Boundary Integral Equations in Elasticity Theory

✍ Scribed by A. M. Linkov (auth.)

• Publisher: Springer Netherlands
• Year: 2002
• Tongue: English
• Leaves: 286
• Series: Solid Mechanics and Its Applications 99
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
Introduction....Pages 1-6
Front Matter....Pages 7-8
Real Potentials of Elasticity Theory....Pages 8-30
Singular Solutions and Potentials in Complex Form....Pages 31-49
Complex Integral Equations of the Indirect Approach....Pages 50-55
Complex Integral Equations of the Direct Approach....Pages 56-70
Functions of Kolosov-Muskhelishvili and Holomorphicity Theorems....Pages 71-86
Complex Variable Integral Equations....Pages 87-111
Periodic Problems....Pages 112-127
Doubly Periodic Problems....Pages 128-148
Problems for Bonded Half-Panes and Circular Inclusion....Pages 149-165
Front Matter....Pages 166-166
Complex Hypersingular and Finite-Part Integrals....Pages 167-180
Complex Variable Hypersingular Integral Equations (CVH-BIE)....Pages 181-198
Front Matter....Pages 199-199
Complex Variable Bondary Element Method (CV-BEM)....Pages 200-224
Numerical Experiments Using CV-BEM....Pages 225-245
Complex Variable Method of Mechanical Quadratures (CV-MMQ)....Pages 246-257
Back Matter....Pages 259-274

✦ Subjects

Mechanics;Appl.Mathematics/Computational Methods of Engineering;Engineering Design;Characterization and Evaluation of Materials