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Boundary element methods in solid mechanics
NEW BOOKS The Boundary Integral Equation Method for Porous Media Flow J. A. Liggett and P. L-F. Liu George Allen & Unwin, November 1982, 272 pp. £17.50, ISBN 0 04 620011 8 The Boundary Integral Equation Method (BIEM) is shown in this book to be a powerful analytical tool whose usefulness rivals the finite element method. Concentrating on flow through porous media in order to illustrate the BIEM's versatility in solving a variety of complex problems, the authors take the reader from an elementary introduction through to a demonstration of the method's application to problems with singularities, non-linear free surface problems, well problems, recharge problems and problems that are inhomogeneous and isotropic. They show that the BIEM not only shares the advantages of the finite element method but is also easier to use and considerably less expensive in terms of computer time and storage requirements, thereby facilitating the routine solution of large problems. Furthermore, it can be coupled to the finite element method in order to exploit the strengths of both. Finally, the BIEM is developed for solutions in a comprehensive groundwater basin of considerabe complexity. Program illustration in the last chapter enables the reader to make a start on his own programs. The treatment in the book allows it to serve as a general introduction to the BIEM. It relates the mathematics to physical problems that can be grasped intuitively. On the other hand, calculation in porous media is explored in detail, providing a guide for readers with limited experience in numerical analysis. Based on four years of research, and tested in the form of a short course given at Cornell University, this book will be useful to hydrologists, numerical analysts and many other engineers faced with the problems posed by porous media.
Boundary Element Methods in Solid Mechanics S. L. Crouch and A. M. Starfield George Allen & Unwin, May 1982, 320 pp. £15.00, ISBN 004620010X The boundary element t e c h n i q u e - an inherently simple and flexible method of numerical analysis for boundary value problems in science and engineering p r o b l e m s - is presented in this book lucidly and with a practical approach. Scientists and engineers acquainted with the finite difference and finite element methods will find this treatment to be a timely introduction to a complementary technique whose range of application is growing rapidly. The authors, drawing on 14 years of research and practical experience, have faced squarely the problems supposedly associated with the boundary element method: computer programs (or packages) of restricted applicability, abstruse theoretical discussion, and limited evidence of its general usefulness beyond the context of a particular practical problem. Throughout the book the mathematics is kept as simple as possible and at every opportunity the physical aspects are emphasised to demonstrate its meaning and usefulness. The modular structure of the methods is highlighted to show how they can be readily modified to meet particular goals. The approach is flexible, structured and problem oriented. Representative computer programs are included for all the main methods, but the authors have deliberately avoided presenting a general computer package.
The book begins with an over view touching on various physical phenomena amenable to boundary element m e t h o d s - electrostatics, heat and fluid flow, elasticity, fracture mechanics - and proceeds to concentrate on solid mechanics. After a review of the relevant aspects of the theory of elasticity, a simple boundary element method is developed from the Flamant solution for a line of concentrated force on the surface of an elastic half-plane, thus demonstrating the constructive connection between solutions to simple and complex problems. Then 'indirect' and 'direct' methods for plane problems are developed, largely from a physical standpoint. The penultimate chapter is devoted to extensions of boundary element methods and to techniques for refining solutions, both general and specific. Finally, applications in rock mechanics and geological engineering are given to illustrate how the methods lend themselves to an easy physical interpretation. All engineers, scientists and numerical analysts concerned with applied mechanics will find this book useful as an introduction to a relative new and very promising body of analytical techniques. Students in particular will value the lucid explanations, while the more advanced reader will appreciate the inclusion of new and previously unpublished results. •
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BOOK REVIEW Programming the Finite Element Method with Application to Geomechanics I. M. Smith John Wiley & Sons, 1982, 345 pp. The aim of this book is to enable the reader to develop his own programs to solve specific problems using finite element methods. The programs in the book are constructed from a library of 'building block' subroutines, some of which are concerned with basic matrix manipulation, while others have more specific purposes. The standard or 'black box' subroutines are not listed in the book, although the author offers to supply a source tape on request. Many of these routines can be found on the NAG library. F O R T R A N is used throughout, but to illustrate its limitations the author gives some examples of ALGOL68. All programs are written in 'structured' style and structure charts are given in place of the usual flow charts. Stiffness and mass matrices are developed for a number of elements (rod, beam, plane stress, plane strain and plate bending) and the process of assembly, inserting boundary conditions and solution is shown. As well as these fairly basic structural applications the book covers a number of more specialised topics including non-tinearity (elasto-plastic and visco-plastic), fluid flow (including coupled solid/fluid problems), vibration analysis and pile drivability. Each chapter has a section dealing with the geotechnical applications and in most chapters there is an example program. The appendices contain specifications and descriptions of the 'black box' subroutines, listings of special purpose subroutines and complete programs for plane strain analysis written in F O R T R A N and ALGOL68. This book will prove very useful for engineers who wish to write their own programs and also should be of interest to those who would like to know more about the theoretical background to commercially available programs.
Stephen Troop
Applied Ocean Research, 1983, Vol. 5, No. 2
117
Boundary Element Methods in Solid Mechanics S. L. Crouch and A. M. Starfield George Allen & Unwin, May 1982, 320 pp. £15.00, ISBN 004620010X The boundary element t e c h n i q u e - an inherently simple and flexible method of numerical analysis for boundary value problems in science and engineering p r o b l e m s - is presented in this book lucidly and with a practical approach. Scientists and engineers acquainted with the finite difference and finite element methods will find this treatment to be a timely introduction to a complementary technique whose range of application is growing rapidly. The authors, drawing on 14 years of research and practical experience, have faced squarely the problems supposedly associated with the boundary element method: computer programs (or packages) of restricted applicability, abstruse theoretical discussion, and limited evidence of its general usefulness beyond the context of a particular practical problem. Throughout the book the mathematics is kept as simple as possible and at every opportunity the physical aspects are emphasised to demonstrate its meaning and usefulness. The modular structure of the methods is highlighted to show how they can be readily modified to meet particular goals. The approach is flexible, structured and problem oriented. Representative computer programs are included for all the main methods, but the authors have deliberately avoided presenting a general computer package.
The book begins with an over view touching on various physical phenomena amenable to boundary element m e t h o d s - electrostatics, heat and fluid flow, elasticity, fracture mechanics - and proceeds to concentrate on solid mechanics. After a review of the relevant aspects of the theory of elasticity, a simple boundary element method is developed from the Flamant solution for a line of concentrated force on the surface of an elastic half-plane, thus demonstrating the constructive connection between solutions to simple and complex problems. Then 'indirect' and 'direct' methods for plane problems are developed, largely from a physical standpoint. The penultimate chapter is devoted to extensions of boundary element methods and to techniques for refining solutions, both general and specific. Finally, applications in rock mechanics and geological engineering are given to illustrate how the methods lend themselves to an easy physical interpretation. All engineers, scientists and numerical analysts concerned with applied mechanics will find this book useful as an introduction to a relative new and very promising body of analytical techniques. Students in particular will value the lucid explanations, while the more advanced reader will appreciate the inclusion of new and previously unpublished results. •
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BOOK REVIEW Programming the Finite Element Method with Application to Geomechanics I. M. Smith John Wiley & Sons, 1982, 345 pp. The aim of this book is to enable the reader to develop his own programs to solve specific problems using finite element methods. The programs in the book are constructed from a library of 'building block' subroutines, some of which are concerned with basic matrix manipulation, while others have more specific purposes. The standard or 'black box' subroutines are not listed in the book, although the author offers to supply a source tape on request. Many of these routines can be found on the NAG library. F O R T R A N is used throughout, but to illustrate its limitations the author gives some examples of ALGOL68. All programs are written in 'structured' style and structure charts are given in place of the usual flow charts. Stiffness and mass matrices are developed for a number of elements (rod, beam, plane stress, plane strain and plate bending) and the process of assembly, inserting boundary conditions and solution is shown. As well as these fairly basic structural applications the book covers a number of more specialised topics including non-tinearity (elasto-plastic and visco-plastic), fluid flow (including coupled solid/fluid problems), vibration analysis and pile drivability. Each chapter has a section dealing with the geotechnical applications and in most chapters there is an example program. The appendices contain specifications and descriptions of the 'black box' subroutines, listings of special purpose subroutines and complete programs for plane strain analysis written in F O R T R A N and ALGOL68. This book will prove very useful for engineers who wish to write their own programs and also should be of interest to those who would like to know more about the theoretical background to commercially available programs.
Stephen Troop
Applied Ocean Research, 1983, Vol. 5, No. 2
117