Boundary Element Programming in Mechanics

Abstract

1R1. Boundary Element Programming in Mechanics. - Xiao-Wei Gao (Dept of Mech and Aerospace Eng, Arizona State Univ, Tempe AZ) and TG Davies (Glasgow Univ, UK). Cambridge UP, Cambridge, UK. 2002. 254 pp. (CD-Rom included). ISBN 0-521-77359-8. $69.95. Reviewed by DE Beskos (Dept of Civil Eng, Univ of Patras, Patras, GR-26500, Greece).This is a really excellent textbook as well as a reference book on the numerical implementation and computer programing of the direct boundary element method as applied to two and three-dimensional problems of linear elasticity and nonlinear elastoplasticity. The book is aimed at both graduate students and researchers as well as practicing engineers in mechanical, aeronautical, and civil engineering fields. The book consists of 254 pages plus a CD-Rom with the computer programs described. The whole book can be divided in two main components: The first one dealing with linear problems (elasticity) and the second one with nonlinear problems (time independent elastostoplasticity). In both parts, the chapter breakdown is the same and consists of the theory (of elasticity or plasticity), the corresponding boundary integral formulation of the problem, the numerical implementation, the detailed (subroutine by subroutine) description of the computer program and a number of applications—numerical examples to illustrate the code and demonstrate its accuracy. The book is completed by an introduction and an epilogue, eight appendices, a list of references, and a subject index. The figures and tables are of very good quality. The list of references is comprehensive, but selective, and the subject index is informative, but somewhat short. The unusual features of this book, in order of importance, are the following: the book is very clearly written and the English language is not just correct and easy to understand, but lively and enjoyable. The authors have proved they are not just very good on technical matters, but they also know to handle the English language superbly. The various computational aspects of the boundary element method, such as singular integration, treatment of edges and corners, computation of boundary stresses, solution of systems of linear equations, return mapping algorithms in plasticity, etc, are all treated in detail. In particular, the authors in every case, first discuss the problem, mention the work of others, and then offer their solution which they consider to be the most effective. The computer programs are explained in detail on a subroutine-by-subroutine basis and serve to illustrate the implementation of the method in the best possible way. In addition, they can be modified by the user, if he wishes to add or replace things. There is an emphasis on three-dimensional problems both in elasticity and plasticity, which cannot be found in other books on the subject. The book succeeds completely relative to the author’s stated aims and the subject matter. As a matter of fact, the book can be the ideal vehicle to teach the boundary element method to engineers who want the theory to go hand-in-hand with the numerical implementation and are not so much interested in mathematical details. Thus, the book can be used either as an ideal introductory text on boundary elements, in general, or as a specialized book on boundary element methods in plasticity. There are many introductory books available on boundary elements, but most of them deal with potential theory and elasticity, and they do not emphasize either the numerical implementation of the method nor 3D problems. This reviewer predicts that this book will prove to be, for boundary element programing, what has been the case with the two texts by Hinton and Owen on finite elements. The only slightly negative about this book has to do with the title, which employs the general and misleading term mechanics instead of the more appropriate term solid mechanics, which would more exactly reflect the contents of the book. Boundary Element Programming in Mechanics is highly recommended for purchase by both individuals and libraries.