Nonlinear Problems Of Elasticity
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Nonlinear Problems Of Elasticity
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Author : Stuart Antman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Nonlinear Problems Of Elasticity written by Stuart Antman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.
Nonlinear Problems Of Elasticity
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Author : S.S Antman
language : en
Publisher: Springer
Release Date : 2012-12-22
Nonlinear Problems Of Elasticity written by S.S Antman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-22 with Mathematics categories.
The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.
Nonlinear Problems Of Elasticity
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Author : Stuart S. Antman
language : en
Publisher:
Release Date : 2005
Nonlinear Problems Of Elasticity written by Stuart S. Antman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Technology & Engineering categories.
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 the 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, and general theories of rods and shells, and dynamical problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.; Reviews of the first edition: 'A scholarly work, it is uncompromising in its approach to model formulation, while achieving striking generality in the analysis of particular problems. It will undoubtedly become a standard research reference in elasticity but will be appreciated also by teachers of both solid mechanics and applied analysis for its clear derivation of equations and wealth of examples.' - JM Ball, ("Bulletin of the American Mathematical Society"), 1996. ''It is destined to become a standard reference in the field which belongs on the bookshelf of anyone working on the application of mathematics to continuum mechanics. For graduate students, it provides a fascinating introduction to an active field of mathematical research.' - M Renardy, ("SIAM Review"), 1995. 'The monograph is a masterpiece for writing a modern theoretical treatise on a field of natural sciences. It is highly recommended to all scientists, engineers and mathematicians interested in a careful treatment of uncompromised nonlinear problems of elasticity, and it is a 'must' for applied mathematicians working on such problems.' - LV Wolfersdorf, ("Zeitschrift fur Angewandte Mathematik und Mechanik"), 1995.
Nonlinear Problems Of Elasticity
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Author : S.S Antman
language : en
Publisher: Springer
Release Date : 2012-02-25
Nonlinear Problems Of Elasticity written by S.S Antman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-25 with Mathematics categories.
Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.
Nonlinear Problems Of Elasticity
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Author : Stuart S. Antman
language : en
Publisher: Springer
Release Date : 2023-08-15
Nonlinear Problems Of Elasticity written by Stuart S. Antman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-15 with Mathematics categories.
This monograph, the second of the two volumes forming the third edition, is an enlarged, completely updated, and extensively revised version of the corresponding material from the authoritative second edition. It is completely self-contained. This volume contains chapters on tensors, three-dimensional continuum mechanics, constitutive equations and their physically natural restrictions for three-dimensional elasticity and strain-rate viscoelasticity, steady-state and dynamical problems for these theories, general geometrically and mechanically exact theories of rods and shells, methods for treating dynamical problems of strain-rate viscoelasticity, and the role of material response for quasilinear hyperbolic systems of elasticity. Each chapter contains a wealth of interesting, challenging, and tractable exercises. From the reviews of the second edition: "This second edition accounts for the developments since the first edition was published, and differs from the first edition in many points. The book has been reorganized and several parts have been added. ... The already impressive body of references has been further expanded. The reviewer highly recommends this book both to graduate students and to scholars interested in the theory of elasticity." (Massimo Lanza de Cristoforis, Mathematical Reviews, Issue 2006e:74001) "The second extended edition of the reviewed monograph gives a fundamental presentation of problems of nonlinear elasticity. Every chapter is equipped by instructive exercises, unsolved problems and exhaustive historical comments. The book could be very useful to applied mathematicians and engineers using in their works the elasticity theory and ... to specialists dealing with applications of differential equations and bifurcation theory." (Boris V. Loginov, Zentralblatt MATH, Vol. 1098 (24), 2006) "Antman’s impressive work is ... a comprehensive treatise on nonlinear elasticity and a quintessential example of applied nonlinear analysis. ... The text has been revised and updated, Several new sections have been added ... This book is a ‘must’ for researchers and graduate students interested in nonlinear continuum mechanics and applied analysis. The work is scholarly and well written. ... ‘This book is directed toward scientists, engineers, and mathematicians who wish to see careful treatments of uncompromised problems.’" (Timothy J. Healey, SIAM Review, Vol. 49 (2), 2007)
Nonlinear Problems Of Elasticity
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Author : Stuart S. Antman
language : en
Publisher: Springer
Release Date : 2023-08-28
Nonlinear Problems Of Elasticity written by Stuart S. Antman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Mathematics categories.
Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.
Singular Problems In Elasticity
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Author : Adair Roberto Aguiar
language : en
Publisher:
Release Date : 1998
Singular Problems In Elasticity written by Adair Roberto Aguiar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Variational Methods In Nonlinear Elasticity
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Author : Pablo Pedregal
language : en
Publisher: SIAM
Release Date : 2000-01-01
Variational Methods In Nonlinear Elasticity written by Pablo Pedregal and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Science categories.
In less than 100 pages, this book covers the main vector variational methods developed to solve nonlinear elasticity problems. Presenting a general framework with a tight focus, the author provides a comprehensive exposition of a technically difficult, yet rapidly developing area of modern applied mathematics. The book includes the classical existence theory as well as a brief incursion into problems where nonexistence is fundamental. It also provides self-contained, concise accounts of quasi convexity, polyconvexity, and rank-one convexity, which are used in nonlinear elasticity. Pedregal introduces the reader to Young measures as an important tool in solving vector variational techniques. Readers are encouraged to pursue nonlinear elasticity as one of the best means to apply these techniques. Although there are other books devoted to nonlinear elasticity or variational methods, none are concerned with Young measures as a tool for proving existence results in nonlinear elasticity.
Non Linear Theory Of Elasticity
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Author : A.I. Lurie
language : en
Publisher: North Holland
Release Date : 1990-11-13
Non Linear Theory Of Elasticity written by A.I. Lurie and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-11-13 with Mathematics categories.
This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.
Problems Of Non Linear Elasticity
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Author : Clifford Truesdell
language : en
Publisher:
Release Date :
Problems Of Non Linear Elasticity written by Clifford Truesdell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Elasticity categories.