**1977**

*Cruse, T.A.*

**Mathematical Foundation of the Boundary-Integral Equation Method in
Solid Mechanics**

1977

AFOSR-TR-77-1002

PWA-5539

*Jaswon, M.A. and Symm, G.T.*

**Integral Equation Methods in Potential Theory and Elastostatics**

1977

Academic Press

London

278 pp

ISBN: 0 12 381050 7

Integral equations, as the authors of this book demonstrate, provide

distinctive formulations of the fundamental boundary-value problems of

potential theory and elastostatics. These formulations often yield

effective solutions which fall beyond the scope of other approaches.

This monograph on the subject brings together theory and practice and

includes much previously unpublished material. The first part of the

volume gives a very clear description of the theory of integral

equations in potential theory and elastostatics, provinding, as one of

its features, the first unifying account of scalar and vector potential

theory using a common formalism. In the second part, the authors

discuss numerical methods for solving the integral equation

formulations of practical problems, using their own extensive research

as a basis. The theory is illustrated by a wealth of numerical

solutions drawn from a variety of fields, including electrostatics,

potential fluid flow, heat conduction, and the stretching and bending

of thin plates. An extensive list of references is provided, which also

covers recent interesting numerical solutions of problems in

three-dimensional elastostatics.

The book should be of direct use to engineers interested in a new

approach to and of the fields mentioned, and it would also be suitable

for postgraduates requiring a guide to this rapidly evolving subject.

**1978**

*Brebbia, C.A.*

**The Boundary Element Method for Engineers**

1978

Pentech Press

Plymouth

189 pp

ISBN: 0 931215 00 5

The book is aimed to introduce the reader to the fundamentals of

boundary elements, and to the application of the method to potential

problems and 2-D elasticity respectively. The book consists of six

chapters: Introduction, Weighted residuals method, Potential problems,

Elasticity problems, 2-D elasticity, and Final remarks. Appendix 1

presents the numerical integration formulae. The Index completes the book.

*Cruse, T.A. and **Wilson**, R.B.*

**Boundary-Integral Equation Methods for Elastic Fracture
Mechanics Analysis**

1978

AFOSR-TR-78-0355

**1980**

*Brebbia, C.A.
and Walker, S.*

**Boundary Element Techniques in Engineering**

1980

Butterworths

ISBN: 0 408 00340 5

The mathematics of the boundary element technique in a simplified form

as well as applications of the BEM as presented. The book contains

seven chapters which cover: boundary element method and weighted

residuals method, direct and indirect formulations, flow of fluid

around a cylinder between parallel plates, linear, quadrilateral and

higher-order elements for 2-D potential problems, boundary elements for

3-D problems, boundary element method and solution of boundary value

problems, 2-D problems of the theory of elasticity, time-dependent and

non-linear problems, problem solutions in connection with the

irregularity or nonhomogeneity (several regions).

**1981**

*Banerjee, P.K.
and Butterfield, R.*

**Boundary Element Methods in Engineering Science**

1981

McGraw-Hill Book Company

452 pp

ISBN: 0 07 084120 9

The book provides an introduction to the fundamentals of BEM, and

demonstrates the power and versatility of the method in different areas

of application. The book contains 15 chapters with the following

topics: an introdcution to BEM, some 1-D problems, 2-D problems of

steady state potential flow, 2-D problems of elastostatics, 3-D

problems of steady state potential flow, 3-D problems in elasticity,

problems of edges and corners, parametric representation of functions

and geometry, transient potential flow (diffusion) problems, transient

problems in elasticity, plate-bending problems, elastoplasticity,

examples in fluid mechanics, combination of BEM with other numerical

methods, and computer implementation of BEM (the program listing is

included). Three appendices and an Index complete the book.

**1982**

*Mukherjee, S.*

**Boundary Element Methods in Creep and Fracture**

1982

Elsevier Applied Science Publishers

Barking

210 pp

ISBN: 0 85334 163

This book presents the development of BEm for non-linear problems in

solid mechanics together with some fracture mechanics applications. The

book contains ten chapters. These cover topics such as: brief

historical account of the BEM development, state variable models for

time-dependent inelastic deformation of metals, numerical integration

strategy for the time domain, 2-D, 3-D and axisymmetric

elastoplasticity and viscoplasticity, viscoplastic torsion and bending

of plates, 2-D problems in fracture mechanics. The index compl;etes the

book.

**1983**

*Crouch, S.L. and Starfield, A.M.*

**Boundary Element Methods in Solid Mechanics**

1983

Allen and Unwin

322 pp

ISBN: 0 04 620010 X

The book can serve as a basic reading on the subject. Useful to the

reader primarily interested in solving problems by these methods. The

book contains eight chapters which cover: comparison of finite element

method with boundary element method, linear elasticity theory, singular

solution, indirect boundary element methods, direct boundary element

method, application to plane classical elasticity, a higher-order

formulation for elements, applications in rock mechanics and geological

engineering. Three appendices contain listings of three programs based

on the text.

*Liggett, J.A. and Liu, P.L.F.*

**Boundary Integral Equation Method for Porous Media Flow**

1983

Allen and Unwin

272 pp

ISBN: 0 04 62001 8

The book provides an introduction to the mathematics and applications

of the subject.

*Telles, J.C.F.*

**The Boundary Element Method Applied to Inelastic Problems**

1983

Lecture Notes in Engineering - Vol 1

Springer-Verlag

Berlin

243 pp

ISBN: 0 387 12387 3

The book can serve as basic reading on the subject. The inelastic 2-D

problems are handled (the current state-of-the-art). A complete review

of the elasticity problems is included. A set of numerical applications

is given. Subjects covered in seven chapters. The book contains: review

of the work up-to-date, basic theory of elasticity, BEM formulation for

elastic problems, BEM formulation for inelastic problems, initial

stress/strain methods and elastoplastic analysis, viscoplasticity and

creep, mathematical aspects for BEM inelastic analysis. Appendices give

some ideas on code developments.

*Venturini, W.S.*

**Boundary Element Methods in Geomechanics**

1983

Lecture Notes in Engineering - Vol 4

Springer-Verlag

Berlin

246 pp

ISBN: 3 540 17497 4

The book can serve as a basic reading on the subject. Topics on the

application of BEM in geomechanics are given in eleven chapters. These

cover: material models associated with geomechanical stress analysis,

formulation for linear problems, initial stress/strain formulations for

2-D continuum analysis, 3-D formulation to the generalized plane strain

problems, reduction of boundary-integral equations to algebraic form,

BEM application to no-tension materials, alternative formulations for

directionally oriented material weakness and slip or separation along

discontinuities types of behaviour for rocks, elasto-plasticity analysis

as applied to soils, elasto-viscoplasticity, viscoplastic analysis

applied to a variety of geomechanics problems (strip footing, slope

stability, tunnels), practical numerical analysis.

**1984**

*Brebbia, C.A.,
Telles, J.C.F. and Wrobel, L.C.*

**Boundary Element Techniques - Theory and Applications in Engineering**

1984

Springer-Verlag

Berlin

464 pp

ISBN: 3 540 12484 5

The book presents up-to-date treatment of the boundary element method.

Chapters included in the book cover: a generalized mathematical

formulation, elastostatics, elastoplasticity, viscoplasticity,

vibration, plate bending, wave propagation, fluid mechanics, coupling

FE method with the BE method. A comprehensive bibliography and listing

of a program complete the book.

*Hromadka II, T.V.*

**The Complex Variable Boundary Element Method**

1984

Lecture Notes in Engineering - Vol 9

243 pp

ISBN: 0 387 13743 2

This book presents the detailed mathematics associated with the CVBEM

(Complex Variable Boundary Element Method). The simplifications which

allow the interpretation of the CVBEM approximation error are

discussed. Computer programs which allow the solution of 2-D problems

are included. Several application problems are solved.

*Ingham, D.B. and Kelmanson, M.A.*

**Boundary Integral Equation Analysis of Singular Potential and
Biharmonic Problems**

1984

Lecture Notes in Engineering - Vol 7

Springer-Verlag

Berlin

173 pp

ISBN: 0 387 13646 0

The book provides an introduction to the mathematics and applications

of BIE to singular, potential, and biharmonic problems. Topics covered:

biharmonic equation for fluid flow problems involving stick-slip

boundary conditions, problems of flow around sharp corners, non-linear

heat transfer, viscous flow with free surfaces, slow flow in bearings

with arbitrary geometries.

*Manzoor Madassar, I.*

**Heat Flow Through Extended Surface Heat Exchangers**

1984

Lecture Notes in Engineering - Vol 5

Springer-Verlag

Berlin

286 pp

ISBN: 0 387 13047 0

The book deals with the application of boundary elements to heat

transfer problems encountered on surface heat exchangers. The book

has six chapters dealing with introduction to heat exchangers and their

design, the one and two dimensional analysis of fin assembly heat

transfer including the numerical solution of the problem using boundary

integral equations, the analysis of fin reduction, the effect of

surface roughness and interfacial bending and conclusions related to

the design of heat exchangers and the applicability of boundary

elements to solve these problems.

**1986**

*Kitahara, M.*

**Boundary Integral Equation Methods in Eigenvalue Problems of
Elastodynamics and Thin Plates**

1986

Studies in Applied Mechanics - Vol 10

Elsevier Science Publishers

Amsterdam

282 pp

ISBN: 0 444 42447 4

This book contains two parts. The first one handles the analytical

formulation and numerical solution for 2-D problems of vibration and

scattering. The second part considers the application of BIE methods to

the vibration and buckling characteristics of thin plates. The first

part of the book consists of seven chapters, the second one of three

chapters. Some topics treated: the basis of the application of integral

equation methods to eigenvalue problems, the integral equation

formulation in terms of the various boundary value problems, eigenvalue

problems for 2-D boundary integral equation formulation, analytical

treatment of the BIE for circular and annular domains, numerical

eigenvalue solution for the integral equation formulation, eigenvalue

problems of antiplane elastodynamics, review of numerical analysis

results for 2-D eigenvalue problems, integral equation fundamentals for

thin plate problems, numerical analysis of eigenvalue problems for plates.

**1987**

*Gipson, G.S.*

**Boundary Element Fundamentals: Basic Concepts of Recent Developments in
the Poisson Equation**

1987

Topics in Engineering - Vol 2

Computational Mechanics Publications

288 pp

ISBN: 0 905451 80 5

The book contains seven chapters, one of them contains a listing of a

boundary element program. It is devoted to discussion of the

fundamentals and the Poisson equation. The presented chapters cover:

integral equations and Green's functions, approximation methods with

emphasis on the weighted residual method, boundary element methods and

Laplace and Poisson types of differential equations, examples of

Laplace problems, solution of the Poisson equation, Monte Carlo method

and boundary elements, examples of the Poisson problem, description and

listing of a FORTRAN code for Laplace and Poisson equations.

*Gravert, P.*

**Numerical Simulation of Extreme Gravity Waves in Time Domain with the
Direct BEM and a Time Stepping Procedure**

1987

VDI-Verlag

ISBN: 3 18 143207 5

A Lagrangian formulation is given for the boundary and initial value

problem of gravity waves. This formulation is solved numerically by the

direct boundary element method (BEM) and a multistep time integration

procedure (Adams-Bashforth-Moulton). For singular integrals suitable

numerical integration formulas are derived from analytical

integrations. The discretization of the boundaries uses higher order

isoparametric elements and, especially for the free and moving surface,

cubic spline elements. The boundary integral equation is solved by a

modified least squares method instead of a collocation or Galerkin

approach. The proposed BEM satisfies in the weighted Gaussian normal

equation constraints exactly by means of a static condensation

algorithm. Steep unsteady and even breaking water waves are calculated

for deep and shallow water conditions. The accuracy and reliability of

the method are shown by comparison of numerical simulations of a wave

channel with experimental results.

*Hartmann, F.*

**Introduction to Boundary Elements**

1987

378 pp

ISBN: 0 387 17336 6

This book consists of an introduction, nine chapters, a list of

references, a bibliography and a description of available computer

programs. The bibliography contains 300 references. In addition to the

text, three computer programs for the solution of the membrane, plane

elasticity, and plate flexure problems are included. These programs are

written in TURBO-PASCAL for the IBM PC and compatible computers. The

book deals with the subjects as: fundamentals of the BEM, 1-D problems,

plane problems of the theory of elasticity, problems with non-linear

materials, plate bending, coupling of FEM and BEM, and dynamic problems.

*Hromadka II, T.V.*

**Complex Variable Boundary Elements**

1987

Software Package Series

Computational Mechanics Publications

226 pp plus diskette

ISBN: 0 905451 62 7

The book describes the Complex Variable Boundary Element Method (CVBEM)

for the solution of two dimensional

part of the software package contains sufficient detail to enable the

reader to comprehend the numerical technique without extensive

prerequisite study. Computer listings in FORTRAN are included for five

different CVBEM programs. A general purpose code is provided on the

floppy disk for use with IBM-PC compatible hardware.

*Hromadka, T.V. and Chintu, Lai*

**Complex Variable Boundary Element Method in Engineering Analysis**

1987

Springer-Verlag

Berlin

389 pp

ISBN: 0 387 96400 2

The authors introduce the complex variable boundary element method as a

new modelling method in computational mechanics and hydraulics. This

book presents the detailed mathematics associated with the CVBEM. The

CVBEM is a generalization of the Cauchy integral formula into a

boundary integral equation method. There are eight chapters in this

book. Partial contents: fundamentals, the development of a computer

algorithm, error analyses, modelling techniques and actual

applications, procedures for the basic potential problems. A number of

numerical programs are included.

*Telles, J.C.F.*

**Two Dimensional Analysis using Boundary Elements**

1987

Software Package Series

Computational Mechanics Publications

Southampton

208 pp plus diskette

ISBN: 0 905451 63 5

This software package has been developed for engineers and applied

mathematicians who would like an introduction to the boundary element

technique particularly applied to elasticity problems. The numerical

aspects of the method are discussed in detail and a fully operational 2-D

FORTRAN code listing is presented. A preprocessor is a part of the

code. A copy of the code on floppy disk running on IBM PC compatible

machines is included.

*Wrobel, L.C.*

**Two Dimensional Potential Analysis using Boundary Elements**

1987

Software Package Series

Computational Mechanics Publications

Southampton

186 pp plus diskette

ISBN: 0 905451 64 3

The book starts by discussing the basic theory of the method and the

formulation of the problem in terms of integral equations and boundary

elements. The development is focused on the solution of

equation which can be used to solve steady state heat conduction,

groundwater flow problems, flow of ideal fluids, electrostatics and other

engineering problems. This part is followed by a description of an

efficient code written in FORTRAN, running on IBM PC compatible

hardware. The program runs interactively and has a preprocessor which

simplifies the input. The program, preprocessor and data files are all

provided on the floppy disk. Several applications of the code are

presented.

**1988**

*Brebbia, C.A.
and Dominguez, J.*

**Boundary Elements - An Introductory Course**

1988

Computational Mechanics Publications

Southampton

300 pp

ISBN: 0 905451 76 7

ISBN: 0 931215 668 (US, Canada, Mexico)

The theory of boundary elements is presented in a form that can be

readily understood and applied by engineering students. The book

stresses the practical uses of the Boundary Element Method and includes

computer codes presented in standard FORTRAN 77 for ease of

comprehension and which can be implemented on an IBM PC. Each copy of

the book includes a diskette with the complete listing in FORTRAN. The

book covers topics such as: formulation of boundary integral equations,

potential problems, elastostatics, treatment of body forces, coupling

with finite elements, anisotropy, curvilinear coordinates and others.

It also includes a special section on numerical integration. The

computer codes listed in the book and included in the diskette are,

constant and linear codes for potential problems and constant and

quadratic codes for elastostatics.

*Cruse, T.A.*

**Boundary Element Analysis in Computational Fracture Mechanics**

1988

Kluwer

Dordrecht

162 pp

ISBN: 90 247 3614 5

The book provides exposition of the BEM to fracture mechanics. The book

contains eight chapters giving critical insight into; key historical

developments, review of fracture mechanics, mathematical foundations of

BEM, modelling of elastic cracks by BEM, demonstration of the power of

the integral equation formulations, BEM applications to inelastic

fracture mechanics, applications of BEM to several 2-D and 3-D fracture

mechanics problems.

*Manolis, G.D. and Beskos, D.E.*

**Boundary Element Methods in Elastodynamics**

1988

Unwin Hyman

London

282 pp

ISBN: 004 6200193

The book gives a brief summary of classical elastodynamics and proceeds

with the integral formulation and numerical treatment of both

steady-state and general transient problems. Other chapters include:

wave propagation problems, soil-structure interaction and fracture

mechanics. Other boundary methods related to the BEM are briefly

described, as well as effects of inhomogeneity, anisotropy, porosity,

viscosity and temperature.

*Tang, W.*

**Transformation Domain into Boundary Integrals in BEM: Generalized
Approach**

1988

Lecture Notes in Engineering

Springer-Verlag

Berlin

209 pp

ISBN: 0 387 19217 4

The purpose of this set of notes on the boundary element method is to

apply a Fourier series representation as a means for reducing certain

domain integrals to equivalent boundary integrals. The author handles

both potential problems and the vector problem for elastostatics.

Numerous numerical evaluations of resulting Fourier coefficients are given.

*Umetani, S.J.*

**Adaptive Boundary Element Methods in Elastostatics**

1988

Topics in Engineering - Vol 5

Computational Mechanics Publications

Southampton

107 pp

ISBN: 0 905451 81 3

This book examines the adaptive Boundary Element Method (BEM) for

applications in 2-dimensional elastostatics. The author first examines

several problems using a commercial BEM package to compare it with the

Finite Element Method. Next the adaptive BEM is developed to obtain

accurate and reliable solutions. The new approach employs the Galerkin

technique to solve integral equations, the Legendre polynomials

(p-version) and an iterative scheme solves the resulting system of

linear equations. The process is controlled by error estimators which

are used to further refine the model (b-version). Finally all adaptive

strategy using p- and h-versions is proposed. The feasibility of the

adaptive method is shown through solving problems in 2-D elastostatics

including cracks.

**1989**

*Bala**š,
J. , Sládek, J. and
Sládek, V**.*

**Stress Analysis by Boundary Element Methods (Studies in Applied Mechanics
23)**

1989

Veda, Publishing House of the

Bratislava

ISBN: 0-444-98830-0 (Vol. 23) (Elsevier)

ISBN: 0-444-41758-3 (Series)

ISBN: 80-224-0004-1 (Veda)

The boundary element method
is an extremely versatile and powerful tool of computational mechanics. The
purpose of this book is to present a comprehensive and up-to-date treatment of
the boundary element method in applications to various fields of continuum
mechanics:

- Elastostatics
- Elastodynamics
- Thermoelasticity
- Micropolar thermoelasticity
- Elastoplasticity
- Viscoelasticity
- Theory of plates and stress
analysis by hybrid methods

In this book, the fundamental
solutions of governing differential equations, integral representations of the
displacement and temperature fields, regularized integral representations of
the stress field and heat flux, boundary integral equations and boundary
integro-differential equations are derived, too.

Besides the mathematical
foundations of the boundary integral method, the book deals with practical
applications of this method. Most applications are devoted to linear fracture
mechanics. The method has been found to be very efficient in stressintensity
factor computations.

Also included are developments
made by the authors in the boundary integral formulation of the
thermoelasticity, micropolar elasticity, viscoelasticity, plate theory, hybrid
method in elasticity and solution of crack problems. The solution of
boundary-value problems of thermoelasticity and micropolar thermoelasticity is
for the first time formulated as the solution of pure boundary problems. A new
unified formulation of general crack problems is presented by integro-diferential
equations.

*Jiang, Y.S.*

**Slope Analysis using Boundary Elements**

1989

Lecture Notes in Engineering - Vol 52

176 pp

ISBN: 0 387 51625 5

*Karami, G.*

**A Boundary Element Method for Two-Dimensional Contact Problems**

1989

Lecture Notes in Engineering - Vol 51

ISBN: 3 540 51562 3

The boundary element method (BEM) has been established as a powerful

numerical tool for the analysis of continua in recent years. The method

is based on an attempt to transfer the governing differential equations

into integral equations over the boundary. Thus, the discretization

scheme or the introduction of any approximations must be done over the

boundary. This book presents a BEM for two-dimensional elastic,

thermo-elastic and body-force contact problems. The formulation is

implemented for the general case of contact with various frictional

conditions. The analysis is limited to linear elastostatics and small

strain theory. Following a review of the basic nature of contact

problems, the analytical basis of the direct formulation of the BEM

method is described. The numerical implementation employs three-noded

isoparametric line elements for the representation of the boundary of

the bodies in contact. Opposite nodal points in equi-length

element-pairs are defined on the two surfaces in the area which is

expected to come into contact under an increasing load. The use of

appropriate contact conditions enables the integral equations for the

two bodies to be coupled together. To find the proper contact

dimensions and the contact load a combined incremental and iterative

approach is utilised. With this approach, the loads are applied

progressively, and the sliding and adhering portion of the contact

region is established for each load increment using an iterative

procedure. A coulomb type of friction law is assumed. The results of

the numerical formulation show excellent agreement with the well known

Hertzian contact solution. Several problems involving more complicated

and non-Hertzian contact are also solved. The BEM solutions agree well

with existing experimental and finite element results. The analytical

and numerical treatment of the boundary integral equations for problems

with body forces and temperature changes is described. In particular,

the pseudo-body force approach which treats the temperature gradients

as a kind of body force, is employed for the thermoelastic analysis. It

is shown that the domain integrals containing the body force and

pseudo-body force terms can be transformed to integrals over the

boundary. Several examples of contact with body forces and temperature

changes are presented.

*Lefeber, D.*

**Solving Problems with Singularities using Boundary Elements**

1989

Topics in Engineering - Vol 4

Computational Mechanics Publications

Southampton

183 pp

ISBN: 0 905451 96 1

This book has considerable bearing on the use of the Boundary Element

Method and other numerical techniques on the all-important area of

finding engineering solutions near singularities. When a linear partial

differential equation has singularities in the boundary conditions, it

is generally impossible to obtain accurate approximations in the

neighbourhood of those points using standard numerical methods. In

practical engineering problems, quantities involving derivatives such

as stresses, bending moments, shear forces, etc., play an important

role in the design process, so that an accurate knowledge of the

behaviour of these quantities, especially near the singular points, is

necessary. In this text, a method is outlined to obtain an accurate

approximation in the domain and on the boundary, especially near the

singularities. In particular, any derived quantity of the proposed

approximate solution can be obtained with sufficient precision, by

analytical derivation. The method is based on a set of singular

functions satisfying the partial differential equation and part of the

boundary conditions. The method is developed in detail in the case of

potential problems with mixed boundary conditions, and for thin plate

problems with any combination of simply-supported, clamped or free

boundary conditions. Special attention is given to skew plates.

**1990**

*BEASY, C.M.I.*

**Beasy Self-Teaching Guide**

1990

Computational Mechanics Publications

ISBN: 1 85312 040 5

ISBN: 1 945824 23 8 (US,

This guide is designed to give a training course in the use of BEASY

and its pre and postprocessor BEASY-IMS. The course is arranged in a

series of sessions which should be followed while sitting at a

terminal. The sessions contain examples of increasing complexity, and

each introduces more modeling features and concepts. While the examples

have been chosen to resemble real engineering applications, they are

necessarily small, because the aim of the book is to teach you how to

use BEASY.

*Kitagawa, K.*

**Boundary Element Method Analysis of Viscous Flow**

1990

Lecture Notes in Engineering - Vol 55

Springer-Verlag

Berlin

136 pp

ISBN: 0 387 51930 0

In this book, applications of the BEM to viscous flow and thermal

convection problems are investigated. The proposed formulation is

based on an analogy between Navier's equations in elastostatics and

Navier-Stokes equations expressed by using a penalty function. After

briefly reviewing the previous research on viscous flow problems and

BEM in the first chapter, the second chapter deals with the proposed

formulation in detail. Chapter 3 presents the numerical

implementation, in particular, the numerical computation methods for

evaluating quasi-singular boundary integrations and domain

integrations. Some two-dimensional results are compared with previous

results in Chapter 4, and finally, three-dimensional results are also

presented.

*Pande, G.N., Beer, G. and Williams, J.R.*

**Numerical Methods in Rock Mechanics**

1990

Wiley

ISBN: 0471 92021 5

Numerical methods are applied to rock mechanics problems in tunnelling,

mining, construction of dams and other areas. The important

developments in the field during the past decade are reflected here,

and the authors describe the most important methods in numerical

modelling of rocks and rock masses: the finite element method, the

boundary element method and the discrete element method.

Numerical Methods in Rock Mechanics highlights the

essential features of the behaviour of rocks, assuming a knowledge of

soil mechanics, and deals with the theory of elasto-plasticity and

elasto-viscoplasticity, which is essential for modelling of the

constitutive behaviour of jointed rock masses.

Mechanical behaviour of intact rocks, rock joints and

jointed masses is covered; simple analytical and numerical models are

discussed and later used as `building blocks' for a comprehensive,

constitutive model of the behaviour of jointed rock masses. Joint

elements and infinite elements are introduced with emphasis on

modelling of discrete major discontinuities such as fault and shear

zones. Various models of behaviour of jointed rock masses of varying

complexities are given and multi-laminate models are described.

Examples of the practical applications for each of the

methods are given and comprehensive reference lists direct the reader

to a more detailed study.

**1991**

*Aliabadi, M.H. and Rooke, D.P.*

**Numerical Fracture Mechanics**

1991

Computational Mechanics Publications

Southampton

276 pp

ISBN:1 85312 057 X

ISBN: 0 945824 39 4 (US, Canada, Mexico)

The purpose of this book is to demonstrate the use of numerical methods

in solving crack problems in fracture mechanics. The text concentrates,

to a large extent, on the application of the Boundary Element Method

(BEM) to fracture mechanics, although an up-to-date account of recent

advances in other numerical methods such as the Finite Element Method

is also presented. The book is an integrated presentation of modern

numerical fracture mechanics, and contains a compilation of the work of

many researchers as well as accounting for some of the authors' most

recent work on the subject. It is hoped that this book will bridge the

gap that exists between specialist books on theoretical fracture

mechanics on the one hand, and texts on numerical methods on the other.

Although most of the methods presented are the latest developments in

the field of numerical mechanics, the authors have also included some

simple techniques which are essential for understanding the physical

principles that govern crack problems in general. Different numerical

techniques are described in detail and where possible simple examples

are included, as well as test results for more complicated

problems.

*Bruch, E.K.*

**The Boundary Element Method for Groundwater Flow**

1991

Lecture Notes in Engineering

Springer-Verlag

Berlin

ISBN: 3 540 54407 0

ISBN: 0387 54407 0

During the last few years rapid progress has been made on the solution

of partial differential equations, which are now routinely solved using

computers. Their implementation is based numerically in three methods

which in chronological order are the finite difference method, the

finite element method and the boundary element method. In comparison

to the other two methods, the latter presents some important advantages

which have motivated its rapid development in the last decade or so.

In this book the application of the boundary element method to the

solution of the

fundamental importance in engineering and science as it describes

different types of phenomena, including the groundwater flow

applications highlighted in this book. Special subjects such as

numerical integration, subdivision of the domain into regions and other

computational aspects are discussed in detail in the first chapters. To

demonstrate the accuracy and efficiency of the boundary element method,

results obtained when solving the

against known analytical solutions. Other chapters deal with problems

such as steady state and unsteady flow in addition to infiltration

problems. The applications demonstrate that the boundary element method

provides a powerful solution technique which can be effectively applied

to solve this type of problem.

*DeFigueiredo, T.G.B.*

**A New Boundary Element Formulation in Engineering**

1991

Lecture Notes in Engineering

ISBN: 3 540 54030 X

ISBN: 0 387 54030 X

*Elzein, A.*

**Plate Stability by Boundary Element Method**

1991

Lecture Notes in Engineering

ISBN: 3 540 53710 4

ISBN: 0 387 53710 4

*Partridge, P.W., **Brebbia**, **C.A.** and Wrobel, L.C.*

**The Dual Reciprocity Boundary Element Method**

1991

Computational Mechanics Publications

ISBN: 1 85312098 7

ISBN: 0 945824 82 3(US,

The boundary element method (BEM) is now a well-established numerical

technique which provides an efficient alternative to 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 integral 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. 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 dual reciprocity procedure is completely general and

conceptually simple. In this book, the method is applied to both two-

and three-dimensional problems, some of which include nonlinear and

transient effects.

*Zhao, Z. *

**Shape Design Sensitivity Analysis and Optimization using the Boundary
Element Method**

1991

Lecture Notes in Engineering - Vol 62

Springer-Verlag

Berlin

ISBN: 3 540 53518 7

ISBN: 0 387 53518 7

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 analysis, is fully investigated. A general formulation of

stress sensitivity using the continuum approach is presented. The

difficulty of the modelling of the adjoint 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 singularity

subtraction method to remove the singular boundary displacements and

tractions from the BEM equation.

A novel finite difference based approach to shape and

design sensitivity is presented, which overcomes the two drawbacks of

the conventional finite difference method. This approach has the

advantage of being simple in concept, and easier in implementation.

A shape optimization program for two-dimensional

continuum structures is developed, including structural analysis using

the BEM, shape design sensitivity analysis, mathematical programming,

and the design boundary modelling. Some numerical examples are used to

demonstrate the proposed formulations for shape design sensitivity

analysis and shape optimization implementation.

**1992**

*Amini, S., Harris, P.J. and Wilton, D.T.*

**Coupled Boundary and Finite Element Methods for the Solution of the
Dynamic Fluid-Structure interaction Problem**

1992

Lecture Notes in Engineering - Vol 77

Springer-Verlag

Berlin

This text considers the problem of the dynamic fluid-structure

interaction between a finite elastic structure and the acoustic field

in an unbounded fluid-filled exterior domain.

The exterior acoustic field is modelled through a boundary

integral equation over the structure surface. However, the classical

boundary integral equation formulations of this problem either have no

solutions or do not have unique solutions at certain characteristic

frequencies (which depend on the surface geometry) and it is necessary

to employ modified boundary integral equation formulations which are

valid for all frequencies. The particular approach adopted here

involves an arbitrary coupling parameter and the effect that this

parameter has on the stability and accuracy of the numerical method

used to solve the integral equation is examined.

The boundary integral analysis of the exterior acoustic problem is

coupled with a finite element analysis of the elastic structure in

order to investigate the interaction between the dynamic behaviour of

the structure and the associated acoustic field. Recently there has

been some controversy over whether or not the coupled problem also

suffers from the non-uniqueness problem associated with the classical

integral equation formulations of the exterior acoustic problem. This

question is resolved by demonstrating that the solution to the coupled

problem is not unique at the characteristic frequencies and that it is

necessary to employ an integral equation formulation valid for all

frequencies.

Numerical results are presented and discussed for both the

uncoupled acoustic problem and the coupled fluid-structure interaction

problem for a number of axisymmetric and fully three-dimensional

problems. In particular, the method is applied to the coupled problem

of a piezoelastic ring sonar transducer transmitting an acoustic signal

in water for which reasonable agreement between the theoretical

predictions and some experimental results is observed.

*Antes, H. and Panagiotopoulos, P.D.*

**The Boundary Integral Approach to Static and Dynamic Contact Problems**

1992

Birkhauser Verlag

ISBN: 3 7643 25925

ISBN: 0 8176 2592 5

The aim of the present book is the formulation and study of boundary

integral equation methods for static and dynamic contact problems. The

cases of equality and inequality constraints are both examined. The

former lead to classical boundary integral equations, whereas the

inequality constraints lead to multivalued boundary integral equations.

In parallel to the formulation and the mathematical study, numerical

examples help to illustrate the theories presented.

This book is the first one to deal with multivalued boundary integral

equations in the theory of elasticity, with cracks involving unilateral

contact and friction interface conditions, with boundary integral equations

formulated on interfaces and boundaries of fractal geometry, and finally

with the neural network approach to multivalued boundary integral

equations resulting in inequality contact problems.

*Becker, A.A.*

**The Boundary Element Method in Engineering-A Complete Course**

1992

McGraw-Hill Book Company

ISBN: 0 07 707415 7, 335 p. , £21.95

This textbook provides a
complete course on the Boundary Element (BE)

method aimed specifically at engineers and engineering students. No

prior knowledge of advanced mathematics or numerical techniques is

assumed. This self-contained book provides an introduction to the BE

method as well as a foundation for further research.

Special features include :

. The mathematical principles are contained in one chapter - this

chapter can either be referred to occasionally or omitted altogether

without affecting the understanding of the BE formulation.

. A step-by-step approach is used to derive the numerical implementation

of the BE method.

. The final chapter fully describes a FORTRAN

computer program using isoparametric quadratic elements for

two-dimensional and axisymmetric elastostatic problems.

. Full listing of the program, a description of the main variables, as well as
a

separate user's manual are provided in appendices.

CONTENTS : Introduction.
Mathematical Background. Two-Dimensional

Potential Problems. Two-Dimensional Elastostatic Problems.

Three-Dimensional Potential and Elastostatic Problems. Axisymmetric

Potential and Elastostatic Problems. Thermoelastic Problems.

Multi-Domain and Contact Problems. Fracture Mechanics Problems. Review

of Non-Linear Problems. Further Applications : coupling BE and FE

techniques, centrifugal loading, axisymmetric geometries with

arbitrary boundary conditions, infinite boundary elements,

time-dependent potential problems. BE Computer Program (BEACON).

User's Manual. List of Main Variables. Full Listing of BEACON.

*Beer, G. and
Watson, J.O.*

**Introduction to Finite and Boundary Element Methods for Engineers**

1992

Wiley

Chichester

ISBN: 0 471 92813 5

This book is a readable yet accurate introduction to the theory and

practice of two computational techniques: the well established and

versatile finite element method (FEM) and the less widely accepted but

very promising boundary element method (BEM). The text is introductory

in the sense that a relatively narrow range of problems is considered, but

advanced in its treatment of the theoretical and practical aspects of that

range of problems.

Where possible, a unified presentation of the numerical

implementations of the two methods is given. By means of examples of

applications it is demonstrated which problems may best be solved by

each method, or by a combination of the methods. Two computer

programs written in FORTRAN are included to show programming

techniques used to implement both methods and to allow readers to

become familiar with their use. The book will appeal to undergraduate

and postgraduate students, practising engineers and developers of

numerical modelling software.

*Camp, C.V. and Gipson, G.S.*

**Boundary Element Analysis of Nonhomogeneous Biharmonic Phenomena**

1992

Lecture Notes in Engineering - Vol 74

260 pp

ISBN: 3 540 55020 8

softcover

*Chen, G. and
Zhou, J.*

**Boundary Element Methods**

1992

Academic Press

ISBN: 0 12 170840 X

*Chen, J.T. and Hong, H.K.*

**Boundary Element Method (Second Editon)**

1992

Taipei Publ

Taipei

Taiwan

509pp

This book gives a compact and unified potential theory of boundary

element methods in selected analysis, Laplace equation and crack

problem. The hypersingular integral formulation is emphasized to treat

the degenerate boundary value problems, eg. Darcy flow around a cutoff

wall and crack problem in elasticity. The dual integral equations are

derived amd the dual boundary element method (DBEM) is implemented. It

consists of nine chapters. Chapter 0 gives a literature review and

introduction. Chapter 1 is concerned with the associated

preliminaries. Chapter 2 is devoted to the computational algorithm

of discretization of integral equations. The applications of the dual

integral formulation in

presented in chapters 3 and 4, respectively. The integral

representations of J2 flow elastoplasticity is derived from the rate

equation model in chapter 5. Chapter 6 discusses the mechanism of the

fictitious eigenvalues of the integral formulation of Helmholtz

equation. Chapter 7 derives a unified integral solution of the time

dependent boundary condition problems and applied to the earthquake

engineering. Chapter 8 contains the comparison of BEM and FEM and

discusses the coupling use. Chapter 9 summarizes a short conclusion.

The references contain three parts, thesis in

*Hayami, K.*

**A Projection Transformation Method for Nearly Singular Surface Boundary
Element Integrals**

1992

VIII+456 pp

ISBN: 3 540 55000 3

softcover

*Pozrikidis, C.*

**Boundary Integral and Singularity Methods for Linearized Viscous Flow**

1992

Cambridge University Press

Cambridge

ISBN: 0 521 40502 5(hardback)

ISBN: 0 521 40693 5 (paperback)

Over the last two decades, boundary integral and singularity methods

have enjoyed increasing popularity, and have become a viable alternative

to traditional theoretical and computational methods of mathematical

engineering and physics. Their development continues to be a topic of

active research, especially in the areas of potential theory, solid

mechanics, and fluid mechanics.

The aim of this book is to bring together classical and recent

developments in the particular field of Newtonian flow at low Reynolds

numbers. The methods are developed from first principles, alternative

formulations are compared, and a variety of configurations are addressed.

The proper mathematical framework is discussed in the context of

functional analysis and integral-equation theory, and procedures of

numerical solutions in the context of the boundary element method are

introduced. The text contains original material pertaining to the properties

and explicit form of the Green's functions, and the theory of the integral

equations that arise from boundary integral representations.

The targeted audience includes graduate students and academic or

industrial researchers in engineering, computer science, and applied

mathematics. The only prerequisites are fundamental knowledge of

fluid mechanics, functional analysis, and numerical methods.

*Wrobel, L.C. and Brebbia, C.A.*

**Boundary Element Methods in Heat Transfer**

1992

Computational Mechanics Publications

Southampton

ISBN: 1 85312103 7

ISBN: 0 945824 86 6 (US, Canada, Mexico)

Heat transfer problems in industry are usually of a very complex

nature, simultaneously involing different transfer modes such as

conduction, convection, radiation and others. Beacause of this, very

few problems can be solved analytically and one generally has to resort

to numerical analysis.

The boundary element method is a numerical technique which has

been receiving growing attention for solving heat transfer problems

because of its unique abiltiy to confine the discretization process to

the boundaries of the problem region. This allows major reductions in

the data preparation and computer effort necessary to solve complex

industrial problems.

The purpose of this book is to present efficient algorithms used

in conjunction with the boundary element method for the solution of

steady and transient, linear and non-linear heat transfer problems. It

represents the state-of-the-art of boundary element application in the

field of heat transfer, and constitutes essential reading for

researchers and practising engineers involved with the important topic.

**1993**

*Dominguez, J.*

**Boundary Elements in Dynamics**

1993

Computational Mechanics Publications

Southampton

ISBN: 1 85312 258 0

ISBN: 1 56252 182 9 (US, Canada, Mexico)

The main emphasis of this book is on the development of the different

boundary element formulations for time-dependent problems and the

necessary mathematical transformations to produce computer codes which

are able to solve scalar, elastic and poroelastic wave propagation

problems. There is also a substantial part of the book which covers the

application of the boundary element method to important engineering

problems in dynamics. The book is a result of the author's involvement

over a period of sixteen years in the field of boundary elements, and

of boundary elements in dynamics in particular. The mathematics

developed in the book is at a level to make it as self-contained as

possible. Readers with almost no background in boundary elements or in

dynamics should be able to follow the text.

The purpose of this book is two-fold. It is intended to provide a

reference book for researchers and engineers, and at the same time

provide a text from which scientists can learn in detail the

formulation, implementation and practical applications of the boundary

element method in dynamics. The book could serve as an advanced level

text to a course on boundary elements in dynamics or as a supplement to

other books in a more general course.

*El-Zafrany, A.*

**Techniques of the Boundary Element Method**

1993

Ellis Horwood

ISBN: 0 13 898511 1

hardcover

This is one of the first books on the boundary element method to be

specifically aimed at students. Written in such a way as to prove

acceptable to engineering students, mathematicians and practising

engineers, the book outlines the basic steps necessary for a full

understanding of the direct boundary element method.

Intended as a `stand alone' text this book's no-nonsense approach

to this complex subject will make it a welcome addition to the

literature.

*Nachbin, A.*

**Modelling of Water Waves in Shallow Channels**

1993

Topics in Engineering - Vol 13

Computational Mechanics Publications

Southampton

ISBN: 1 85312 135 5

ISBN: 1 56252 062 8 (US, Canada, Mexico)

ISSN: 0952 5300 (series)

This book constitutes an invaluable tool in the numerical study of

a wide range of linear water wave problems. It is expected that the material

presented will appeal to scientists and engineers, from both the theoretical

and computational point of view.

Chapter 1 presents an introduction to the theory and the partial

differential equations governing water wave propagation. For the reader

inclined towards computations, Chapters 2, 3 and 4 contain a very

detailed presentation of each method, a careful study of their numerical

stability, (i.e. numerical dispersion relation) and a series of numerical

experiments showing that the boundary element method performs very

well. Not only is this method accurate over a long time interval, but the

method is sensitive to small scale components of the topography. This

is a useful property because it allows the modelling of a more complete

and detailed bottom surface. Chapter 5 includes new results which

account for the quantitative agreement between theory and computations.

*Portela, A.*

**Dual Boundary Element Analysis of Crack Growth**

1993

Topics in Engineering - Vol 14

Computational Mechanics Publications

Southampton

ISBN: 1 85312 187 8

ISBN: 1 56252 116 0 (US, Canada, Mexico)

ISBN: 0952 5300 (series)

This book describes the dual boundary element method and its application

to the analysis of fatigue crack-growth problems, in the context of the

damage tolerance analysis with linear elastic fracture mechanics.

The dual boundary element method which incorporates two

independent boundary integral equations, uses the displacement equation

to model one of the crack boundaries and the traction equation to model

the other. As a consequence, the analysis of general crack problems can

be performed effectively in a single-region formulation. The dual

boundary integral equations, derived from the work theorem, are

defined in terms of Cauchy and Hadamard principal value integrals that

are computed directly over discontinuous boundary elements by means

of finite-part integrals.

The stress intensity factors are evaluated by the techniques of the

singularity subtraction and the J-integral. The basic formulation of the

singularity subtraction technique is first extended for the single-region

analysis of non-symmetrical problems. A general formulation of this

technique is then presented for the solution of problems of piece-wise

straight cracks, through an automatic partition of the problem domain.

The J-integral is the most efficient technique used in the dual boundary

element method to solve general crack problems. The decomposition

method, used to decouple the stress intensity factors in mixed-mode

problems, is implemented automatically by considering a small circular

contour path around each crack tip.

Fatigue crack growth is simulated with an incremental crack-

extension analysis. Each crack-path increment is first predicted by the

maximum principal stress criterion and then corrected to account for the

discreteness of the analysis. For each increment of the crack extension.

the dual boundary element method is applied to perform a stress analysis

of the structure and the J-integral technique is applied to compute the

stress intensity factors. When the crack extension is discretized with

new boundary elements, remeshing is not required by virtue of the

single-region analysis, an intrinsic feature of the dual boundary element

method. As a consequence, the solution of the system of algebraic

equations that is usually the most time-consuming stage, can be

performed quite efficiently by an incremental LU decomposition

method.

The accuracy and efficiency of the dual boundary element method

are both demonstrated with the solution of several crack problems.

Finally, an engineering application of the dual boundary element

incremental analysis of fatigue crack growth is presented for a pin-

loaded lug problem.

**1994**

*Banerjee, P.K.*

**The Boundary Element Methods in Engineering**

1994

McGraw-Hill

London

ISBN: 0 07 707769 5

The last two decades have seen the emergence of a versatile and

powerful method of computational engineering mechanics, namely the

boundary element method.

The Boundary Element Methods in Engineering looks at the massive

development of this technology and describes its formulation for almost

all applications. For ease of use, a simple utilitarian and tutorial

approach is adopted in the initial chapters, introducing the basic

background necessary to learn the method. Simple, but detailed

instructions for its application to heat transfer (potential flow) and

stress analyses are offered, before the book moves on to a

progressively advanced level in later chapters. Numerous case studies

are employed for a large number of applications in dynamics, vibration,

fluid flow and nonlinear mechanics, making this a comprehensive guide

for all engineers interested in the use of these methods in a wide

range of engineering problems.

Special features include:

* Accessible design, with numerous examples

* Detailed discussion of computer applications

* A new approach to the analysis of solids with holes and

inclusions

*do Rego Silva, J.J.*

**Acoustic and Elastic Wave Scattering using Boundary Elements**

1994

Topics in Engineering - Vol 18

Computational Mechanics Publications

ISBN: 1 85312293 9

ISBN: 1 56252 217 5 (US,

ISSN: 0952 5300

The present work deals with the propagation of acoustic and elastic

harmonic waves in three-dimesional regions. The problems are formulated

using integral equations, and their numerical solution obtained through

the boundary element method. The book contains both the theoretical

support to the integral equation theory and extensive discussions on

the numerical aspects involved in the computational implementation.

The main focus of the book is on formulations involving

hypersingular integrals. The smoothness conditions for the existence of

these integrals are examined in detail, forming the basis for the

mathematical justification of the algorithms employed. Their numerical

implementation is discussed in a coherent manner, especially regarding

the use of isoparametric continuous elements.

An important aspect of the present work is a formulation for

exterior acoustic problems which is valid for any value of frequency.

This formulation, originally suggested by Panich, is implemented and

compared to the more popular formulation of

Finally, a new integral formulation is presented for elastic wave

propagation problems. A rigorous proof of uniqueness of solution and

the requirement condition for the existence of the hypersingular

integral is included, showing that this new technique is numerically

reliable for any value of frequency.

*Hall, W.S.*

**The Boundary Element Method**

1994

Kluwer Academic Publishers

Dordrecht

ISBN: 0 7923 2580 X

The Boundary Element Method sets out a simple, efficient and cost

effective computational technique which provides numerical solutions -

for objects of any shape - for a wide range of scientific and

engineering problems.

The Boundary Element Method provides a complete approach to

formulating boundary integral equations for scientific and engineering

problems and solving them numerically using an element approximation.

Only a knowledge of elementary calculus is required, since the text

begins by relating familiar differential equations to integral

equations and then moves on to the simple solution of integral

equations. From this starting point, the mathematics of formulation and

numerical approximation are developed progressively with every

mathematical step being provided. Particular attention is paid to the

problem of accurate evaluation of singular integrands and to the use of

increasing levels of accuracy provided by constant, linear and

quadratic approximations. This enables a full solution to be given for

both two dimensional and three dimensional potential problems and

finally, for the two dimensional elastostatics problem.

The Boundary Element Method develops the mathematics of the text

progressively both within chapters and from chapter to chapter. It is

a self-contained, step by step, exposition of the Boundary Element

Method leading to its application to the key problem of elastostatics.

The Boundary Element Method serves as a standard introductory

reference text for the mathematics of this method and is ideal for

final year undergraduate study as well as for postgraduates, scientists

and engineers new to the subject. Worked examples and exercises are

provided throughout the text.

*Ingham, D.B. and Yuan, Y.*

**The Boundary Element Method for Solving Improperly Posed Problems**

1994

Topics in Engineering - Vol 19

Computational Mechanics Publications

Southampton

ISBN: 1 85312291 2

ISBN: 1 56252 215 9 (US, Canada, Mexico)

ISSN: 0952 5300

In recent years an increasing amount of research work has been carried

out on the application of the Boundary Element Method (BEM) to a

growing variety of problems. The purpose of this book is to extend the

range of applications of the BEM, with a view to establishing a sound

basis on which to build new solution procedures with particular

attention being paid to problems which arise in inverse heat conduction.

The minimal energy technique has been introduced to modify the BEM

for solving inverse heat conduction problems which are improperly posed

and the results indicate that excellent convergent and stable numerical

approximate solutions may be obtained for various inverse heat

conduction problems, which may be linear or nonlinear, steady or

unsteady. Examples show that the agreement between the numerical

results and the analytical solutions, where available, is excellent.

*Kane, J.H.*

**Boundary Element Analysis in Engineering Continuum Mechanics**

1994

Prentice Hall

ISBN: 0 13 086927 9

*Leitao, V.M.A.*

**Boundary Elements in Fracture Mechanics**

1994

Topics in Engineering - Vol 21

Computational Mechanics Publications

ISBN: 1 85312335 8

ISBN: 1 56252 259 0 (US,

ISSN: 0952 5300

This book provides a new elastoplastic formulation for the analysis of

problems in nonlinear fracture mechanics. The method relies on the use

of two independent boundary integral equations, thus `the elastoplastic

dual boundary element method' (EPDBEM). The two equations of the method

are the displacement equation on one face of the crack and the traction

equation on the opposite face. This feature allows for the analysis of

general mixed-mode crack problems within a single-region formulation.

The EPDBEM formulation was applied to the problem of cracks

growing in ductile materials in the presence of residual stresses. In

particular, the formulation is used to investigate the effect of

prestressing on the behaviour of fatigue cracks. Special emphasis is

given to the redistribution (relaxation) of the residual stresses due

to the presence and growth of the cracks. This application is

complemented by another, based on linear elastic fracture mechanics

concepts, in which the superposition of the residual stress and fatigue

stress fields is used. Superposition is also used to investigate the

effect of cold-working open holes on the behaviour of fatigue cracks.

An elastic boundary element formulation incorporating weight functions

is used for the calculation of stress intensity factors. Crack growth

rates are predicted and compared to experimental results.

*Man, K.W.*

**Contact Mechanics using Boundary Elements**

1994

Topics in Engineering - Vol 22

Computational Mechanics Publications

Southampton

ISBN: 1 85312334 X

ISBN: 1 56252 258 2 (US, Canada, Mexico)

In this book, a Boundary Element formulation for solving structural

problems associated with frictional contact is presented; it develops

and uses an efficient iterative and fully loaded-incremental technique.

Problems with any number of two-dimensional bodies in contact can be

analysed using this technique; the bodies may be conforming or

non-conforming, of similar or dissimilar materials. The interface may

be frictionless or frictional and may undergo slip or partial slip.

Both symmetrical and non-symmetrical progressive contact problems in

the presence of friction are solved. Numerical solutions of both normal

and tangential traction distributions can be obtained automatically for

successive load increments.

The problem of ensuring that stress intensity factor solutions for

cracked bodies are accurately calculated continues to be a major

consideration in design, particularly in the presence of fretting

forces. In this book, the technique for solving problems in cracked

structures is presented for configurations which require a non-linear

analysis of the contact conditions. Stress intensity factors are

evaluated at the end of each load step using the J-integral method.

*Power, H. and Wrobel, L.C.*

**Boundary Integral Methods in Fluid Mechanics**

1994

Computational Mechanics Publications

ISBN: 1 85312252 1

ISBN: 1 56252 176 4 (US,

Physical phenomena are usually described methematically in terms of

partial differential equations. In many cases, an alternative (and

equivalent) mathematical representation of the problem can be found in

terms of integral equations. The theory of integral equations was

originally developed in mathematics as a tool for proving uniqueness

and existance of solutions of related partial differential equations.

Since the beginning of the century, the integral equations theory has

been an important subject in applied mathematics. Nowadays, due to

advances in numerical methods and computer facilities, this approach

can be used in the actual simulation of physical phenomena. One of the

most effective numerical techniques to solve integral equations is the

boundary element method.

Fluid mechanics is one of the main topics of applied mathematics

and physics. Some of the most relevant theories of these sciences have

been found during the study of fluid flow problems. Fluid dynamics is

also one of the most challenging areas of computational mechanics, the

simulation of fluid motion being a series test for any numerical

method, particularly for nonlinear problems. Integral equation

techniques offer an attractive alternative for the numerical solution

of a wide variety of problems in fluid dynamics.

The majority of mathematical books on integral equations are

purely theoretical, while the majority of engineering books give

emphasis on numerical solutions using boundary elements, with very

little theoretical background. This book intends to provide a bridge

between the engineering and mathematics literature on integral equation

techniques, particularly in the field of fluid dynamics. The main

subject of this book is the integral equation modelling of the flow of

incompressible viscous fluids.

The book is divided into seven chapters. The first three are

introductory, presnting an in-depth review of basic concepts of fluid

mechanics, integral equations, and potential theory, respectively.

Chapter 4 describes numerical techniques for solution of selected

potential problems with particular features like moving boundaries.

Chapters 5 to 7 cover the mathematical formulation and numerical

solution of creeping flow problems described by the Stokes equations,

and includes a thorough description of the completed double-layer

integral equation method originally developed by one of the authors.

Finally, Chapter 8 presents several numerical algorithms for solution

of the Navier-Stokes equations.

*Schclar, N.A.*

**Anisotropic Analysis using Boundary Elements**

1994

Topics in Engineering - Vol 20

Computational Mechanics Publications

ISBN: 1 85312333 1

ISBN: 1 56252 257 4 (US,

This book investigates the use of the Boundary Element Method to solve

three dimensional anisotropic potential and elastic problems.

Anisotropic analysis has been one of the major stumbling blocks for the

application of boundary elements in solving practical engineering

problems. This work comprises the numerical implementation of the well

known anisotropic fundamental solution and a new formulation based on

more recent work on the Dual Reciprocity Method. In both cases the

objective of the research is to produce a boundary only formulation

which retains the main advantage of the technique.

The new Dual Reciprocity Boundary Element formulation presented

here uses the fundamental solution for isotropic elasticity. The Dual

Reciprocity Method is used to model the anisotropy by expressing the

elastic constants as the sum of average isotropic values plus a

deviation and taking the resulting domain integrals to the boundary in

the usual manner. The technique is also extended to deal with any type

of body force.

A series of representative numerical examples are presented and

discussed to demonstrate the accuracy of the two methods used by the

author. Comparisons are carried out with analytical and other numerical

results.

Finally, a new adaptive technique is developed for the automatic

definition of the number and position of the internal points in the

Dual Reciprocity Boundary Element and error estimators are presented.

This book constitutes the most up to date work on the use of

boundary elements for anisotropic problems. It is addressed to

engineers involved in the development of boundary element computer

codes as well as researchers in academia and industry.

*Trevelyan, J.*

**Boundary Elements for Engineers: Theory and Applications**

1994

Computational Mechanics Publications

Southampton

ISBN: 1 85312279 3

ISBN: 1 56252 203 5 (US,

The book is designed to make BEM more accessible to students and

engineers looking for a concise overview of the method and the

mathematics behind it. The book also contains many examples of

realistic engineering analysis problems, describing how the BEM can be

applied most effectively.

The problem with the boundary element method is that, although the

end-user BEM software appears refreshingly simple, the theory behind it

is rarely described with anything approaching that simplicity. Text

books are widely available for the academic engineer, but not so for

the practising engineer. This book addresses the engineer's

requirements of a technical book including: the need to see an overview

of the theoretical formulation written in terms of engineering instead

of pure mathematics; and enough theory to feel comfortable with the use

of BEM software in production analysis, but not in a level of detail

which overcomplicates and clouds the main issues. The book provides

example application areas, and most importantly some indications of how

to use BEM software effectively in practice for real engineering problems.

This book results from several years of experience in working with

a commercial boundary element software package, BEASY, in a training

and support environment to industrial corporations using this code. In

this way, the book provides a combination of theory and practice in the

application of boundary elements to real world engineering.

**1995**

**1996**

**1997**

**1998**

*Kirkup, S.*

**The Boundary Element
Method in Acoustics**

1998

Integrated Sound

*Sládek,
V. and Sládek J.*

**Singular Integrals in Boundary Element Methods**

1998

Computational Mechanics Publications

ISBN: 1 85312 533 4

ISSN: 1460-1419

Boundary Element Methods (BEM) use
singular solutions, in contrast to other discretization methods, such as finite
element or finite difference methods. The presence of the mathematical
singularity gives rise to the need for accurate computation of singular
integrals. The appearance of singular integrals in BEM formulations is often
considered a handicap in computation. However, they can be a source of
effectiveness and stability in numerical solutions, if they are properly
treated.

This book provides a theoretical
and numerical treatment for singular integrals in BEMs. Both the boundary and
domain integrals are considered in two and three dimensional boundary value
problems, while the use of symbolic computation and the formulation using
complex arithmetic in the case of plane problems are outlines. The formulations
given deal with potential problems, elasticity, plate and crack problems.

Describing techniques which are
universal in character and can be applied to a wide variety of engineering
problems, this book will enable readers to understand the nature and treatment
of singular integrals in BEMs.

**1999**

*M. Bonnet*

**Boundary Integral Equation Methods for Fluids and Solids**

1999

J. Wiley and Sons

ISBN 0471 97184 7

Hardcover

Going far beyond the standard texts, this book extensively covers boundary
integral equation (BIE) formulations and the boundary element method (BEM). The
first section introduces BIE formulations for potential and elasticity
problems, following the modern regularization approach- the fundamental
starting point for research in this field. Secondly, a clear description of BIE
formulations for wave and elastodynamics problems, in both time and frequency
domains is presented. Finally, recent research in the field, related to
variational integral formulations, use of geometrical symmetry, shape
sensitivity and fracture mechanics is summarised. Within the text a broad range
of application areas, industrial as well as research related, are examined.
These include:

- elasticity and small-strain
elastoplasticity;
- time-domain and
frequency-domain scalar and elastic waves
- fracture mechanics

Including an extensive bibliography, this text
will be of considerable value and interest to graduate students, researchers
and lecturers in engineering mechanics, applied maths and physics, as well as
industrial practitioners working within these areas.

**2000-**

Books published in year 2000 and onward are listed in New Books section