Beer / Smith / Duenser The Boundary Element Method with Programming

For Engineers and Scientists
1. Auflage 2008
ISBN: 978-3-211-71576-5
Verlag: Springer Vienna
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 498 Seiten

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.

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.

Autoren/Hrsg.

Beer, Gernot

Smith, Ian

Duenser, Christian

Inhaltsverzeichnis

1;Contents;5
2;Preface;12
2.1;COMPUTER PROGRAMS;12
3;Acknowledgements;13
4;1 Preliminaries;14
4.1;1.1 INTRODUCTION;14
4.2;1.2 OVERVIEW OF BOOK;17
4.3;1.3 MATHEMATICAL PRELIMINARIES;19
4.4;1.4 CONCLUSIONS;24
4.5;1.5 REFERENCES;24
5;2 Programming;25
5.1;2.1 STRATEGIES;25
5.2;2.2 FORTAN 90/95/2000 FEATURES;26
5.3;2.3 CHARTS AND PSEUDO CODE;35
5.4;2.4 PARALLEL PROGRAMMING;37
5.5;2.5 BLAS LIBRARIES;39
5.6;2.6 PRE- AND POST-PROCESSING;39
5.7;2.7 CONCLUSIONS;39
5.8;2.8 EXERCISES;40
5.9;2.9 REFERENCES;41
6;3 Discretisation and Interpolation;42
6.1;3.1 INTRODUCTION;42
6.2;3.2 ONE-DIMENSIONAL BOUNDARY ELEMENTS;43
6.3;3.3 TWO-DIMENSIONAL ELEMENTS;47
6.4;3.4 THREE-DIMENSIONAL CELLS;54
6.5;3.5 ELEMENTS OF INFINITE EXTENT;55
6.6;3.6 SUBROUTINES FOR SHAPE FUNCTIONS;57
6.7;3.7 INTERPOLATION;58
6.8;3.8 COORDINATE TRANSFORMATION;64
6.9;3.9 DIFFERENTIAL GEOMETRY;65
6.10;3.10 INTEGRATION OVER ELEMENTS;70
6.11;3.11 PROGRAM 3.1: CALCULATION OF SURFACE AREA;74
6.12;3.12 CONCLUDING REMARKS;76
6.13;3.13 EXERCISES;76
6.14;3.14 REFERENCES;78
7;4 Material Modelling andFundamental Solutions;79
7.1;4.1. INTRODUCTION;79
7.2;4.2. STEADY STATE POTENTIAL PROBLEMS;80
7.3;4.3. STATIC ELASTICITY PROBLEMS;86
7.4;4.4. CONCLUSIONS;104
7.5;4.5. REFERENCES;104
8;5 Boundary Integral Equations;105
8.1;5.1 INTRODUCTION;105
8.2;5.2 TREFFTZ METHOD;106
8.3;5.3 PROGRAM 5.1: FLOW AROUND CYLINDER, TREFFTZ METHOD;109
8.4;5.4 DIRECT METHOD;114
8.5;5.5 COMPUTATION OF RESULTS INSIDE THE DOMAIN;126
8.6;5.6 PROGRAM 5.2: FLOW AROUND CYLINDER, DIRECT METHOD;128
8.7;5.7 CONCLUSIONS;135
8.8;5.8 EXERCISES;137
8.9;5.9 REFERENCES;137
9;6 Boundary Element Methods –Numerical Implementation;138
9.1;6.1 INTRODUCTION;138
9.2;6.2 DISCRETISATION WITH ISOPARAMETRIC ELEMENTS;139
9.3;6.3 INTEGRATION OF KERNEL SHAPE FUNCTION PRODUCTS;142
9.4;6.4 CONCLUSIONS;175
9.5;6.5 EXERCISES;176
9.6;6.6 REFERENCES;177
10;7 Assembly and Solution;178
10.1;7.1 INTRODUCTION;178
10.2;7.2 ASSEMBLY OF SYSTEM OF EQUATIONS;179
10.3;7.3 SOLUTION OF SYSTEM OF EQUATIONS;193
10.4;7.4 PROGRAM 7.1: GENERAL PURPOSE PROGRAM, DIRECT METHOD, ONE REGION;196
10.5;7.5 CONCLUSIONS;208
10.6;7.6 EXERCISES;209
10.7;7.7 REFERENCES;211
11;8 Element-by-element techniques and Parallel Programming;212
11.1;8.1 INTRODUCTION;212
11.2;8.1 THE ELEMENT-BY-ELEMENT CONCEPT;213
11.3;8.2 PROGRAM 8.1 : REPLACING DIRECT BY ITERATIVE SOLUTION;215
11.4;8.3 PROGRAM 8.2 : REPLACING ASSEMBLY BY THE ELEMENT- BY- ELEMENT PROCEDURE;222
11.5;8.4 PROGRAM 8.3 : PARALLELISING THE ELEMENT_ BY_ ELEMENT PROCEDURE;229
11.6;8.5 CONCLUSIONS;238
11.7;8.6 REFERENCES;238
12;9 Postprocessing;239
12.1;9.1 INTRODUCTION;239
12.2;9.2 COMPUTATION OF BOUNDARY RESULTS;240
12.3;9.3 COMPUTATION OF INTERNAL RESULTS;249
12.4;9.4 PROGRAM 9.1: POSTPROCESSOR;258
12.5;9.5 GRAPHICAL DISPLAY OF RESULTS;267
12.6;9.6 CONCLUSIONS;269
12.7;9.7 EXERCISES;270
12.8;9.8 REFERENCES;270
13;10 Test Examples;271
13.1;10.1 INTRODUCTION;271
13.2;10.2 CANTILEVER BEAM;272
13.3;10.3 CIRCULAR EXCAVATION IN INFINITE DOMAIN;279
13.4;10.4 SQUARE EXCAVATION IN INFINITE ELASTIC SPACE;284
13.5;10.5 SPHERICAL EXCAVATION;291
13.6;10.6 CONCLUSIONS;298
13.7;10.7 REFERENCES;299
14;11 Multiple regions;300
14.1;11.1 INTRODUCTION;300
14.2;11.2 STIFFNESS MATRIX ASSEMBLY;301
14.3;11.3 COMPUTER IMPLEMENTATION;311
14.4;11.4 PROGRAM 11.1: GENERAL PURPOSE PROGRAM, DIRECT METHOD, MULTIPLE REGIONS;318
14.5;11.5 CONCLUSIONS;333
14.6;11.6 EXERCISES;334
14.7;11.7 REFERENCES;335
15;12 Dealing with corners andchanging geometry;336
15.1;12.1 INTRODUCTION;336
15.2;12.2 CORNERS AND EDGES;337
15.3;12.3 DEALING WITH CHANGING GEOMETRY;353
15.4;12.4 ALTERNATIVE STRATEGY;358
15.5;12.5 CONCLUSIONS;360
15.6;12.6 REFERENCES;360
16;13 Body Forces;361
16.1;13.1 INTRODUCTION;361
16.2;13.2 GRAVITY;362
16.3;13.3 INTERNAL CONCENTRATED FORCES;367
16.4;13.4 INTERNAL DISTRIBUTED LINE FORCES;369
16.5;13.5 INITIAL STRAINS;371
16.6;13.6 INITIAL STRESSES;378
16.7;13.7 NUMERICAL INTEGRATION OVER CELLS;379
16.8;13.8 IMPLEMENTATION;380
16.9;13.9 SAMPLE INPUT FILE AND RESULTS;384
16.10;13.10 CONCLUSIONS;387
16.11;13.11 EXERCISES;388
16.12;13.12 REFERENCES;389
17;14 Dynamic Analysis;390
17.1;14.1 INTRODUCTION;390
17.2;14.2 SCALAR WAVE EQUATION, FREQUENCY DOMAIN;391
17.3;14.3 SCALAR WAVE EQUATION, TIME DOMAIN;395
17.4;14.4 ELASTODYNAMICS;403
17.5;14.5 MULTIPLE REGIONS;406
17.6;14.6 EXAMPLES;408
17.7;14.7 REFERENCES;411
18;15 Nonlinear Problems;412
18.1;15.1 INTRODUCTION;412
18.2;15.2 GENERAL SOLUTION PROCEDURE;413
18.3;15.3 PLASTICITY;415
18.4;15.4 CONTACT PROBLEMS;432
18.5;15.5 CONCLUSIONS;438
18.6;15.6 REFERENCES;438
19;16 Coupled Boundary Element / Finite Element Analysis;440
19.1;16.1 INTRODUCTION;440
19.2;16.2 COUPLING THEORY;441
19.3;16.3 EXAMPLE;449
19.4;16.4 DYNAMICS;451
19.5;16.5 CONCLUSION;453
19.6;16.6 REFERENCES;454
20;17 Industrial Applications;455
20.1;17.1 INTRODUCTION;455
20.2;17.2 MECHANICAL ENGINEERING;457
20.3;17.3 GEOTECHNICAL ENGINEERING;461
20.4;17.4 GEOLOGICAL ENGINEERING;465
20.5;17.5 CIVIL ENGINEERING;468
20.6;17.6 RESERVOIR ENGINEERING;474
20.7;17.7 CONCLUSIONS;476
20.8;17.8 REFERENCES;477
21;18 Advanced topics;478
21.1;18.1 INTRODUCTION;478
21.2;18.2 HETEROGENEOUS DOMAINS;479
21.3;18.3 LINEAR INCLUSIONS;482
21.4;18.4 PIEZO-ELECTRICITY;488
21.5;18.5 CONCLUSIONS;492
21.6;18.6 REFERENCES;492
22;Appendix;493
22.1;A.1. DISPLACEMENT SOLUTION;493
22.2;A.2. STRAIN SOLUTION;495
22.3;A.3. STRESS SOLUTION;496