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E-raamat: Boundary Element Method with Programming: For Engineers and Scientists

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 03-Sep-2008
  • Kirjastus: Springer Verlag GmbH
  • Keel: eng
  • ISBN-13: 9783211715765
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Boundary Element Method with Programming: For Engineers and ScientistsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 03-Sep-2008
  • Kirjastus: Springer Verlag GmbH
  • Keel: eng
  • ISBN-13: 9783211715765
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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.

Muu info

An up-to-date Introductory for Engineers and Scientists
Preface xiii
Acknowledgements xiv
1 Preliminaries
1
1.1 Introduction
1
1.2 Overview of book
4
1.3 Mathematical preliminaries
6
1.3.1 Vector algebra
7
1.3.2 Stress and strain
10
1.4 Conclusions
11
1.5 References
11
2 Programming
13
2.1 Strategies
13
2.2 FORTAN 90/95/2000 features
14
2.2.1 Representation of numbers
14
2.2.2 Arrays
15
2.2.3 Array operations
16
2.2.4 Control
20
2.2.5 Subroutines and functions
21
2.2.6 Subprogram libraries and common variables
23
2.3 Charts and pseudo code
24
2.4 Parallel programming
25
2.5 BLAS libraries
27
2.6 Pre- and Postprocessing
27
2.7 Conclusions
27
2.8 Exercises
28
2.9 References
29
3 Discretisation and Interpolation
31
3.1 Introduction
32
3.2 One-dimensional boundary elements
32
3.3 Two-dimesional elements
36
3.4 Three-dimensional cells
44
3.5 Elements of infinite extent
44
3.6 Subroutines for shape functions
46
3.7 Interpolation
47
3.7.1 Isoparametric elements
47
3.7.2 Infinite elements
49
3.7.3 Discontinuous elements
50
3.8 Coordinate transformation
53
3.9 Differential geometry
54
3.10 Integration over elements
59
3.10.1 Integration over boundary elements
59
3.10.2 Integration over cells
59
3.10.3 Numerical integration
60
3.11 PROGRAM 3.1: Calculation of surface area
64
3.12 Concluding remarks
65
3.13 Exercises
65
3.14 References
67
4 Material Modelling and Fundamental Solutions
69
4.1. Introduction
69
4.2. Steady state potential problems
70
4.3. Static elasticity problems
76
4.3.1 Constitutive equations
82
4.3.2 Fundamental solutions
85
4.4. Conclusions
94
4.5. References
94
5 Boundary Integral Equations
95
5.1 Introduction
95
5.2 Trefftz method
96
5.3 PROGRAM 5.1: Flow around cylinder, Trefftz method
99
5.3.1 Sample input and output
102
5.4 Direct method
104
5.4.1 Theorem of Betti and integral equations
104
5.4.2 Limiting values of integrals as P coincides with Q
107
5.4.3 Solution of integral equations
110
5.5 Computation of results inside the domain
116
5.6 PROGRAM 5.2: Flow around cylinder, direct method
118
5.6.1 Sample input and output
122
5.7 Conclusions
125
5.8 Exercises
127
5.9 References
127
6 Boundary Element Methods – Numerical Implementation
129
6.1 Introduction
129
6.2 Discretisation with isoparametric elements
130
6.3 Integration of kernel shape function products
133
6.3.1 Singular integrals
134
6.3.2 Rigid body motion
135
6.3.3 Numerical integration
139
6.3.4 Numerical integration over one-dimensional elements
142
6.3.5 Subdivision of region of integration
146
6.3.6 Implementation for plane problems
148
6.3.7 Numerical integration for two-dimensional elements
155
6.3.8 Subdivision of region of integration
159
6.3.9 Infinite elements
160
6.3.10 Implementation for three-dimensional problems
161
6.4 Conclusions
166
6.5 Exercises
167
6.6 References
168
7 Assembly and Solution
169
7.1 Introduction
169
7.2 Assembly of system of equations
170
7.2.1 Symmetry
176
7.2.2 Subroutine MIRROR
180
7.2.3 Subroutine Assembly
183
7.3 Solution of system of equations
184
7.3.1 Gauss elimination
185
7.3.2 Scaling
187
7.4 PROGRAM 7.1: general purpose program, direct method, one region
187
7.4.1 User's manual
195
7.4.2 Sample input file
198
7.5 Conclusions
199
7.6 Exercises
200
7.7 References
202
8 Element-by-element techniques and Parallel Programming
203
8.1 Introduction
203
8.1 The Element by Element Concept
204
8.1.1 Element-by-element storage requirements
206
8.2 PROGRAM 8.1: Replacing direct by iterative solution
206
8.2.1 Sample input file
211
8.2.2 Sample output file
212
8.3 PROGRAM 8.2: Replacing assembly by element-by-element procedure
213
8.3.1 Sample input file
219
8.3.2 Sample output file
219
8.4 PROGRAM 8.3: Parallelising the element-by-element procedure
220
8.4.1 Sample input file
227
8.4.2 Sample output file
227
8.4.3 Results from larger analyses
228
8.5 Conclusions
229
8.6 References
229
9 Postprocessing
231
9.1 Introduction
231
9.2 Computation of boundary results
232
9.2.1 Potential problems
232
9.2.2 Elasticity problems
236
9.3 Computation of internal results
241
9.3.1 Potential problems
241
9.3.2 Elasticity problems
245
9.4 PROGRAM 9.1: Postprocessor
250
9.4.1 Input specification
258
9.5 Graphical display of results
259
9.6 Conclusions
261
9.7 Exercises
262
9.8 References
262
10 Test Examples 263
10.1. Introduction
263
10.2. Cantilever beam
264
10.2.1 Problem statement
264
10.2.2 Boundary element discretisation and input
264
10.2.3 Results
266
10.2.4 Comparison with FEM
269
10.2.5 Conclusions
271
10.3. Circular excavation in infinite domain
271
10.3.1 Problem statement
271
10.3.2 Boundary element discretisation and input
272
10.3.3 Results
274
10.3.4 Comparison with FEM
275
10.3.5 Conclusions
276
10.4. Square excavation in infinite elastic space
276
10.4.1 Problem statement
276
10.4.2 Boundary element discretisation and input
277
10.4.3 "Quarter point" elements
281
10.4.4 Comparison with finite elements
282
10.4.5 Conclusions
282
10.5. Spherical excavation
283
10.5.1 Problem statement
283
10.5.2 Boundary element discretisation and input
283
10.5.3 Results
289
10.5.4 Comparison with FEM
290
10.6. Conclusions
290
10.7. References
291
11 Multiple regions 293
11.1 Introduction
293
11.2 Stiffness matrix assembly
294
11.2.1 Partially coupled problems
296
11.2.2 Example
299
11.3 Computer implementation
304
11.3.1 Subroutine Stiffness_BEM
306
11.4 Program 11.1: General purpose program, direct method, multiple regions
311
11.4.1 User's manual
321
11.4.2 Sample problem
323
11.5 Conclusions
326
11.6 Exercises
327
11.7 References
328
12 Dealing with corners and changing geometry 329
12.1 Introduction
329
12.2 Corners and edges
330
12.2.1 Discontinuous elements
331
12.2.2 Numerical integration for one-dimensional elements
331
12.2.3 Numerical implementation
335
12.2.4 Test example — single region
343
12.2.5 Test example — multi region
344
12.3 Dealing with changing geometry
346
12.3.1 Example
348
12.4 Alternative Strategy
351
12.5 Conclusions
353
12.6 References
353
13 Body Forces 355
13.1 Introduction
355
13.2 Gravity
356
13.2.1 Post-processing
358
13.3 Internal concentrated forces
361
13.3.1 Post-processing
363
13.4 Internal distributed line forces
363
13.4.1 Post-processing
365
13.5 Initial strains
365
13.5.1 Post-processing
369
13.6 Initial stresses
372
13.7 Numerical integration over cells
373
13.8 Implementation
374
13.8.1 Input data specification for Body force
377
13.9 Sample input file and results
378
13.10 Conclusions
381
13.11 Exercises
382
13.12 References
383
14 Dynamic Analysis 385
14.1 Introduction
385
14.2 Scalar wave equation, frequency domain
385
14.2.1 Fundamental solutions
387
14.2.2 Boundary Integral Equations
388
14.2.3 Numerical Implementation
389
14.3 Scalar wave equation, time domain
390
14.3.1 Fundamental solutions
390
14.3.2 Boundary integral equations
392
14.3.3 Numerical implementation
395
14.4 Elastodynamics
398
14.4.1 Fundamental solutions
399
14.4.2 Boundary integral equations
399
14.4.3 Numerical implementation
400
14.5 Multiple regions
401
14.6 Examples
403
14.6.1 Test example
403
14.6.2 Practical application
405
14.7 References
406
15 Nonlinear Problems 407
15.1 Introduction
407
15.2 General solution procedure
408
15.3 Plasticity
410
15.3.1 Elasto-plasticity
410
15.3.2 Visco-plasticity
413
15.3.3 Method of solution
415
15.3.4 Calculation of residual {R}
417
15.3.5 Computation of stresses at cell nodes
421
15.3.6 Computation of boundary stresses
423
15.3.7 Example
425
15.4 Contact problems
427
15.4.1 Method of analysis
427
15.4.2 Solution procedure
430
15.4.3 Example of application
431
15.5 Conclusions
433
15.6 References
433
16 Coupled Boundary Element/Finite Element Analysis 435
16.1 Introduction
435
16.2 Coupling theory
436
16.2.1 Coupling to finite elements
436
16.2.2 Coupling to boundary elements
443
16.3 Example
444
16.4 Dynamics
446
16.4.1 Example
447
16.5 Conclusion
447
16.6 References
449
17 Industrial Applications 451
17.1 Introduction
451
17.2 Mechanical engineering
453
17.2.1 A cracked extrusion press causes concern
453
17.3 Geotechnical Engineering
457
17.3.1 CERN Caverns
457
17.4 Geological engineering
461
17.4.1 How to find gold with boundary elements
461
17.5 Civil engineering
464
17.5.1 Masi ed-o-Soleiman underground power house
464
17.6 Reservoir engineering
470
17.6.1 Borehole stability
470
17.7 Conclusions
472
17.8 References
473
18 Advanced topics 475
18.1 Introduction
475
18.2 Heterogeneous Domains
476
18.2.1 Theory
476
18.2.2 Example
477
18.3 Linear inclusions
479
18.3.1 Theory
479
18.3.2 Example
484
18.4 Piezo-electricity
485
18.4.1 Changes required in General_Purpose_BEM
487
18.5 Conclusions
488
18.6 References
489
Appendix 491
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.
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