Some Problems In Nonlinear Elasticity

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Nonlinear Problems of Elasticity

Author : Stuart Antman
Publisher : Springer Science & Business Media
ISBN 13 : 1475741472
Total Pages : 762 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Nonlinear Problems of Elasticity by : Stuart Antman

Download or read book Nonlinear Problems of Elasticity written by Stuart Antman and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Some Problems in Nonlinear Elasticity

Author : Michael Alan Kosecoff
Publisher :
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.:/5 (436 download)

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Book Synopsis Some Problems in Nonlinear Elasticity by : Michael Alan Kosecoff

Download or read book Some Problems in Nonlinear Elasticity written by Michael Alan Kosecoff and published by . This book was released on 1975 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-Linear Elastic Deformations

Author : R. W. Ogden
Publisher : Courier Corporation
ISBN 13 : 0486318710
Total Pages : 562 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Non-Linear Elastic Deformations by : R. W. Ogden

Download or read book Non-Linear Elastic Deformations written by R. W. Ogden and published by Courier Corporation. This book was released on 2013-04-26 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

Nonlinear Elasticity

Author : Y. B. Fu
Publisher : Cambridge University Press
ISBN 13 : 0521796954
Total Pages : 541 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Nonlinear Elasticity by : Y. B. Fu

Download or read book Nonlinear Elasticity written by Y. B. Fu and published by Cambridge University Press. This book was released on 2001-05-07 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction to nonlinear elasticity for graduates and researchers, covering new developments in the field.

Non-Linear Theory of Elasticity and Optimal Design

Author : L.W. Ratner
Publisher : Elsevier
ISBN 13 : 008053760X
Total Pages : 281 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Non-Linear Theory of Elasticity and Optimal Design by : L.W. Ratner

Download or read book Non-Linear Theory of Elasticity and Optimal Design written by L.W. Ratner and published by Elsevier. This book was released on 2003-11-12 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it can be done only with a destructive test for each structure. For building and explaining the theory, a new logical structure was introduced as the basis of the theory. One of the important physical implications of this logic is that it describes mathematically the universal domain of the possible stable physical relations.

Nonlinear Theory Of Elasticity: Applications In Biomechanics

Author : Larry A Taber
Publisher : World Scientific
ISBN 13 : 9814483397
Total Pages : 417 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Nonlinear Theory Of Elasticity: Applications In Biomechanics by : Larry A Taber

Download or read book Nonlinear Theory Of Elasticity: Applications In Biomechanics written by Larry A Taber and published by World Scientific. This book was released on 2004-02-19 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soft biological tissues often undergo large (nearly) elastic deformations that can be analyzed using the nonlinear theory of elasticity. Because of the varied approaches to nonlinear elasticity in the literature, some aspects of the subject may be difficult to appreciate. This book attempts to clarify and unify those treatments, illustrating the advantages and disadvantages of each through various examples in the mechanics of soft tissues. Applications include muscle, arteries, the heart, and embryonic tissues.

Variational Methods in Nonlinear Elasticity

Author : Pablo Pedregal
Publisher : SIAM
ISBN 13 : 9780898719529
Total Pages : 110 pages
Book Rating : 4.7/5 (195 download)

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Book Synopsis Variational Methods in Nonlinear Elasticity by : Pablo Pedregal

Download or read book Variational Methods in Nonlinear Elasticity written by Pablo Pedregal and published by SIAM. This book was released on 2000-01-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Elasticity

Author : R. W. Dickey
Publisher : Academic Press
ISBN 13 : 1483264793
Total Pages : 415 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Nonlinear Elasticity by : R. W. Dickey

Download or read book Nonlinear Elasticity written by R. W. Dickey and published by Academic Press. This book was released on 2014-05-10 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Elasticity presents a description of research and result on various nonlinear problems arising in elasticity. This book covers a variety of topics, including shallow elastic membranes, nonlinear elasticity, finite deformations of elastic solids, and nonlinear thermoelasticity. Organized into 11 chapters, this book begins with an overview of the nonlinear theory of buckling of elastic shells. This text then examines the ways in which the energy criterion supplies a necessary condition for asymptotic stability. Other chapters consider some of the phenomena, both physical and mathematical, that typify the large deformation of a nonlinearly elastic body. This book discusses as well the concepts leading to a criterion for instabilities and discusses how the criterion applies to some well-known ideal materials. The final chapter deals with the structure of strong shocks and studies the evolution of such a shock produced by a suddenly-applied strain. This book is a valuable resource for mathematicians.

Contact Problems in Elasticity

Author : N. Kikuchi
Publisher : SIAM
ISBN 13 : 9781611970845
Total Pages : 508 pages
Book Rating : 4.9/5 (78 download)

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Book Synopsis Contact Problems in Elasticity by : N. Kikuchi

Download or read book Contact Problems in Elasticity written by N. Kikuchi and published by SIAM. This book was released on 1988-01-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.

Nonlinear Mesoscopic Elasticity

Author : Robert A. Guyer
Publisher : John Wiley & Sons
ISBN 13 : 3527407030
Total Pages : 410 pages
Book Rating : 4.5/5 (274 download)

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Book Synopsis Nonlinear Mesoscopic Elasticity by : Robert A. Guyer

Download or read book Nonlinear Mesoscopic Elasticity written by Robert A. Guyer and published by John Wiley & Sons. This book was released on 2009-09-28 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook brings together a great deal of new data on the static and dynamic elastic properties of granular and other composite material. The authors are at the very center of today's research and present new and imported theoretical tools that have enabled our current understanding of the complex behavior of rocks. There are three central themes running throughout the presentation: · Rocks as the prototypical material for defining a class of materials · The PM space model as a useful theoretical construct for developing a phenomenology · A sequence of refined analysis methods. This suite of new methods for both recording and analyzing data is more than a single framework for interpretation, it is also a toolbox for the experimenter. A comprehensive and systematic book of utmost interest to anybody involved in non-destructive testing, civil engineering, and geophysics.

Nonlinear Problems of Elasticity

Author : S.S Antman
Publisher : Springer
ISBN 13 : 9781475741483
Total Pages : 752 pages
Book Rating : 4.7/5 (414 download)

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Book Synopsis Nonlinear Problems of Elasticity by : S.S Antman

Download or read book Nonlinear Problems of Elasticity written by S.S Antman and published by Springer. This book was released on 2012-12-22 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Problems of Non-linear Elasticity

Author : Clifford Truesdell
Publisher :
ISBN 13 :
Total Pages : 263 pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Problems of Non-linear Elasticity by : Clifford Truesdell

Download or read book Problems of Non-linear Elasticity written by Clifford Truesdell and published by . This book was released on with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Large Elastic Deformations

Author : Albert Edward Green
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Large Elastic Deformations by : Albert Edward Green

Download or read book Large Elastic Deformations written by Albert Edward Green and published by Oxford University Press, USA. This book was released on 1970 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Problems of Elasticity

Author : Stuart S. Antman
Publisher :
ISBN 13 : 9783540941996
Total Pages : 750 pages
Book Rating : 4.9/5 (419 download)

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Book Synopsis Nonlinear Problems of Elasticity by : Stuart S. Antman

Download or read book Nonlinear Problems of Elasticity written by Stuart S. Antman and published by . This book was released on 1995-01-01 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Problems of Non-linear Elasticity

Author : Clifford Truesdell
Publisher :
ISBN 13 :
Total Pages : 284 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Problems of Non-linear Elasticity by : Clifford Truesdell

Download or read book Problems of Non-linear Elasticity written by Clifford Truesdell and published by . This book was released on 1965 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Problems of Elasticity

Author : Stuart S. Antman
Publisher : Springer
ISBN 13 : 9783031313295
Total Pages : 0 pages
Book Rating : 4.3/5 (132 download)

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Book Synopsis Nonlinear Problems of Elasticity by : Stuart S. Antman

Download or read book Nonlinear Problems of Elasticity written by Stuart S. Antman and published by Springer. This book was released on 2023-08-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : S.S Antman
Publisher : Springer
ISBN 13 : 9780387501024
Total Pages : 0 pages
Book Rating : 4.5/5 (1 download)

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Book Synopsis Nonlinear Problems of Elasticity by : S.S Antman

Download or read book Nonlinear Problems of Elasticity written by S.S Antman and published by Springer. This book was released on 2012-02-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.