The Integral Equations Of The Theory Of Elasticity
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The Integral Equations Of The Theory Of Elasticity
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Author : N. F. Morozov
language : de
Publisher: Springer-Verlag
Release Date : 2013-11-21
The Integral Equations Of The Theory Of Elasticity written by N. F. Morozov and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Technology & Engineering categories.
The Integral Equations Of The Theory Of Elasticity
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Author : S. G. Mikhlin
language : en
Publisher: Vieweg+teubner Verlag
Release Date : 1995
The Integral Equations Of The Theory Of Elasticity written by S. G. Mikhlin 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 1995 with Mathematics categories.
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.
Integral Equation Methods For Electromagnetic And Elastic Waves
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Author : Weng Cho Chew
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2009
Integral Equation Methods For Electromagnetic And Elastic Waves written by Weng Cho Chew and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Elastic waves categories.
Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms
Boundary Integral Equations
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Author : George C. Hsiao
language : en
Publisher: Springer Nature
Release Date : 2021-03-26
Boundary Integral Equations written by George C. Hsiao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-26 with Mathematics categories.
This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.
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.
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.
Integral Equations
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Author : S. G. Mikhlin
language : en
Publisher: Elsevier
Release Date : 2014-07-22
Integral Equations written by S. G. Mikhlin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-22 with Mathematics categories.
Integral Equations: And their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Second Revised Edition contains an account of the general theory of Fredholm and Hilbert-Schmidt. This edition discusses methods of approximate solution of Fredholm's equation and, in particular, their application to the solution of basic problems in mathematical physics, including certain problems in hydrodynamics and the theory of elasticity. Other topics include the equations of Volterra type, determination of the first eigenvalue by Ritz's method, and systems of singular integral equations. The generalized method of Schwarz, convergence of successive approximations, stability of a rod in compression, and mixed problem of the theory of elasticity are also elaborated. This publication is recommended for mathematicians, students, and researchers concerned with singular integral equations.
Analysis Of Structures On Elastic Foundation
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Author : Levon G. Petrosian
language : en
Publisher: CRC Press
Release Date : 2022-06-12
Analysis Of Structures On Elastic Foundation written by Levon G. Petrosian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-12 with Technology & Engineering categories.
This book is devoted to the static and dynamic analysis of structures on elastic foundation. Through comprehensive analysis, the book shows analytical and mechanical relationships among classic and modern methods of solving boundary value problems. The book provides a wide spectrum of applications of modern techniques and methods of calculation of static and dynamic problems of engineering design. It pursues both methodological and practical purposes, and the accounting of all methods is accompanied by solutions of the specific problems, which are not merely illustrative in nature but may represent an independent interest in the study of various technical issues. Two special features of the book are the extensive use of the generalized functions for describing the impacts on structures and the substantiations of the methods of the apparatus of the generalized functions. The book illustrates modern methods for solving boundary-value problems of structural mechanics and soil mechanics based on the application of boundary equations. The book presents the philosophy of boundary equations and boundary element methods. A number of examples of solving different problems of static and dynamic calculation of structures on an elastic foundation are given according to the methods presented in the book. Introduces a general approach to the method of integral transforms based on the spectral theory of the linear differential operators. The Spectral Method of Boundary Element (SMBE) is developed based on using integral transforms with an orthogonal kernel in the extended domain. Presents a new, versatile foundation model with a number of advantages over the ground-based models currently used in practical calculations. Provides new transforms which will aid in solving various problems relevant to bars, beams, plates, and shells in particular for the structures on elastic foundation. Examines the methods of solving boundary-value problems typical for structural mechanics and related fields.
Adaptive Stochastic Methods
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Author : Dmitry G. Arseniev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-01-09
Adaptive Stochastic Methods written by Dmitry G. Arseniev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-09 with Mathematics categories.
This monograph develops adaptive stochastic methods in computational mathematics. The authors discuss the basic ideas of the algorithms and ways to analyze their properties and efficiency. Methods of evaluation of multidimensional integrals and solutions of integral equations are illustrated by multiple examples from mechanics, theory of elasticity, heat conduction and fluid dynamics. Contents Part I: Evaluation of Integrals Fundamentals of the Monte Carlo Method to Evaluate Definite Integrals Sequential Monte Carlo Method and Adaptive Integration Methods of Adaptive Integration Based on Piecewise Approximation Methods of Adaptive Integration Based on Global Approximation Numerical Experiments Adaptive Importance Sampling Method Based on Piecewise Constant Approximation Part II: Solution of Integral Equations Semi-Statistical Method of Solving Integral Equations Numerically Problem of Vibration Conductivity Problem on Ideal-Fluid Flow Around an Airfoil First Basic Problem of Elasticity Theory Second Basic Problem of Elasticity Theory Projectional and Statistical Method of Solving Integral Equations Numerically