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Boundary Integral Equations in Elasticity Theory

  • Book
  • © 2002

Overview

Authors:
  1. A. M. Linkov

    1. Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

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Part of the book series: Solid Mechanics and Its Applications (SMIA, volume 99)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    1. Introduction

      • A. M. Linkov
      Pages 1-6

  3. Method of Potentials

    1. Front Matter

      Pages 7-8
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    2. Real Potentials of Elasticity Theory

      • A. M. Linkov
      Pages 8-30

    3. Singular Solutions and Potentials in Complex Form

      • A. M. Linkov
      Pages 31-49

    4. Complex Integral Equations of the Indirect Approach

      • A. M. Linkov
      Pages 50-55

    5. Complex Integral Equations of the Direct Approach

      • A. M. Linkov
      Pages 56-70

  4. Methods Based on the Theory by Kolosov-Muskhelishvili

    1. Functions of Kolosov-Muskhelishvili and Holomorphicity Theorems

      • A. M. Linkov
      Pages 71-86

    2. Complex Variable Integral Equations

      • A. M. Linkov
      Pages 87-111

    3. Periodic Problems

      • A. M. Linkov
      Pages 112-127

    4. Doubly Periodic Problems

      • A. M. Linkov
      Pages 128-148

    5. Problems for Bonded Half-Panes and Circular Inclusion

      • A. M. Linkov
      Pages 149-165

  5. Theory of Complex Integral Equations

    1. Front Matter

      Pages 166-166
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    2. Complex Hypersingular and Finite-Part Integrals

      • A. M. Linkov
      Pages 167-180

    3. Complex Variable Hypersingular Integral Equations (CVH-BIE)

      • A. M. Linkov
      Pages 181-198

  6. Numerical Solution of Complex Variable Boundary Integral Equations

    1. Front Matter

      Pages 199-199
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    2. Complex Variable Bondary Element Method (CV-BEM)

      • A. M. Linkov
      Pages 200-224

    3. Numerical Experiments Using CV-BEM

      • A. M. Linkov
      Pages 225-245

    4. Complex Variable Method of Mechanical Quadratures (CV-MMQ)

      • A. M. Linkov
      Pages 246-257

  7. Back Matter

    Pages 259-274
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Keywords

About this book

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.

Reviews

From the reviews:

"The present book aims to present a powerful new tool of computational mechanics, complex variable boundary integral equations. … The subject matter is presented carefully, step by step with many helpful introductory pieces of text. And it is therefore a pleasure to read the book; the pleasant printing and binding also contribute to the pleasure. The book is addressed to a wide range of readers: graduate students, academics, researchers and engineers." (Søren Christiansen, Zentralblatt MATH, Vol. 1046 (21), 2004)

Authors and Affiliations

  • Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    A. M. Linkov

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