Nonlinear Theory Of Elasticity
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Nonlinear Theory Of Elasticity
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Author : Larry Alan Taber
language : en
Publisher: World Scientific
Release Date : 2004
Nonlinear Theory Of Elasticity written by Larry Alan Taber and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
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.
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 Theory Of Dislocations And Disclinations In Elastic Bodies
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Author : Leonid M. Zubov
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-10-10
Nonlinear Theory Of Dislocations And Disclinations In Elastic Bodies written by Leonid M. Zubov 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 1997-10-10 with Mathematics categories.
The author applies methods of nonlinear elasticity to the investigation of the defects in the crystal structure of solids such as dislocations and disclinations. These defects characterize mainly the plastic and strength properties of many constructional materials. Contrary to the well-developed nonlinear continual theory of dislocations continuously distributed in the body, which is based on geometrical ideas, the nonlinear analysis of isolated dislocations and disclinations is less developed; it is given for the first time in this book. This analysis is essential since the deformation near the axes of an isolated defect is rather big, so the linear theory is not applicable here. The general theory of Volterra's dislocations in elastic media under large deformations is developed. A number of exact solutions of the problems are found. The nonlinear approach to investigating the isolated defects produces the results that often differ qualitatively from those of the linear theory. The book addresses students and researchers.
Foundations Of The Nonlinear Theory Of Elasticity
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Author : V. V. Novozhilov
language : en
Publisher: Courier Corporation
Release Date : 1999-01-01
Foundations Of The Nonlinear Theory Of Elasticity written by V. V. Novozhilov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Technology & Engineering categories.
This is an essential book for students and academicians alike. In addition to discussing theory, topics include the connection between stresses and strains in an isotropic elastic body, the geometry of strain, and much more. Deductions are explained in the simplest, most intuitive manner for wide accessibility. 1953 edition.
Linear Theories Of Elasticity And Thermoelasticity
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Author : Clifford Truesdell
language : en
Publisher: Springer
Release Date : 2013-12-17
Linear Theories Of Elasticity And Thermoelasticity written by Clifford Truesdell and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-17 with Technology & Engineering categories.
Non Linear Elastic Deformations
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Author : R. W. Ogden
language : en
Publisher: Courier Corporation
Release Date : 2013-04-26
Non Linear Elastic Deformations written by R. W. Ogden and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-26 with Technology & Engineering categories.
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.
The Linearized Theory Of Elasticity
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Author : William S. Slaughter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Linearized Theory Of Elasticity written by William S. Slaughter 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 2012-12-06 with Technology & Engineering categories.
This book is derived from notes used in teaching a first-year graduate-level course in elasticity in the Department of Mechanical Engineering at the University of Pittsburgh. This is a modern treatment of the linearized theory of elasticity, which is presented as a specialization of the general theory of continuum mechanics. It includes a comprehensive introduction to tensor analysis, a rigorous development of the governing field equations with an emphasis on recognizing the assumptions and approximations in herent in the linearized theory, specification of boundary conditions, and a survey of solution methods for important classes of problems. Two- and three-dimensional problems, torsion of noncircular cylinders, variational methods, and complex variable methods are covered. This book is intended as the text for a first-year graduate course in me chanical or civil engineering. Sufficient depth is provided such that the text can be used without a prerequisite course in continuum mechanics, and the material is presented in such a way as to prepare students for subsequent courses in nonlinear elasticity, inelasticity, and fracture mechanics. Alter natively, for a course that is preceded by a course in continuum mechanics, there is enough additional content for a full semester of linearized elasticity.
Foundations Of The Nonlinear Theory Of Elasticity
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Author : V. V. Novožilov
language : en
Publisher:
Release Date : 1953
Foundations Of The Nonlinear Theory Of Elasticity written by V. V. Novožilov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with categories.
Theory Of Elasticity
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Author : A.I. Lurie
language : en
Publisher: Springer
Release Date : 2005-03-30
Theory Of Elasticity written by A.I. Lurie and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-30 with Technology & Engineering categories.
The classical theory of elasticity maintains a place of honour in the science ofthe behaviour ofsolids. Its basic definitions are general for all branches of this science, whilst the methods forstating and solving these problems serve as examples of its application. The theories of plasticity, creep, viscoelas ticity, and failure of solids do not adequately encompass the significance of the methods of the theory of elasticity for substantiating approaches for the calculation of stresses in structures and machines. These approaches constitute essential contributions in the sciences of material resistance and structural mechanics. The first two chapters form Part I of this book and are devoted to the basic definitions ofcontinuum mechanics; namely stress tensors (Chapter 1) and strain tensors (Chapter 2). The necessity to distinguish between initial and actual states in the nonlinear theory does not allow one to be content with considering a single strain measure. For this reason, it is expedient to introduce more rigorous tensors to describe the stress-strain state. These are considered in Section 1.3 for which the study of Sections 2.3-2.5 should precede. The mastering of the content of these sections can be postponed until the nonlinear theory is studied in Chapters 8 and 9.
Theory Of Elasticity
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Author : A.I. Lurie
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-30
Theory Of Elasticity written by A.I. Lurie 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 2010-05-30 with Technology & Engineering categories.
The classical theory of elasticity maintains a place of honour in the science ofthe behaviour ofsolids. Its basic definitions are general for all branches of this science, whilst the methods forstating and solving these problems serve as examples of its application. The theories of plasticity, creep, viscoelas ticity, and failure of solids do not adequately encompass the significance of the methods of the theory of elasticity for substantiating approaches for the calculation of stresses in structures and machines. These approaches constitute essential contributions in the sciences of material resistance and structural mechanics. The first two chapters form Part I of this book and are devoted to the basic definitions ofcontinuum mechanics; namely stress tensors (Chapter 1) and strain tensors (Chapter 2). The necessity to distinguish between initial and actual states in the nonlinear theory does not allow one to be content with considering a single strain measure. For this reason, it is expedient to introduce more rigorous tensors to describe the stress-strain state. These are considered in Section 1.3 for which the study of Sections 2.3-2.5 should precede. The mastering of the content of these sections can be postponed until the nonlinear theory is studied in Chapters 8 and 9.