Download or read book Some Uniqueness Theorems in the Theory of Elasticity written by James H. Bramble and published by . This book was released on 1961 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Uniqueness Theorems in Linear Elasticity written by Robin J. Knops and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On Some New Continuation Formulas and Uniqueness Theorems in the Theory of Elasticity written by James H. Bramble and published by . This book was released on 1960 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: New formulas for the continuation of the solution to the equations of elasticity across a spherical boundary are obtained. In addition to certain new boundary value problems in elasticity are considered.
Download or read book Boundary Value Problems of Finite Elasticity written by Tullio Valent and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear Theories of Elasticity and Thermoelasticity written by Clifford Truesdell and published by Springer. This book was released on 2013-12-17 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Basic Problems of the Mathematical Theory of Elasticity written by N.I. Muskhelishvili and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topics in Finite Elasticity written by Morton E. Gurtin and published by SIAM. This book was released on 1981-01-01 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Uniqueness Theorem in the Linear Theory of Elasticity with Microstructure written by Warren S. Edelstein and published by . This book was released on 1968 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that in the Mindlin theory of elastic materials with microstructure, uniqueness holds for the traction, the displacement, and a wide variety of mixed problems, provided the potential energy function W is homogeneous of order two. (Author).
Download or read book Mathematical Theory of Elastic Equilibrium written by Giuseppe Grioli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Trends in Applications of Mathematics to Mechanics written by Gerard Iooss and published by CRC Press. This book was released on 1999-10-22 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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:
Download or read book Elastic And Inelastic Stress Analysis written by Irving H Shames and published by CRC Press. This book was released on 1997-02-01 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting certain key aspects of inelastic solid mechanics centered around viscoelasticity, creep, viscoplasticity, and plasticity, this text is conveniently divided into three parts. The sections focus on the fundamentals of elasticity, useful constitutive laws, and applications to simple structural members. The book provides extended treatment of basic problems in static structural mechanics, including elastic and inelastic effects. It contains worked-out examples and end-of-chapter problems to clarify concepts.
Download or read book Thermal Stresses Advanced Theory and Applications written by Richard B. Hetnarski and published by Springer Science & Business Media. This book was released on 2008-11-23 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book U S Government Research Reports written by and published by . This book was released on 1964 with total page 2180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Technical Abstract Bulletin written by Defense Documentation Center (U.S.) and published by . This book was released on 1961-10 with total page 1540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Collected Papers of R S Rivlin written by Grigory I. Barenblatt and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 2868 pages. Available in PDF, EPUB and Kindle. Book excerpt: R.S. Rivlin is one of the principal architects of nonlinear continuum mechanics: His work on the mechanics of rubber (in the 1940s and 50s) established the basis of finite elasticity theory. These volumes make most of his scientific papers available again and show the full scope and significance of his contributions.
Download or read book Proceedings of the IUTAM Symposium on Finite Elasticity written by Donald E. Carlson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although finite elasticity theory has its roots in the nineteenth century, its development was largely neglected until the end of the Second World War. Since then it has attracted a substantial amount of attention and considerable progress has been made both in our understanding of the basis of the subject and in its applications. It occurred to me about three years ago that finite elasticity had reached a level of development at which an international symposium on the subject was overdue. Accordingly, with strong encouragement from Professor P. M. Naghdi and numerous other colleagues, I submitted to the International Union of Theoretical and Applied Mechanics a proposal for their support of such a symposium to be held at Lehigh University during the period August 10-15, 1980. The proposal received enthusiastic support from the International Union and an international scientific committee under my chairmanship, consisting of Professors G. Fichera (Rome), W. T. Koiter (Delft), L. I. Sedov (Moscow), and A. J. M. Spencer (Nottingham), was assigned responsibility for the scientific program. In constructing the program we aimed at as broad a coverage as possible of the many aspects of the subject on which significant progress is currently being made. These range from theoretical studies of existence and uniqueness of solutions of the governing equations of finite elasticity theory to experimental studies of its application to such problems as tear resistance and friction in vulcanized rubbers.
Download or read book Spectral Geometry and Inverse Scattering Theory written by Huaian Diao and published by Springer Nature. This book was released on 2023-10-31 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering problems are a vital subject for both theoretical and experimental studies and remain an active field of research in applied mathematics. This book provides a detailed presentation of typical setup of inverse scattering problems for time-harmonic acoustic, electromagnetic and elastic waves. Moreover, it provides systematical and in-depth discussion on an important class of geometrical inverse scattering problems, where the inverse problem aims at recovering the shape and location of a scatterer independent of its medium properties. Readers of this book will be exposed to a unified framework for analyzing a variety of geometrical inverse scattering problems from a spectral geometric perspective. This book contains both overviews of classical results and update-to-date information on latest developments from both a practical and theoretical point of view. It can be used as an advanced graduate textbook in universities or as a reference source for researchers in acquiring the state-of-the-art results in inverse scattering theory and their potential applications.
