The boundary element method (BEM) is now a well-established numerical technique which provides an efficient alternative to the prevailing finite difference and finite element methods for the solution of a wide range of engineering problems. The main advantage of the BEM is its unique ability to provide a complete problem solution in terms of boundary values only, with substantial savings in computer time and data preparation effort. An initial restriction of the BEM was that the fundamental solution to the original partial differential equation was required in order to obtain an equivalent boundary in tegral equation. Another was that non-homogeneous terms accounting for effects such as distributed loads were included in the formulation by means of domain integrals, thus making the technique lose the attraction of its "boundary-only" character. Many different approaches have been developed to overcome these problems. It is our opinion that the most successful so far is the dual reciprocity method (DRM), which is the subject matter of this book. The basic idea behind this approach is to employ a fundamental solution corresponding to a simpler equation and to treat the remaining terms, as well as other non-homogeneous terms in the original equation, through a procedure which involves a series expansion using global approximating functions and the application of reciprocity principles.

The fields of boundary integral equations and of inequality problems, or more gen erally, of nonsmooth mechanics, have seen, in a remarkably short time, a considerable development in mathematics and in theoretical and applied mechanics. The engineering sciences have also benefited from these developments in that open problems have been attacked succesfully and entirely new methodologies have been developed. The contact problems of elasticity is a class of problems which has offered many open questions to deal with, both to the research workers working on the theory of boundary integral equations and to those working on the theory of inequality problems. Indeed, the area of static and dynamic contact problems could be considered as the testing workbench of the new developments in both the inequality problems and in the boundary integral equations. This book is a first attempt to formulate and study the boundary integral equations arising in inequality contact problems. The present book is a result of more than two decades of research and teaching activity of the first author on boundary integral equations and, of the second author, on inequality problems, as well as the outgrowth of seminars and courses for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessa loniki, the Universities of Bochum, of Hamburg and Braunschweig, the Pontificia Univ. Catolica in Rio de Janeiro etc.

The IUTAM Symposium on Advanced Boundary Element Methods brought together both established and current researchers in the broad context of applications of BEM technology. The goal of the Symposium was to provide both a formal and an informal forum for the interchange of ideas and the stimulation of new research directions.

This book investigates the various aspects of shape optimization of two dimensional continuum structures, including shape design sensitivity analysis, structural analysis using the boundary element method (BEM), and shape optimization implementation. The book begins by reviewing the developments of shape optimization, followed by the presentation of the mathematical programming methods for solving optimization problems. The basic theory of the BEM is presented which will be employed later on as the numerical tool to provide the structural responses and the shape design sensitivities. The key issue of shape optimization, the shape design sensitivity analy sis, is fully investigated. A general formulation of stress sensitivity using the continuum approach is presented. The difficulty of the modelling of the ad joint problem is studied, and two approaches are presented for the modelling of the adjoint problem. The first approach uses distributed loads to smooth the concentrated adjoint loads, and the second approach employs the singu larity subtraction method to remove the singular boundary displacements and tractions from the BEM equation. A novel finite difference based approach to shape design sensitivity is pre sented, which overcomes the two drawbacks of the conventional finite difference method. This approach has the advantage of being simple in concept, and eas ier implementation. A shape optimization program for two-dimensional continuum structures is developed, including structural analysis using the BEM, shape design sensitiv ity analysis, mathematical programming, and the design boundary modelling.

The Boundary Element Method has now become a powerful tool of engineering analysis and is routinely applied for the solution of elastostatics and potential problems. More recently research has concentrated on solving a large variety of non-linear and time dependent applications and in particular the method has been developed for viscous fluid flow problems. This book presents the state of the art on the solution of viscous flow using boundary elements and discusses different current approaches which have been validated by numerical experiments. . Chapter 1 of the book presents a brief review of previous work on viscous flow simulation and in particular gives an up-to-date list of the most important BEM references in the field. Chapter 2 reviews the governing equations for general viscous flow, including compressibility. The authors present a compre hensive treatment of the different cases and their formulation in terms of boundary integral equations. This work has been the result of collaboration between Computational Mechanics Institute of Southampton and Massa chusetts Institute of Technology researchers. Chapter 3 describes the gen eralized formulation for unsteady viscous flow problems developed over many years at Georgia Institute of Technology. This formulation has been extensively applied to solve aer09ynamic problems.

The boundary element method (BEM) is a modern numerical techniquewhich has enjoyed increasing popularity over the last two decades,and is now an established alternative to traditional computationalmethods of engineering analysis. The main advantage of the BEM isits unique ability to provide a complete solution in terms ofboundary values only, with substantial savings in modelling effort. This two-volume book set is designed to provide the readers with acomprehensive and up-to-date account of the boundary element methodand its application to solving engineering problems. Each volume isa self-contained book including a substantial amount of materialnot previously covered by other text books on the subject. Volume 1covers applications to heat transfer, acoustics, electrochemistryand fluid mechanics problems, while volume 2 concentrates on solidsand structures, describing applications to elasticity, plasticity,elastodynamics, fracture mechanics and contact analysis. The earlychapters are designed as a teaching text for final yearundergraduate courses. Both volumes reflect the experience of theauthors over a period of more than twenty years of boundary element research. This volume, Applications in Thermo-Fluids and Acoustics, provides acomprehensive presentation of the BEM from fundamentals to advancedengineering applications and encompasses: Steady and transient heat transfer Potential and viscous fluid flows Frequency and time-domain acoustics Corrosion and other electrochemical problems. A unique feature of this book is an in-depth presentation of BEMformulations in all the above fields, including detaileddiscussions of the basic theory, numerical algorithms and practicalengineering applications of the method. Written by an internationally recognised authority in the field,this is essential reading for postgraduates, researchers andpractitioners in civil, mechanical and chemical engineering andapplied mathematics.

This book contains updated, reviewed versions of the best papers on “Modelling Coastal Sea Processes” presented at the International Ocean and Atmosphere Pacific Conference, held in Adelaide, South Australia, on 23-27 October 1995. The articles were selected on both scientific merit and usefulness to coastal engineers, physical oceanographers and marine biologists. They cover a range of topics including the modelling of tides and storm surges (especially inundation due to surges), the analysis of modelled or recorded data to permit prediction of tide heights over tidal flats and tidal currents in the presence of coastal eddies, and the modelling of dispersion of fish larvae from spawning grounds to coastal nurseries. Computational techniques are emphasised in line with modern applications, but some analytical techniques have also been included.