Mathematical Theory In Periodic Plane Elasticity

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Mathematical Theory In Periodic Plane Elasticity

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Author : Hai-Tao Cai
language : en
Publisher: CRC Press
Release Date : 2000-07-06

Mathematical Theory In Periodic Plane Elasticity written by Hai-Tao Cai and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-06 with Mathematics categories.

Presenting the mathematical theory of period problems in plane elasticity by methods of complex variables. The most general formulations of such problems are proposed under the assumption that the stresses are periodic and the displacements are quasi-periodic. The general expression of complex displacements are illustrated. Periodic welding problems are studied by reducing them to periodic Riemann boundary value problems. Various periodic problems of the elastic half-plane (fundamental problems, contact problems) are treated and solved by reduction to Riemann-Hilbert boundary value problems with discontinuous coefficient. Periodic crack problems are investigated which are transferred to singular integral equations whose unique solvability is guaranteed.

Boundary Integral Equations In Elasticity Theory

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Author : A.M. Linkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

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 2013-11-11 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.

Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications

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Author : Tian-You Fan
language : en
Publisher: Springer
Release Date : 2016-09-20

Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications written by Tian-You Fan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-20 with Science categories.

This interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket method and its application in deriving hydrodynamic equations. These new sections make the book an even more useful and comprehensive reference guide for researchers working in Condensed Matter Physics, Chemistry and Materials Science.

Perspectives In Mathematical Sciences

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Author : Yisong Yang
language : en
Publisher: World Scientific
Release Date : 2010-01-18

Perspectives In Mathematical Sciences written by Yisong Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-18 with Science categories.

Mathematical sciences have been playing an increasingly important role in modern society. They are in high demand for investigating complex problems in physical science, environmental and geophysical sciences, materials science, life science and chemical sciences.This is a review volume on some timely and interesting topics in applied mathematical sciences. It surveys new developments and presents some future research directions in these topics. The chapters are written by experts in these fields, with a wide audience in mind and hence will be accessible to graduate students, junior researchers and other professionals who are interested in the subjects. The contributions of Professor Youzhong Guo, a leading expert in these areas, will be celebrated. His life and academic achievements are highlighted in the Preface and Postscript of the book. The underlying theme that binds the various chapters seamlessly is a set of dedicated ideas and techniques from partial differential equations and dynamical systems.

Complex Variable Methods In Plane Elasticity

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Author : Jian-ke Lu
language : en
Publisher: World Scientific
Release Date : 1995-09-30

Complex Variable Methods In Plane Elasticity written by Jian-ke Lu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-30 with Mathematics categories.

This book deals systematically with the mathematical theory of plane elasto-statics by using complex variable methods, together with many results originated by the author. The problems considered are reduced to integral equations, Fredholem or singular, which are rigorously proved to be uniquely solvable. Particular attention is paid to the subjects of crack problems in the quite general case, especially those of composite media, which are solved by a unified method. The methods used in this book are constructive so that they may be used in practice.

Fundamentals Of Structural Optimization

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Author : Vladimir Kobelev
language : en
Publisher: Springer Nature
Release Date : 2023-12-01

Fundamentals Of Structural Optimization written by Vladimir Kobelev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-01 with Technology & Engineering categories.

This book serves as a complementary resource to the courses "Advanced structural optimization" and "Structural optimization in automotive engineering" taught by the author at the University of Siegen, North-Rhine-Westphalia, Germany since 2001. Focusing on optimization problems in the field of structural engineering, this book offers a rigorous and analytical approach to problem-solving. Each chapter of the book begins with a brief overview of classical results and the derivation of governing equations. The solutions to optimization problems are then presented in a closed form, with the author guiding readers through several analytical methods for solving stability and contact tasks. Throughout the book, the author takes care to ensure that even readers without extensive experience in numerical computations can understand the conclusion of each relation. The book features several basic optimization problems, selected from a large pool of previously solvedproblems, with a particular emphasis on the unique features of optimization problems. By presenting analytical solutions, readers can better understand other known optimization problems and gain the skills needed to independently set and solve new problems. With its comprehensive and rigorous approach to problem-solving, this book is sure to enhance the reader's understanding of the field and equip them with the skills needed to tackle new challenges.

Approximate Methods And Numerical Analysis For Elliptic Complex Equation

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Author : Guo Chun Wen
language : en
Publisher: CRC Press
Release Date : 1999-06-11

Approximate Methods And Numerical Analysis For Elliptic Complex Equation written by Guo Chun Wen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-11 with Mathematics categories.

Numerical methods for elliptic partial differential equations have been the subject of many books in recent years, but few have treated the subject of complex equations. In this important new book, the author introduces the theory of, and approximate methods for, nonlinear elliptic complex equations in multiple connected domains. Constructive methods are systematically applied to proper boundary value problems which include very general boundary conditions. Approximate and numerical methods, such as the Newton imbedding method, the continuity method, the finite element method, the difference method and the boundary integral method, as well as their applications, are discussed in detail. The book will be of interest to all scientists studying the theory or applications of complex analysis.

Constructive Methods For Linear And Nonlinear Boundary Value Problems For Analytic Functions

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Author : v Mityushev
language : en
Publisher: CRC Press
Release Date : 1999-11-29

Constructive Methods For Linear And Nonlinear Boundary Value Problems For Analytic Functions written by v Mityushev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-29 with Mathematics categories.

Constructive methods developed in the framework of analytic functions effectively extend the use of mathematical constructions, both within different branches of mathematics and to other disciplines. This monograph presents some constructive methods-based primarily on original techniques-for boundary value problems, both linear and nonlinear. From among the many applications to which these methods can apply, the authors focus on interesting problems associated with composite materials with a finite number of inclusions. How far can one go in the solutions of problems in nonlinear mechanics and physics using the ideas of analytic functions? What is the difference between linear and nonlinear cases from the qualitative point of view? What kinds of additional techniques should one use in investigating nonlinear problems? Constructive Methods for Linear and Nonlinear Boundary Value Problems serves to answer these questions, and presents many results to Westerners for the first time. Among the most interesting of these is the complete solution of the Riemann-Hilbert problem for multiply connected domains. The results offered in Constructive Methods for Linear and Nonlinear Boundary Value Problems are prepared for direct application. A historical survey along with background material, and an in-depth presentation of practical methods make this a self-contained volume useful to experts in analytic function theory, to non-specialists, and even to non-mathematicians who can apply the methods to their research in mechanics and physics.

Integral Equations Boundary Value Problems And Related Problems

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Author : Xing Li
language : en
Publisher: World Scientific
Release Date : 2013-03-07

Integral Equations Boundary Value Problems And Related Problems written by Xing Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Mathematics categories.

In this volume, we report new results about various theories and methods of integral equation, boundary value problems for partial differential equations and functional equations, and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theories and methods for inverse problems of mathematical physics, Clifford analysis and related problems.

An Elementary Treatise On The Mathematical Theory Of Perfectly Elastic Solids

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Author : William John Ibbetson
language : en
Publisher:
Release Date : 1887

An Elementary Treatise On The Mathematical Theory Of Perfectly Elastic Solids written by William John Ibbetson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1887 with Curvilinear coordinates categories.