Boundary Integral Equations in Elasticity Theory

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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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
• computational mechanics
• elasticity
• fracture mechanics
• materials
• materials science
• mechanical engineering
• mechanics
• micromechanics
• stress

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)

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

  A. M. Linkov

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