppliedMechanics (ICTAM04) took place August 15 - 21, 2004, in Warsaw, Poland. It was organized by Polish National Committee of IUTAM, Institute of Fundamental Technological Research of the Polish Academy of Sciences (IPPTPAN)andWarsawUniversityofTechnology. TheCongressvenue was the main building of Warsaw University of Technology. The idea of congresses devoted to mechanics, can be traced back to a conference on problems of?uid mechanics in Innsbruck, 1922. It was organized by four individuals, whose names, are and will, remain very wellknowntonextgenerationsofscientists,C.W.Oseen,T.Levi-Civite, T.vonKarm ' ' ' an,andL.Prandtl. Thisconferencewassofruitful,thatthe organizers decided to arrange similar meetings in the future, every four years, and to extend the scope of the future meetings to include solid mechanics. Hence a series of meetings started eighty years agowiththe st 1 ICTAM held in Delft, Netherlands. From the meetingsoftheCongress Committee sprang the idea of a more permanent organization to look out for the world interests in the mechanical sciences. Thus, IUTAM, theInternational Unionof Theor- ical and Applied Mechanics, was formed on September 26, 1946. In 1947 IUTAM became a member of ICSU, the International Council of Sci- ti?c Unions, itself founded in 1931. The highest authority of IUTAMis the General Assembly, with delegates from the Adhering Organizations, each of which is a?liated with a national learned society in a given country. Scienti?cProgram Contemporary mechanics poses both, the fundamental problems from the area of pure science, and its strong links with modern technology.

One of the key aspects of this volume is to cut across the traditional taxonomy of disciplines in the study of alloys. Hence there has been a deliberate attempt to integrate the different approaches taken towards alloys as a class of materials in different fields, ranging from geology to metallurgical engineering. The emphasis of this book is to highlight commonalities between different fields with respect to how alloys are studied. The topics in this book fall into several themes, which suggest a number of different classification schemes. We have chosen a scheme that classifies the papers in the volume into the categories Microstructural Considerations, Ordering, Kinetics and Diffusion, Magnetic Considerations and Elastic Considerations. The book has juxtaposed apparently disparate approaches to similar physical processes, in the hope of revealing a more dynamic character of the processes under consideration. This monograph will invigorate new kinds of discussion and reveal challenges and new avenues to the description and prediction of properties of materials in the solid state and the conditions that produce them.

This volume contains the articles presented at the 18th International Meshing Roundtable (IMR) organized, in part, by Sandia National Laboratories and held October 25-28, 2009 in Salt Lake City, Utah, USA. The volume presents recent results of mesh generation and adaptation which has applications to finite element simulation. It introduces theoretical and novel ideas with practical potential.

The present volume of Modern Aspects of Electrochemistry is composed of four chapters covering topics having relevance both in corrosion science and materials engineering. All of the chapters provide comprehensive coverage of recent advances in corrosion science. The first chapter, by Maurice and Marcus, provides a comprehensive review on the structural aspects and anti-corrosion properties of passive films on metals and alloys. These authors look at recent experimental data collected by in-situ microscopic techniques coupled with electrochemical methods. A detailed description is given of the nucleation and growth of 2-dimensional passive films at earlier stages, their effect on the corrosion properties of metal surfaces, and the nanostructures of- dimensional passive films. On the basis of the experimental data reviewed, the authors present a model for passivity breakdown and pit initiation, which takes into account the preferential role of grain boundaries. In Chapter 2, Takahashi and his co-workers give a specialized account on the electrochemical and structural properties of anodic oxide films formed on aluminum. In addition to the electrochemical corrosion-related problems of anodic oxide films, the chapter reviews state-of-the-art research of nano-/mic- fabrications based on anodizing treatments combined with chemical/mechanical processes such as laser irradiation, atomic force micro-probe processing and thin film deposition techniques.

Cracks can develop in rotating shafts and can propagate to relevant depths without affecting consistently the normal operating conditions of the shaft. In order to avoid catastrophic failures, accurate vibration analyses have to be performed for crack detection. The identification of the crack location and depth is possible by means of a model based diagnostic approach, provided that the model of the crack and the model of the cracked shaft dynamical behavior are accurate and reliable. This monograph shows the typical dynamical behavior of cracked shafts and presents tests for detecting cracks. The book describes how to model cracks, how to simulate the dynamical behavior of cracked shaft, and compares the corresponding numerical with experimental results. All effects of cracks on the vibrations of rotating shafts are analyzed, and some results of a numerical sensitivity analysis of the vibrations to the presence and severity of the crack are shown. Finally the book describes some crack identification procedures and shows some results in model based crack identification in position and depth. The book is useful for higher university courses in mechanical and energetic engineering, but also for skilled technical people employed in power generation industries.

This book deals with the management of calculations in linear and nonlinear mechanics. Particular attention is given to error estimators and indicators for structural analysis. The accent is on the concept of error in constitutive relation. An important part of the work is also devoted to the utilization of the error estimators involved in a calculation, beginning with the parameters related to the mesh. Many of the topics are taken from the most recent research by the authors: local error estimators, extention of the concept of error in constitutive relation to nonlinear evolution problems and dynamic problems, adaptive improvement of calculations in nonlinear mechanics. This work is intended for all those interested in mechanics: students, researchers and engineers concerned with the construction of models as well as their simulation for industrial purposes.

Theuseoflasersinmaterialsprocessinghasbecomewidespreadinrecent years,sothatanunderstandingofthenatureofheatandmasstransferin thisbranchofmoderntechnologyisofincreasingimportance. Theaimofthe authorsofthisbookistoconcentrateonthephysicalprocesses;thesecanbe developedfromamathematicalpointofview,orfromdirectexperimental- derivedobservation. Thetwoapproachesarecomplementary;eachcanprovide insightsandthesynthesisofthetwocanleadtoaverypowerfulunderstanding oftheprocessesinvolved. Mathematicalmodellingofphysicalprocesseshas hadanimportantroletoplayinthedevelopmentoftechnologyoverthe centuriesandparticularlysointhelastonehundredand?ftyyearsorso. Itcanbearguedthatitismoreimportanttodaythaneverbeforesincethe availabilityofhigh-speedcomputersallowsaccuratenumericalsimulationof industrialprocessesatafractionofthecostofthecorrespondingexperiments. Thisisoneaspectofmathematicalmodelling,highpro?leandmuchvalued, butitisnottheonlyone. Inthepastmathematicalmodellinghadtorelyonqualitativeinves- gation,veryspecialanalyticalsolutions,orinaccurateandtime-consuming calculationsperformedwithlittleinthewayoftabulatedormechanical assistance. Logtablesandsliderulesarestillrememberedbypeopleworking today,thoughtherearesurelyfewwhoregrettheirdisappearance. Thevalueanddistinctivefunctionofmethodsbasedontheanalytical approachisnowbecomingmuchclearer,nowthattheyarenolongerexpected toproducedetailedimitationsofwhathappensinrealexperimentsofind- trialprocesses,afunctionnowful?lledmostlybynumericalmethods,c- sideredbelow. Theemphasistodayisontheirabilitytocon?rmandextend ourunderstandingofthebasicphysicalmechanismsinvolvedintheprocesses of interest. These are essential for any intelligent use of numerical simulation. Theargumentaboutthevalueofteachingpeoplehowtodoarithmetic themselveswithouttheaidofacalculatorseemstobepassingintohistory, vi Preface butitisanimportantoneandprovidesasimpleanalogy. Ifsomeonedoes nothaveafeelingfornumbersandthewayarithmeticworks,theywillalltoo easilyfailtospotanerrorproducedbyamachine. Computersarenotinfallible -andneitherarethosewhobuildorprogramthem. Computersarenow takingonlessmundanemathematicaltasksandthesamecontroversiesare appearinginconnectionwithalgebraicmanipulation. Equally,andwitheven greaterpenaltiesintermsofcostintheeventoferrors,thesameconsiderations applytonumericalsimulationofmajorindustrialprocesses. Awarenessofthe analyticalsolutionscanbeinvaluableindistinguishingtherightfromthe wrong,i. e. forthepractitionertounderstandthebasisofthework,andto haveanideaofthekindsofoutcomesthatareplausible-andtorecognise thosewhicharenot. Thephrase"mathematicalmodelling"is,however,ambiguous,perhaps morenowthanithaseverbeen. Thereisanenormousamountofworkdone todayonsimulationbasedontheuseofverypowerfulcomputerprograms, anditisquitecorrectlyreferredtoasmathematicalmodelling. Theprograms aresometimesconstructedin-housebutareusuallycommercialpackages. This isanentirelyvalidapproachwithspeci?c(generallycommercial)objectives. Ingeneraltherearetwouses. Thedominantobjectiveisnumericalagreement withaparticularexperimentinthe?rstinstance,leadingtopredictivec- mercialuseinthesecondinstance. Thesecondobjectiveistheclari?cation ofphysicalmechanisms,aimedatthegenerationofunderstandingofcomplex interconnectedprocesses,ratherthantheexactreproductionofaparticular experiment. Itissometimesoverlookedthat,withsu?cientcare,anum- icalapproachisequallyvalidintheinvestigationofphysicalfundamentals. Numericalsimulationisnotacentraltopicofthisbook,butbecauseofits crucialimportancetoeachofthetwousestowhichnumericalmodellingcan beput,itisvitalthatthecomputationalbasisoftheworkshouldbec- pletelysound. Inaddition,thelevelofprocessdetailwhichcanbeconsidered bythenumericalapproachusuallyexceedswhatispossiblewiththeanaly- calapproachsigni?cantly,leavinglittlechoicebuttoreverttothenumerical treatmentwheninvestigatingtheinterconnectionsbetweenprocesses. Itis forthesereasonsthatthebookconcludeswithachapteroncomprehensive numericalsimulation. Inmanyways,theapproachadoptedhereiscomplementarytothemore phenomenologicalapproach. Itisalwaysimportantina?eldwhichhasvery directindustrialapplicationstobearinmindhowtechniquessuchasthose describedherewillbeused,butitisessentialnottolosesightofthef- damentals. Thereareserioussafetyimplications;therearecostimplications; therearemoralimplications;thereareconsiderationsoftheappropriateness ofthetechnologytotheapplicationunderconsideration. Aproperrespectfor alltheserequiresanunderstandingofthefundamentals. Wearealltoowellawarethatthisbookdoeslittlemorethanscratch thesurfaceoftheproblemsinvolvedinafundamentalunderstandingofthese phenomena. Ifwehaveprovidedideasandinformationthatcauseothersto Preface vii testthemexperimentallyorintellectually,agreewiththemordisputethem vigorously,anddevelopthemfurther,wewillconsiderthatwehaveachieved ouraim. Colchester April,2008 JohnDowden Contents 1MathematicsinLaserProcessing JohnDowden...1 1. 1 MathematicsanditsApplication...1 1. 2 FormulationinTermsofPartialDi?erentialEquations...3 1. 2. 1 LengthScales...3 1. 2. 2 ConservationEquationsandtheirGeneralisations...4 1. 2. 3 GoverningEquationsofGeneralised ConservationType...7 1. 2. 4 Gauss'is,however,ambiguous,perhaps morenowthanithaseverbeen. Thereisanenormousamountofworkdone todayonsimulationbasedontheuseofverypowerfulcomputerprograms, anditisquitecorrectlyreferredtoasmathematicalmodelling. Theprograms aresometimesconstructedin-housebutareusuallycommercialpackages. This isanentirelyvalidapproachwithspeci?c(generallycommercial)objectives. Ingeneraltherearetwouses. Thedominantobjectiveisnumericalagreement withaparticularexperimentinthe?rstinstance,leadingtopredictivec- mercialuseinthesecondinstance. Thesecondobjectiveistheclari?cation ofphysicalmechanisms,aimedatthegenerationofunderstandingofcomplex interconnectedprocesses,ratherthantheexactreproductionofaparticular experiment. Itissometimesoverlookedthat,withsu?cientcare,anum- icalapproachisequallyvalidintheinvestigationofphysicalfundamentals. Numericalsimulationisnotacentraltopicofthisbook,butbecauseofits crucialimportancetoeachofthetwousestowhichnumericalmodellingcan beput,itisvitalthatthecomputationalbasisoftheworkshouldbec- pletelysound. Inaddition,thelevelofprocessdetailwhichcanbeconsidered bythenumericalapproachusuallyexceedswhatispossiblewiththeanaly- calapproachsigni?cantly,leavinglittlechoicebuttoreverttothenumerical treatmentwheninvestigatingtheinterconnectionsbetweenprocesses. Itis forthesereasonsthatthebookconcludeswithachapteroncomprehensive numericalsimulation. Inmanyways,theapproachadoptedhereiscomplementarytothemore phenomenologicalapproach. Itisalwaysimportantina?eldwhichhasvery directindustrialapplicationstobearinmindhowtechniquessuchasthose describedherewillbeused,butitisessentialnottolosesightofthef- damentals. Thereareserioussafetyimplications;therearecostimplications; therearemoralimplications;thereareconsiderationsoftheappropriateness ofthetechnologytotheapplicationunderconsideration. Aproperrespectfor alltheserequiresanunderstandingofthefundamentals. Wearealltoowellawarethatthisbookdoeslittlemorethanscratch thesurfaceoftheproblemsinvolvedinafundamentalunderstandingofthese phenomena. Ifwehaveprovidedideasandinformationthatcauseothersto Preface vii testthemexperimentallyorintellectually,agreewiththemordisputethem vigorously,anddevelopthemfurther,wewillconsiderthatwehaveachieved ouraim. Colchester April,2008 JohnDowden Contents 1MathematicsinLaserProcessing JohnDowden...1 1. 1 MathematicsanditsApplication...1 1. 2 FormulationinTermsofPartialDi?erentialEquations...3 1. 2. 1 LengthScales...3 1. 2. 2 ConservationEquationsandtheirGeneralisations...4 1. 2. 3 GoverningEquationsofGeneralised ConservationType...7 1. 2. 4 Gauss'Theuseoflasersinmaterialsprocessinghasbecomewidespreadinrecent years,sothatanunderstandingofthenatureofheatandmasstransferin thisbranchofmoderntechnologyisofincreasingimportance. Theaimofthe authorsofthisbookistoconcentrateonthephysicalprocesses;thesecanbe developedfromamathematicalpointofview,orfromdirectexperimental- derivedobservation. Thetwoapproachesarecomplementary;eachcanprovide insightsandthesynthesisofthetwocanleadtoaverypowerfulunderstanding oftheprocessesinvolved. Mathematicalmodellingofphysicalprocesseshas hadanimportantroletoplayinthedevelopmentoftechnologyoverthe centuriesandparticularlysointhelastonehundredand?ftyyearsorso. Itcanbearguedthatitismoreimportanttodaythaneverbeforesincethe availabilityofhigh-speedcomputersallowsaccuratenumericalsimulationof industrialprocessesatafractionofthecostofthecorrespondingexperiments. Thisisoneaspectofmathematicalmodelling,highpro?leandmuchvalued, butitisnottheonlyone. Inthepastmathematicalmodellinghadtorelyonqualitativeinves- gation,veryspecialanalyticalsolutions,orinaccurateandtime-consuming calculationsperformedwithlittleinthewayoftabulatedormechanical assistance. Logtablesandsliderulesarestillrememberedbypeopleworking today,thoughtherearesurelyfewwhoregrettheirdisappearance. Thevalueanddistinctivefunctionofmethodsbasedontheanalytical approachisnowbecomingmuchclearer,nowthattheyarenolongerexpected toproducedetailedimitationsofwhathappensinrealexperimentsofind- trialprocesses,afunctionnowful?lledmostlybynumericalmethods,c- sideredbelow. Theemphasistodayisontheirabilitytocon?rmandextend ourunderstandingofthebasicphysicalmechanismsinvolvedintheprocesses of interest. These are essential for any intelligent use of numerical simulation. Theargumentaboutthevalueofteachingpeoplehowtodoarithmetic themselveswithouttheaidofacalculatorseemstobepassingintohistory, vi Preface butitisanimportantoneandprovidesasimpleanalogy. Ifsomeonedoes nothaveafeelingfornumbersandthewayarithmeticworks,theywillalltoo easilyfailtospotanerrorproducedbyamachine. Computersarenotinfallible -andneitherarethosewhobuildorprogramthem. Computersarenow takingonlessmundanemathematicaltasksandthesamecontroversiesare appearinginconnectionwithalgebraicmanipulation. Equally,andwitheven greaterpenaltiesintermsofcostintheeventoferrors,thesameconsiderations applytonumericalsimulationofmajorindustrialprocesses. Awarenessofthe analyticalsolutionscanbeinvaluableindistinguishingtherightfromthe wrong,i. e. forthepractitionertounderstandthebasisofthework,andto haveanideaofthekindsofoutcomesthatareplausible-andtorecognise thosewhicharenot. Thephrase"mathematicalmodelling"is,however,ambiguous,perhaps morenowthanithaseverbeen. Thereisanenormousamountofworkdone todayonsimulationbasedontheuseofverypowerfulcomputerprograms, anditisquitecorrectlyreferredtoasmathematicalmodelling. Theprograms aresometimesconstructedin-housebutareusuallycommercialpackages. This isanentirelyvalidapproachwithspeci?c(generallycommercial)objectives. Ingeneraltherearetwouses. Thedominantobjectiveisnumericalagreement withaparticularexperimentinthe?rstinstance,leadingtopredictivec- mercialuseinthesecondinstance. Thesecondobjectiveistheclari?cation ofphysicalmechanisms,aimedatthegenerationofunderstandingofcomplex interconnectedprocesses,ratherthantheexactreproductionofaparticular experiment. Itissometimesoverlookedthat,withsu?cientcare,anum- icalapproachisequallyvalidintheinvestigationofphysicalfundamentals. Numericalsimulationisnotacentraltopicofthisbook,butbecauseofits crucialimportancetoeachofthetwousestowhichnumericalmodellingcan beput,itisvitalthatthecomputationalbasisoftheworkshouldbec- pletelysound. Inaddition,thelevelofprocessdetailwhichcanbeconsidered bythenumericalapproachusuallyexceedswhatispossiblewiththeanaly- calapproachsigni?cantly,leavinglittlechoicebuttoreverttothenumerical treatmentwheninvestigatingtheinterconnectionsbetweenprocesses. Itis forthesereasonsthatthebookconcludeswithachapteroncomprehensive numericalsimulation. Inmanyways,theapproachadoptedhereiscomplementarytothemore phenomenologicalapproach. Itisalwaysimportantina?eldwhichhasvery directindustrialapplicationstobearinmindhowtechniquessuchasthose describedherewillbeused,butitisessentialnottolosesightofthef- damentals. Thereareserioussafetyimplications;therearecostimplications; therearemoralimplications;thereareconsiderationsoftheappropriateness ofthetechnologytotheapplicationunderconsideration. Aproperrespectfor alltheserequiresanunderstandingofthefundamentals. Wearealltoowellawarethatthisbookdoeslittlemorethanscratch thesurfaceoftheproblemsinvolvedinafundamentalunderstandingofthese phenomena. Ifwehaveprovidedideasandinformationthatcauseothersto Preface vii testthemexperimentallyorintellectually,agreewiththemordisputethem vigorously,anddevelopthemfurther,wewillconsiderthatwehaveachieved ouraim. Colchester April,2008 JohnDowden Contents 1MathematicsinLaserProcessing JohnDowden...1 1. 1 MathematicsanditsApplication...1 1. 2 FormulationinTermsofPartialDi?erentialEquations...3 1. 2. 1 LengthScales...3 1. 2. 2 ConservationEquationsandtheirGeneralisations...4 1. 2. 3 GoverningEquationsofGeneralised ConservationType...7 1. 2. 4 Gauss'sLaw...10 1. 3 BoundaryandInterfaceConditions...11 1. 3. 1 GeneralisedConservationConditions...11 1. 3. 2 TheKinematicConditioninFluidDynamics...13 1. 4 Fick'sLaws...15 1. 5 Electromagnetism...15 1. 5. 1 Maxwell'sEquations...15 1. 5. 2 Ohm'sLaw...18 References...19 2SimulationofLaserCutting WolfgangSchulz,MarkusNiessen,UrsEppelt,KerstinKowalick...21 2. 1 Introduction...22 2. 1. 1 PhysicalPhenomenaandExperimentalObservation...23 2. 2 MathematicalFormulationandAnalysis...26 2. 2. 1 TheOne-PhaseProblem...29 2. 2. 2 TheTwo-PhaseProblem...42 2. 2. 3 Three-PhaseProblem...51 2. 3 Outlook...64 2. 4 Acknowledgements...65 References...65 x Contents 3KeyholeWelding:TheSolidandLiquidPhases AlexanderKaplan...71 3. 1 HeatGenerationandHeatTransfer...71 3. 1. 1 Absorption...

Mathematical optimization encompasses both a rich and rapidly evolving body of fundamental theory, and a variety of exciting applications in science and engineering. The present book contains a careful selection of articles on recent advances in optimization theory, numerical methods, and their applications in engineering. It features in particular new methods and applications in the fields of optimal control, PDE-constrained optimization, nonlinear optimization, and convex optimization. The authors of this volume took part in the 14th Belgian-French-German Conference on Optimization (BFG09) organized in Leuven, Belgium, on September 14-18, 2009. The volume contains a selection of reviewed articles contributed by the conference speakers as well as three survey articles by plenary speakers and two papers authored by the winners of the best talk and best poster prizes awarded at BFG09. Researchers and graduate students in applied mathematics, computer science, and many branches of engineering will find in this book an interesting and useful collection of recent ideas on the methods and applications of optimization.

Availability of advanced computational technology has fundamentally altered the investigative paradigm in the field of biomechanics. Armed with sophisticated computational tools, researchers are seeking answers to fundamental questions by exploring complex biomechanical phenomena at the molecular, cellular, tissue and organ levels. The computational armamentarium includes such diverse tools as the ab initio quantum mechanical and molecular dynamics methods at the atomistic scales and the finite element, boundary element, meshfree as well as immersed boundary and lattice-Boltzmann methods at the continuum scales. Multiscale methods that link various scales are also being developed. While most applications require forward analysis, e.g., finding deformations and stresses as a result of loading, others involve determination of constitutive parameters based on tissue imaging and inverse analysis. This book provides a glimpse of the diverse and important roles that modern computational technology is playing in various areas of biomechanics including biofluids and mass transfer, cardiovascular mechanics, musculoskeletal mechanics, soft tissue mechanics, and biomolecular mechanics.

This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract but powerful mathematical notions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value problems for mechanical objects. This second edition includes more extended coverage of the classical and abstract portions of functional analysis. Taken together, the first three chapters now constitute a regular text on applied functional analysis. This potential use of the book is supported by a significantly extended set of exercises with hints and solutions. A new appendix, providing a convenient listing of essential inequalities and imbedding results, has been added. The book should appeal to graduate students and researchers in physics, engineering, and applied mathematics. Reviews of first edition: "This book covers functional analysis and its applications to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. ... Detailed solutions of the exercises are provided in an appendix." (L'Enseignment Mathematique, Vol. 49 (1-2), 2003) "The reader comes away with a profound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood. Numerous exercises ... test the reader's comprehension at every stage. Summing Up: Recommended." (F. E. J. Linton, Choice, September, 2003)

Concrete is still the most widely used construction material since it has the lowest ratio between cost and strength as compared to other available materials. However, it has two undesirable properties, namely: low tensile strength and large brittleness that cause the collapse to occur shortly after the formation of the first crack. To improve these two negative properties and to achieve a partial substitute of conventional reinforcement, an addition of short discontinuous randomly oriented steel fibres can be practiced among others. In spite of positive properties, fibrous concrete did not find such acknowledgment and application as usual concrete. There do not still exist consistent dimensioning rules due to the lack sufficient large-scale static and dynamic experiments taking into account the effect of the fibre orientation. The intention of the book is twofold: first to summarize the most important mechanical and physical properties of steel-fibre-added concrete and reinforced concrete on the basis of numerous experiments described in the scientific literature, and second to describe a quasi-static fracture process at meso-scale both in plain concrete and fibrous concrete using a novel discrete lattice model. In 2D and 3D simulations of fibrous concrete specimens under uniaxial tension, the effect of the fibre volume, fibre distribution, fibre orientation, fibre length, fibrous bond strength and specimen size on both the stress-strain curve and fracture process was carefully analyzed.

Contact mechanics is an active research area with deep theoretical and numerical roots. The links between nonsmooth analysis and optimization with mechanics have been investigated intensively during the last decades, especially in Europe. The study of complementarity problems, variational -, quasivariational- and hemivariational inequalities arising in contact mechanics and beyond is a hot topic for interdisciplinary research and cooperation. The needs of industry for robust solution algorithms suitable for large scale applications and the regular updates of the respective elements in major commercial computational mechanics codes, demonstrate that this interaction is not restricted to the academic environment. The contributions of this book have been selected from the participants of the CMIS 2009 international conference which took place in Crete and continued a successful series of specialized contact mechanics conferences.

This book serves both as a textbook and a scientific work. As a textbook, the work gives a clear, thorough and systematic presentation of the fundamental postulates, theorems and principles and their applications of the classical mathematical theories of plasticity and creep. In addition to the mathematical theories, the physical theory of plasticity, the book presents the Budiansky concept of slip and its modification by M. Leonov. Special attention is given to the analysis of the advantages and shortcomings of the classical theories. In its main part, the book presents the synthetic theory of irreversible deformations, which is based on the mathematical Sanders flow plasticity theory and the physical theory, the Budiansky concept of slip. The main peculiarity of the synthetic theory is that the formulae for both plastic and creep deformation, as well their interrelations, can be derived from the single constitutive equation. Furthermore, the synthetic theory, as physical one, can take into account the real processes that take place in solids at irreversible deformation. This widens considerably the potential of the synthetic theory. In the framework of the synthetic theory such problems as creep delay, the Hazen-Kelly effect, the deformation at the break of the load trajectory, the influence of the rate of loading on the stress-strain diagram, creep at the changes of load, creep at unloading and reversed creep, have been analytically described. In the last chapter, the book shows the solution of some contemporary problems of plasticity and creep: Creep deformation at cyclic abrupt changes of temperature, The influence of irradiation on the plastic and creep deformation, Peculiarities of deformation at the phase transformation of some metals.

The idea of this monograph is to present the latest results related to design and analysis of materials and engineering structures. The contributions cover the field of mechanical and civil engineering, ranging from automotive to dam design, transmission towers and up to machine design and exmaples taken from oil industry. Well known experts present their research on damage and fracture of material and structures, materials modelling and evaluation up to image processing and visualization for advanced analyses and evaluation