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.

This book is a comprehensive exposition of the theory of boundary integral equations for single and double layer potentials on curves with exterior and interior cusps. Three chapters cover harmonic potentials, and the final chapter treats elastic potentials.

The Boundary Element Methods (BEM) has become one of the most efficient tools for solving various kinds of problems in engineering science. The International Association for Boundary Element Methods (IABEM) was established in order to promote and facilitate the exchange of scientific ideas related to the theory and applications of boundary element methods. The aim of this symposium is to provide a forum for researchers in boundary element methods and boundary-integral formulations in general to present contemporary concepts and techniques leading to the advancement of capabilities and understanding of this com putational methodology. The topics covered in this symposium include mathematical and computational aspects, applications to solid mechanics, fluid mechanics, acoustics, electromagnetics, heat transfer, optimization, control, inverse problems and other interdisciplinary problems. Papers deal ing with the coupling of the boundary element method with other computational methods are also included. The editors hope that this volume presents some innovative techniques and useful knowl edge for the development of the boundary element methods. February, 1992 S. Kobayashi N. Nishimura Contents Abe, K.

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.

Boundary Element Analysis: Theory and Programming introduces the theory behind the boundary element method and its computer applications. The author uses Cartesian tensor notation throughout the book and includes the steps involved in deriving many of the equations. The text includes computer programs in Fortran 77 for elastostatic, plate bending, and free and forced vibration problems with detailed descriptions of the code.

This book compiles solutions of linear theory of elasticity problems for isotropic and anisotropic bodies with sharp and rounded notches. It contains an overview of established and recent achievements, and presents the authors’ original solutions in the field considered with extensive discussion. The volume demonstrates through numerous, useful examples the effectiveness of singular integral equations for obtaining exact solutions of boundary problems of the theory of elasticity for bodies with cracks and notches. Incorporating analytical and numerical solutions of the problems of stress concentrations in solid bodies with crack-like defects, this volume is ideal for scientists and PhD students dealing with the problems of theory of elasticity and fracture mechanics.

The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It provides the only self-contained description of the method and fills a gap in the literature. No-one seriously interested in eigenvalue problems of elasticity or in the boundary integral equation method can afford not to read this book. Research workers, practising engineers and students will all find much of benefit to them.Contents: Introduction. Part I. Applications of Boundary Integral Equation Methods to Eigenvalue Problems of Elastodynamics. Fundamentals of BIE Methods for Elastodynamics. Formulation of BIEs for Steady-State Elastodynamics. Formulation of Eigenvalue Problems by the BIEs. Analytical Treatment of Integral Equations for Circular and Annular Domains. Numerical Procedures for Eigenvalue Problems. Numerical Analysis of Eigenvalue Problems in Antiplane Elastodynamics. Numerical Analysis of Eigenvalue Problems in Elastodynamics. Appendix: Dominant mode analysis around caverns in a semi-infinite domain. Part II. Applications of BIE Methods to Eigenvalue Problems of Thin Plates. Fundamentals of BIE Methods for Thin Plates. Formulation of BIEs for Thin Plates and Eigenvalue Problems. Numerical Analysis of Eigenvalue Problems in Plate Problems. Indexes.

This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts. The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications. The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory.