Some Uniqueness Theorems in the Theory of Elasticity PDF Download
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Author: James H. Bramble
Publisher:
ISBN:
Category : Elasticity
Languages : en
Pages : 32
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Book Description
It is known that in the first boundary value problem of classical elasticity the range of values of Poisson's ratio for which the solution is unique may be extended to include values outside the range of physical interest. It is shown that certain other interesting boundary value problems in classical elasticity have unique solutions for an extended range of values of Poisson's ratio. Such results may prove useful in non-linear elasticity.
Author: James H. Bramble
Publisher:
ISBN:
Category : Elasticity
Languages : en
Pages : 32
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Book Description
It is known that in the first boundary value problem of classical elasticity the range of values of Poisson's ratio for which the solution is unique may be extended to include values outside the range of physical interest. It is shown that certain other interesting boundary value problems in classical elasticity have unique solutions for an extended range of values of Poisson's ratio. Such results may prove useful in non-linear elasticity.
Author: Robin J. Knops
Publisher: Springer Science & Business Media
ISBN: 3642651011
Category : Science
Languages : en
Pages : 140
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Book Description
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniqueness in elasticity theory in the hope that such an exposition will provide a convenient access to the literature while at the same time indicating what progress has been made and what problems still await solution. Naturally, the continuing announcement of new results thwarts any attempt to provide a complete assessment. Apart from linear elasticity theory itself, there are several other areas where elastic uniqueness is significant.
Author: Clifford Truesdell
Publisher: Springer
ISBN: 3662397765
Category : Technology & Engineering
Languages : en
Pages : 755
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Book Description
Author: Tullio Valent
Publisher: Springer Science & Business Media
ISBN: 146123736X
Category : Science
Languages : en
Pages : 201
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Book Description
In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be sides being quite spontaneous, allows us to consider a great many inter esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b], in order to obtain local existence and uniqueness for the traction problem in hyperelasticity under dead loads, inspired many of the ideas which led to this monograph. Chapter I aims to give a very brief introduction to some general concepts in the mathematical theory of elasticity, in order to show how the boundary value problems studied in the sequel arise. Chapter II is very technical; it supplies the framework for all sub sequent developments.
Author: N.I. Muskhelishvili
Publisher: Springer Science & Business Media
ISBN: 9789001607012
Category : Technology & Engineering
Languages : en
Pages : 774
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Book Description
TO THE FIRST ENGLISH EDITION. In preparing this translation, I have taken the liberty of including footnotes in the main text or inserting them in small type at the appropriate places. I have also corrected minor misprints without special mention .. The Chapters and Sections of the original text have been called Parts and Chapters respectively, where the latter have been numbered consecutively. The subject index was not contained in the Russian original and the authors' index represents an extension of the original list of references. In this way the reader should be able to find quickly the pages on which anyone reference is discussed. The transliteration problem has been overcome by printing the names of Russian authors and journals also in Russian type. While preparing this translation in the first place for my own informa tion, the knowledge that it would also become accessible to a large circle of readers has made the effort doubly worthwhile. I feel sure that the reader will share with me in my admiration for the simplicity and lucidity of presentation.
Author: Morton E. Gurtin
Publisher: SIAM
ISBN: 9781611970340
Category : Technology & Engineering
Languages : en
Pages : 63
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Book Description
Finite elasticity is a theory of elastic materials that are capable of undergoing large deformations. This theory is inherently nonlinear and is mathematically quite complex. This monograph presents a derivation of the basic equations of the theory, a discussion of the general boundary-value problems, and a treatment of several interesting and important special topics such as simple shear, uniqueness, the tensile deformations of a cube, and antiplane shear. The monograph is intended for engineers, physicists, and mathematicians.
Author: Giuseppe Grioli
Publisher: Springer Science & Business Media
ISBN: 3642874320
Category : Mathematics
Languages : en
Pages : 177
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Book Description
It is not my intention to present a treatise of elasticity in the follow ing pages. The size of the volume would not permit it, and, on the other hand, there are already excellent treatises. Instead, my aim is to develop some subjects not considered in the best known treatises of elasticity but nevertheless basic, either from the physical or the analytical point of view, if one is to establish a complete theory of elasticity. The material presented here is taken from original papers, generally very recent, and concerning, often, open questions still being studied by mathematicians. Most of the problems are from the theory of finite deformations [non-linear theory], but a part of this book concerns the theory of small deformations [linear theory], partly for its interest in many practical questions and partly because the analytical study of the theory of finite strain may be based on the infinitesimal one.
Author: Gerard Iooss
Publisher: CRC Press
ISBN: 9781584880356
Category : Mathematics
Languages : en
Pages : 340
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Book Description
The International Society for the Interaction of Mechanics and Mathematics has a long-standing and respected tradition of hosting symposia that provide a forum for disseminating new developments and methods. Trends in Applications of Mathematics to Mechanics represents the proceedings of the eleventh such symposium, held at the University of Nice in May 1998. Comprising invited lectures and refereed papers, this volume includes recent results that open perspectives on fields in mechanics and their methodological counterparts in mathematics. It also surveys important advances in the areas where mathematics and mechanics interact. The applications addressed include:
Author: Irving H Shames
Publisher: CRC Press
ISBN: 1560326867
Category : Science
Languages : en
Pages : 740
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Book Description
Presents certain key aspects of inelastic solid mechanics centered around viscoelasticity, creep, viscoplasticity, and plasticity. It is divided into three parts consisting of the fundamentals of elasticity, useful constitutive laws, and applications to simple structural members, providing extended treatment of basic problems in static structural mechanics, including elastic and inelastic effects. It contains worked-out examples and end-of-chapter problems.
Author: Richard B. Hetnarski
Publisher: Springer Science & Business Media
ISBN: 1402092474
Category : Technology & Engineering
Languages : en
Pages : 579
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Book Description
The authors are pleased to present Thermal Stresses – Advanced Theory and Applications. This book will serve a wide range of readers, in particular, gr- uate students, PhD candidates, professors, scientists, researchers in various industrial and government institutes, and engineers. Thus, the book should be considered not only as a graduate textbook, but also as a reference handbook to those working or interested in areas of Applied Mathematics, Continuum Mechanics, Stress Analysis, and Mechanical Design. In addition, the book p- vides extensive coverage of great many theoretical problems and numerous references to the literature. The ?eld of Thermal Stresses lies at the crossroads of Stress Analysis, T- ory of Elasticity, Thermodynamics, Heat Conduction Theory, and advanced methods of Applied Mathematics. Each of these areas is covered to the extend it is necessary. Therefore, the book is self-contained, so that the reader should not need to consult other sources while studying the topic. The book starts from basic concepts and principles, and these are developed to more advanced levels as the text progresses. Nevertheless, some basic preparation on the part of the reader in Classical Mechanics, Stress Analysis, and Mathematics, - cluding Vector and Cartesian Tensor Analysis is expected. While selecting material for the book, the authors made every e?ort to present both classical topics and methods, and modern, or more recent, dev- opments in the ?eld. The book comprises ten chapters.
