Boundary Integral Equations In Elasticity Theory
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Boundary Integral Equations In Elasticity Theory
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Author : A.M. Linkov
language : en
Publisher: Springer
Release Date : 2014-03-14
Boundary Integral Equations In Elasticity Theory written by A.M. Linkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-14 with Science categories.
by the author to the English edition The book aims to present a powerful new tool of computational mechanics, complex variable boundary integral equations (CV-BIE). The book is conceived as a continuation of the classical monograph by N. I. Muskhelishvili into the computer era. Two years have passed since the Russian edition of the present book. We have seen growing interest in numerical simulation of media with internal structure, and have evidence of the potential of the new methods. The evidence was especially clear in problems relating to multiple grains, blocks, cracks, inclusions and voids. This prompted me, when preparing the English edition, to place more emphasis on such topics. The other change was inspired by Professor Graham Gladwell. It was he who urged me to abridge the chain of formulae and to increase the number of examples. Now the reader will find more examples showing the potential and advantages of the analysis. The first chapter of the book contains a simple exposition of the theory of real variable potentials, including the hypersingular potential and the hypersingular equations. This makes up for the absence of such exposition in current textbooks, and reveals important links between the real variable BIE and the complex variable counterparts. The chapter may also help readers who are learning or lecturing on the boundary element method.
Boundary Integral Equations In Elasticity Theory
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Author : A.M. Linkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-30
Boundary Integral Equations In Elasticity Theory written by A.M. Linkov 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 2002-04-30 with Science categories.
by the author to the English edition The book aims to present a powerful new tool of computational mechanics, complex variable boundary integral equations (CV-BIE). The book is conceived as a continuation of the classical monograph by N. I. Muskhelishvili into the computer era. Two years have passed since the Russian edition of the present book. We have seen growing interest in numerical simulation of media with internal structure, and have evidence of the potential of the new methods. The evidence was especially clear in problems relating to multiple grains, blocks, cracks, inclusions and voids. This prompted me, when preparing the English edition, to place more emphasis on such topics. The other change was inspired by Professor Graham Gladwell. It was he who urged me to abridge the chain of formulae and to increase the number of examples. Now the reader will find more examples showing the potential and advantages of the analysis. The first chapter of the book contains a simple exposition of the theory of real variable potentials, including the hypersingular potential and the hypersingular equations. This makes up for the absence of such exposition in current textbooks, and reveals important links between the real variable BIE and the complex variable counterparts. The chapter may also help readers who are learning or lecturing on the boundary element method.
Boundary Integral Equations
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Author : George C. Hsiao
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-07
Boundary Integral Equations written by George C. Hsiao 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 2008-05-07 with Mathematics categories.
This book is devoted to the mathematical foundation of boundary integral equations. The combination of ?nite element analysis on the boundary with these equations has led to very e?cient computational tools, the boundary element methods (see e.g., the authors [139] and Schanz and Steinbach (eds.) [267]). Although we do not deal with the boundary element discretizations in this book, the material presented here gives the mathematical foundation of these methods. In order to avoid over generalization we have con?ned ourselves to the treatment of elliptic boundary value problems. The central idea of eliminating the ?eld equations in the domain and - ducing boundary value problems to equivalent equations only on the bou- ary requires the knowledge of corresponding fundamental solutions, and this idea has a long history dating back to the work of Green [107] and Gauss [95, 96]. Today the resulting boundary integral equations still serve as a major tool for the analysis and construction of solutions to boundary value problems.
Boundary Integral Equations On Contours With Peaks
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Author : Vladimir Maz'ya
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-08
Boundary Integral Equations On Contours With Peaks written by Vladimir Maz'ya 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 2010-01-08 with Mathematics categories.
This book is a comprehensive exposition of the theory of boundary integral equations for single and double layer potentials on curves with exterior and interior cusps. Three chapters cover harmonic potentials, and the final chapter treats elastic potentials.
The Integral Equations Of The Theory Of Elasticity
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Author : N. F. Morozov
language : de
Publisher: Vieweg+Teubner Verlag
Release Date : 2014-04-18
The Integral Equations Of The Theory Of Elasticity written by N. F. Morozov and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-18 with Technology & Engineering categories.
It was the last book the outstanding mathematician, mechanician and lecturer S. G. Mikhlin took an active part in writing. Having been completed during his lifetime, this book could not be published in Russia due to well know difficulties. Since that time new results in integral equations of elasticity theory have appeared. The works of W. Wendland and his school on numerical methods of solving boundary integral equations, the works of I. Chudinovich on inves tigation of non-stationary integral equations, the works of S. Kuznetsov con nected with the construction of the fundamental solutions for anisotropic me dia and others deserve special mentioning. The authors recognize that though the book is devoted to integral equations of elasticity theory, its contents do not cover all possible directions in this field. So the book does not contain the investigations of pseudo-differential equations of three-dimensional prob lems of elasticity theory, connected with the works of R. Goldstein, I. Klein, G. Eskin; the questions of solving by integral transformations (I. Ufland, L. Slepian, B. Buda. e:v); the theory of symbols of pseudo-differential operators on non-smooth surfaces developed in the works of B. Plamenevski et al. and the new methods of numerical solution of pseudo-differential equations as developed by a school of V. Mazya. The present book gives the classical methods of potential theory in elas ticity and their development and also the solution of a number of problems which here are published in English for the first time.
On Solvability Of Boundary Integral Equations Of Elasticity Theory In Domains With Inward Peaks
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Author : Vladimir G. Mazʹja
language : en
Publisher:
Release Date : 1993
On Solvability Of Boundary Integral Equations Of Elasticity Theory In Domains With Inward Peaks written by Vladimir G. Mazʹja and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Toeplitz Matrices And Singular Integral Equations
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Author : Albrecht Böttcher
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Toeplitz Matrices And Singular Integral Equations written by Albrecht Böttcher and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts. The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications. The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory.
Integral Equations In Elasticity
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Author : Vladimir Zalmanovich Parton
language : en
Publisher:
Release Date : 1982
Integral Equations In Elasticity written by Vladimir Zalmanovich Parton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Boundary value problems categories.
Stationary Oscillations Of Elastic Plates
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Author : Gavin R. Thomson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Stationary Oscillations Of Elastic Plates written by Gavin R. Thomson 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 2011-06-28 with Mathematics categories.
Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations. Stationary Oscillations of Elastic Plates studies the latter in the context of stationary vibrations of thin elastic plates. The techniques presented here reduce the complexity of classical elasticity to a system of two independent variables, modeling problems of flexural-vibrational elastic body deformation with the aid of eigenfrequencies and simplifying them to manageable, uniquely solvable integral equations. The book is intended for an audience with a knowledge of advanced calculus and some familiarity with functional analysis. It is a valuable resource for professionals in pure and applied mathematics, and for theoretical physicists and mechanical engineers whose work involves elastic plates. Graduate students in these fields can also benefit from the monograph as a supplementary text for courses relating to theories of elasticity or flexural vibrations.
Boundary Elements Theory And Applications
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Author : John T. Katsikadelis
language : en
Publisher: Elsevier
Release Date : 2002-05-28
Boundary Elements Theory And Applications written by John T. Katsikadelis and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-28 with Technology & Engineering categories.
The author's ambition for this publication was to make BEM accessible to the student as well as to the professional engineer. For this reason, his maintask was to organize and present the material in such a way so that the book becomes "user-friendly" and easy to comprehend, taking into account only the mathematics and mechanics to which students have been exposed during their undergraduate studies. This effort led to an innovative, in many aspects, way of presentingBEM, including the derivation of fundamental solutions, the integral representation of the solutions and the boundary integral equations for various governing differentialequations in a simple way minimizing a recourse to mathematics with which the student is not familiar. The indicial and tensorial notations, though they facilitate the author's work and allow to borrow ready to use expressions from the literature, have been avoided in the present book. Nevertheless, all the necessary preliminary mathematical concepts have been included in order to make the book complete and self-sufficient.Throughout the book, every concept is followed by example problems, which have been worked out in detail and with all the necessary clarifications. Furthermore, each chapter of the book is enriched with problems-to-solve. These problems serve a threefold purpose. Some of them are simple and aim at applying and better understanding the presented theory, some others are more difficult and aim at extending the theory to special cases requiring a deeper understanding of the concepts, and others are small projects which serve the purpose of familiarizing the student with BEM programming and the programs contained in the CD-ROM.The latter class of problems is very important as it helps students to comprehend the usefulness and effectiveness of the method by solving real-life engineering problems. Through these problems students realize that the BEM is a powerful computational tool and not an alternative theoretical approach for dealing with physical problems. My experience in teaching BEM shows that this is the students' most favorite type of problems. They are delighted to solve them, since they integrate their knowledge and make them feel confident in mastering BEM.The CD-ROM which accompanies the book contains the source codes of all the computer programs developed in the book, so that the student or the engineer can use them for the solution of a broad class of problems. Among them are general potential problems, problems of torsion, thermal conductivity,deflection of membranes and plates, flow of incompressible fluids, flow through porous media, in isotropic or anisotropic, homogeneous or composite bodies, as well as plane elastostatic problems in simply or multiply connected domains. As one can readily find out from the variety of the applications, the book is useful for engineers of all disciplines. The author is hopeful that the present book will introduce the reader to BEM in an easy, smooth and pleasant way and also contribute to itsdissemination as a modern robust computational tool for solving engineering problems.