This is a thorough, yet understandable text about the boundary element method (BEM), an attractive alternative to the finite element method (FEM). It not only explains the theory, but also deals with the implementation into computer code written in FORTRAN 95 (software can be freely downloaded). Applications range from potential problems to static and dynamic problems in elasticity and plasticity. The book also addresses the issue of fast solution of large scale problems, using parallel processing hardware. Special topics such as the treatment of inclusions, heterogeneous domains and changing geometry are also addressed. Most chapters contain exercises and this makes the book suitable for teaching. Applications of the method to industrial problems are shown. The book is designed for engineers and scientists that want to understand how the method works and to apply the method and solve real problems.
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
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 Dunser 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.