Introductory text for engineers and scientists
Covers theory and implementation
Deals with a wide range of applications
Gernot Beer is Professor and head of the Institute for Structural Analysis at the Graz University of Technology. He has been involved in the development, teaching and application of the BEM and the coupled BEM/FEM and has written several texts on the subject. He is the author of the commercial program BEFE and heads the development of its successor BEFE++.
Ian M. Smith is Professor of Engineering at the University of Manchester. He has consulted widely on engineering projects and has written several texts on applied numerical analysis.
Christian Dünser is staff scientist at the Institute for Structural Analysis at the Graz University of Technology. Since his diploma thesis he has been working on the BEM and its application to geotechnical problems, in particular tunnelling.
This thorough yet understandable introduction to the boundary element method presents an attractive alternative to the finite element method. It not only explains the theory but also presents the implementation of the theory into computer code, the code in FORTRAN 95 can be freely downloaded. The book also addresses the issue of efficiently using parallel processing hardware in order to considerably speed up the computations for large systems. The applications range from problems of heat and fluid flow to static and dynamic elasto-plastic problems in continuum mechanics. After each chapter several exercises are shown, which makes the book suitable as teaching material in a class on the BEM. In addition, the book includes several applications of the method to industrial problems, that show the advantage over other methods.
Preface.- Acknowledgements.- Preliminaries: Introduction; Overview of book; Mathematical preliminaries; Conclusions; References.- Programming: Strategies; FORTAN 90/95/2000 features; Charts and pseudo code; Parallel programming; BLAS libraries; Pre- and Postprocessing; Conclusions; Exercises; References.- Discretisation and Interpolation: Introduction; One-dimensional boundary elements; Two-dimesional elements; Three-dimensional cells; Elements of infinite extent; Subroutines for shape functions; Interpolation; Coordinate transformation; Differential geometry; Integration over elements; PROGRAM 3.1: Calculation of surface area; Concluding remarks; Exercises; References.- Material Modelling and Fundamental Solutions: Introduction; Steady state potential problems; Static elasticity problems; Conclusions; References.- Boundary Integral Equations: Introduction; Trefftz method; PROGRAM 5.1: Flow around cylinder, Trefftz method; Direct method; Computation of results inside the domain; PROGRAM 5.2: Flow around cylinder, direct method; Conclusions; Exercises; References.- Boundary Element Methods – Numerical Implementation: Introduction; Discretisation with isoparametric elements; Integration of kernel shape function products; Conclusions; Exercises; References.- Assembly and Solution: Introduction; Assembly of system of equations; Solution of system of equations; PROGRAM 7.1: general purpose program, direct method, one region; Conclusions; Exercises; References.- Element-by-element techniques and Parallel Programming: Introduction; The Element by Element Concept; PROGRAM 8.1 : Replacing direct by iterative solution; PROGRAM 8.2 : Replacing assembly by element-by-element procedure; PROGRAM 8.3 : Parallelising the element-by-element procedure; Conclusions; References.- Postprocessing : Introduction; Computation of boundaryresults; Computation of internal results; PROGRAM 9.1: Postprocessor; Graphical display of results; Conclusions; Exercises; References.- Test Examples : Introduction; Cantilever beam; Circular excavation in infinite domain; Square excavation in infinite elastic space; Spherical excavation; Conclusions; References.- Multiple regions: Introduction; Stiffness matrix assembly; Computer implementation; Program 11.1: General purpose program, direct method, multiple regions; Conclusions; Exercises; References.- Dealing with corners and changing geometry: Introduction; Corners and edges; Dealing with changing geometry; Alternative Strategy; Conclusions; References.- Body Forces: Introduction; Gravity; Internal concentrated forces; Internal distributed line forces; Initial strains; Initial stresses; Numerical integration over cells; Implementation; Sample input file and results; Conclusions; Exercises; References.- Dynamic Analysis: Introduction; Scalar wave equation, frequency domain; Scalar wave equation, time domain; Elastodynamics; Multiple regions; Examples; References.- Nonlinear Problems: Introduction; General solution procedure; Plasticity; Contact problems; Conclusions; References.- Coupled Boundary Element/ Finite Element Analysis: Introduction; Coupling theory; Example; Dynamics; Conclusion; References.- Industrial Applications: Introduction; Mechanical engineering; Geotechnical Engineering; Geological engineering; Civil engineering; Reservoir engineering; Conclusions; References.- Advanced topics: Introduction; Heterogeneous Domains; Linear inclusions; Piezo-electricity; Conclusions; References.- Appendix.
An up-to-date Introductory for Engineers and Scientists
This thorough yet understandable introduction to the boundary element method presents an attractive alternative to the finite element method. It not only explains the theory but also presents the implementation of the theory into computer code.
This is a sequel to the book "Programming the Boundary Element Method" by G. Beer published by Wiley in 2001. The scope of this book is different however and this is reflected in the title. Whereas the previous book concentrated on explaining the implementation of a limited range of problems into computer code and the emphasis was on programming, in the current book the problems covered are extended, the emphasis is on explaining the theory and computer code is not presented for all topics. The new topics covered range from dynamics to piezo-electricity. However, the main idea, to provide an explanation of the Boundary Element Method (BEM), that is easy for engineers and scientists to follow, is retained. This is achieved by explaining some aspects of the method in an engineering rather than mathematical way. Another new feature of the book is that it deals with the implementation of the method on parallel processing hardware. I. M. Smith, who has been involved in programming the finite element method for decades, illustrates that the BEM is "embarrassingly parallelisable". It is shown that the conversion of the BEM programs to run efficiently on parallel processing hardware is not too difficult and the results are very impressive, such as solving a 20 000 element problem during a "coffee break".
Preliminaries.- Programming.- Discretisation and Interpolation.- Material Modelling and Fundamental Solutions.- Boundary Integral Equations.- Boundary Element Methods - Numerical Implementation.- Assembly and Solution.- Element-by-element techniques and Parallel Programming.- Postprocessing.- Test Examples.- Multiple regions.- Dealing with corners and changing geometry.- Body Forces.- Dynamic Analysis.- Nonlinear Problems.- Coupled Boundary Element/Finite Element Analysis.- Industrial Applications.- Advanced topics.
Über den Autor
Gernot Beer is Professor and head of the Institute for Structural Analysis at the Graz University of Technology. He has been involved in the development, teaching and application of the BEM and the coupled BEM/FEM and has written several texts on the subject. He is the author of the commercial program BEFE and heads the development of its successor BEFE++.nIan M. Smith is Professor of Engineering at the University of Manchester. He has consulted widely on engineering projects and has written several texts on applied numerical analysis. nChristian Dünser is staff scientist at the Institute for Structural Analysis at the Graz University of Technology. Since his diploma thesis he has been working on the BEM and its application to geotechnical problems, in particular tunnelling.
Inhaltsverzeichnis
Preface.- Acknowledgements.-nPreliminaries:nIntroduction; Overview of book; Mathematical preliminaries; Conclusions; References.-nProgramming:nStrategies; FORTAN 90/95/2000 features; Charts and pseudo code; Parallel programming; BLAS libraries; Pre- and Postprocessing; Conclusions; Exercises; References.-nDiscretisation and Interpolation:nIntroduction; One-dimensional boundary elements; Two-dimesional elements; Three-dimensional cells; Elements of infinite extent; Subroutines for shape functions; Interpolation; Coordinate transformation; Differential geometry; Integration over elements; PROGRAM 3.1: Calculation of surface area; Concluding remarks; Exercises; References.-nMaterial Modelling and Fundamental Solutions:nIntroduction; Steady state potential problems; Static elasticity problems; Conclusions; References.-nBoundary Integral Equations:nIntroduction; Trefftz method; PROGRAM 5.1: Flow around cylinder, Trefftz method; Direct method; Computation of results inside the domain; PROGRAM 5.2: Flow around cylinder, direct method; Conclusions; Exercises; References.-nBoundary Element Methods - Numerical Implementation:nIntroduction; Discretisation with isoparametric elements; Integration of kernel shape function products; Conclusions; Exercises; References.-nAssembly and Solution:nIntroduction; Assembly of system of equations; Solution of system of equations; PROGRAM 7.1: general purpose program, direct method, one region; Conclusions; Exercises; References.-nElement-by-element techniques and Parallel Programming:nIntroduction; The Element by Element Concept; PROGRAM 8.1 : Replacing direct by iterative solution; PROGRAM 8.2 : Replacing assembly by element-by-element procedure; PROGRAM 8.3 : Parallelising the element-by-element procedure; Conclusions; References.-nPostprocessing :nIntroduction; Computation of boundary results; Computation of internal results; PROGRAM 9.1: Postprocessor; Graphical display of results; Conclusions; Exercises; References.-nTest Examples :nIntroduction; Cantilever beam; Circular excavation in infinite domain; Square excavation in infinite elastic space; Spherical excavation; Conclusions; References.-nMultiple regions:nIntroduction; Stiffness matrix assembly; Computer implementation; Program 11.1: General purpose program, direct method, multiple regions; Conclusions; Exercises; References.-nDealing with corners and changing geometry:nIntroduction; Corners and edges; Dealing with changing geometry; Alternative Strategy; Conclusions; References.-nBody Forces:nIntroduction; Gravity; Internal concentrated forces; Internal distributed line forces; Initial strains; Initial stresses; Numerical integration over cells; Implementation; Sample input file and results; Conclusions; Exercises; References.-nDynamic Analysis:nIntroduction; Scalar wave equation, frequency domain; Scalar wave equation, time domain; Elastodynamics; Multiple regions; Examples; References.-nNonlinear Problems:nIntroduction; General solution procedure; Plasticity; Contact problems; Conclusions; References.-nCoupled Boundary Element/ Finite Element Analysis:nIntroduction; Coupling theory; Example; Dynamics; Conclusion; References.-nIndustrial Applications:nIntroduction; Mechanical engineering; Geotechnical Engineering; Geological engineering; Civil engineering; Reservoir engineering; Conclusions; References.-nAdvanced topics:nIntroduction; Heterogeneous Domains; Linear inclusions; Piezo-electricity; Conclusions; References.-nAppendix.
Klappentext
This thorough yet understandable introduction to the boundary element method presents an attractive alternative to the finite element method. It not only explains the theory but also presents the implementation of the theory into computer code, the code in FORTRAN 95 can be freely downloaded. The book also addresses the issue of efficiently using parallel processing hardware in order to considerably speed up the computations for large systems. The applications range from problems of heat and fluid flow to static and dynamic elasto-plastic problems in continuum mechanics.
This thorough yet understandable introduction to the boundary element method presents an attractive alternative to the finite element method. It not only explains the theory but also presents the implementation of the theory into computer code, the code in FORTRAN 95 can be freely downloaded. The book also addresses the issue of efficiently using parallel processing hardware in order to considerably speed up the computations for large systems. The applications range from problems of heat and fluid flow to static and dynamic elasto-plastic problems in continuum mechanics. After each chapter several exercises are shown, which makes the book suitable as teaching material in a class on the BEM. In addition, the book includes several applications of the method to industrial problems, that show the advantage over other methods.
