Boundary Element Methods (eBook)

Principles and Applications

Q. Du, Mana Tanaka (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
428 Seiten
Elsevier Science (Verlag)
978-1-4832-9794-1 (ISBN)

Infos

Significant developments in the boundary element method during the last two decades have made it a powerful alternative to the domain-type numerical methods of solution such as the finite element method. The advances made in the BEM are more or less due to the innovation of efficient computational techniques by introducing boundary elements for discretization of the boundary integral equations resulting from the so-called direct formulation. BEM has therefore become an efficient tool for optimal design and other inverse problems. These proceedings include discussion of the applications of BEM in mechanical engineering and the principles that have developed to make it an increasingly useful method of problem solving.

Inhalt

Front Cover 4
Boundary Element Methods: Principles and Applications 4
Copyright Page 5
Table of Contents 6
Preface 10
COMMITTEES 12
Part 1: Crack Analysis I 14
CHAPTER 1. BOUNDARY ELEMENT ANALYSIS OF THREE DIMENSIONAL 
16 
ABSTRACT 16
KEYWORDS 16
INTRODUCTION 16
PROCEDURE OF ANALYSIS 17
NUMERICAL INTEGRATION OF THE FUNDAMENTAL SOLUTIONS 18
NUMERICAL EXAMPLES 19
CONCLUDING REMARKS 20
REFERENCES 20
CHAPTER 2. BEM FOR ELASTO-PLASTIC ANALYSIS OF 3-D 
26 
ABSTRACT 26
KEYWORDS 26
INTRODUCTION 26
FUNDAMENTAL EQUATIONS AND DISCRETIZATION 27
J-INTEGRAL FOR THREE DIMENTIONAL 27
SOME NUMERICAL SOLUTION TECHNIQUES 28
NUMERICAL EXAMPLES 29
DISCUSSIONS 32
REFERENCES 32
CHAPTER 3. BOUNDARY ELEMENT ELASTOSTATIC ANALYSIS OF 
34 
ABSTRACT 34
KEYWORDS 34
INTRODUCTION 34
BEM PROGRAM USING TWO KINDS OF FUNDAMENTAL SOLUTION 35
STRESS DISTRIBUTION ALONG INTERFACE AND THE SINGULARITY 36
ANALYSIS OF INTERFACE CRACK PROBLEMS 36
RESIDUAL STRESS ANALYSIS OF DISSIMILAR MATERIALS 41
CONCLUSIONS 42
REFERENCES 43
Part 2: Elastodynamics I 44
CHAPTER 4. BOUNDARY ELEMENT METHOD WITH FOURIER EIGEN 
46 
ABSTRACT 46
KEYWORDS 46
INTRODUCTION 46
FUNDAMENTAL EQUATIONS OF ELASTODYNAMICS 47
BOUNDARY INTEGRAL EQUATIONS OF ELASTODYNAMICS 48
FOURIER EIGEN TRANSFORM 49
EXAMPLE OF FET 51
EXAMPLE OF ELASTODYNAMICS 52
ACKNOWLEDGMENT 52
REFERENCES 53
CHAPTER 5. TRANSIENT BOUNDARY ELEMENT ANALYSIS OF TWO–DIMENSIONAL SCALAR WAVE PROBLEMS BASED ON TIME– 
54 
ABSTRACT 54
KEY WORDS 54
INTRODUCTION 54
FORMULATION BASED ON TIME-STEPPING SCHEMES 55
CONCLUSIONS 63
REFERENCES 63
Part 3: Fluid Flows I 64
CHAPTER 6. BEM-FEM Coupled Analysis for Salt Water 
66 
ABSTRACT 66
KEYWORDS 66
INTRODUCTION 66
GOVERNING EQUATIONS 67
FEM FORMULATION 67
BEM FORMULATION 71
COUPLING 72
NUMERICAL EXAMPLE 74
CONCLUSION 75
REFERENCES 75
CHAPTER 7. BOUNDARY METHOD FOR TRANSIENT DIFFUSION PROBLEM BY USE OF FRACTIO 
76 
ABSTRACT 76
INTRODUCTION 76
FRACTIONAL STEP BE PROCEDURE 77
ERROR ESTIMATE 79
NUMERICAL EXAMPLE 80
CONCLUSION 80
REFERENCES 80
Part 4: Computational Aspects 84
CHAPTER 8. FORMULATION FOR STRESS CALCULATION 
86 
ABSTRACT 86
KEYWORDS 86
INTRODUCTION 86
GENERAL BEM FORMULATION 86
STRESS FORMULATION OF BOUNDARY LAYER POINT 87
CONCLUSION 94
REFERENCES 94
APPENDIX 94
CHAPTER 9. BOUNDARY ELEMENT METHOD FOR A CLASS OF ELLIPTIC DIFFERENTIAL EQUATIONAND ITS APPLICATION : ANALYSIS OF HELICAL COIL SPRING 96
ABSTRACT 96
KEYWORDS 96
INTRODUCTION 96
STRESS IN HELICAL SPRING 97
BOUNDARY INTEGRAL EQUATION 98
NUMERICAL EXAMPLES AND DISCUSSION 100
CONCLUDING REMARKS 103
REFERENCES 104
CHAPTER 10. p-ADAPTIVE BEM FOR TWO–DIMENSIONAL 
106 
ABSTRACT 106
KEYWORDS 106
INTRODUCTION 106
ERROR INDICATION AND ESTIMATION 107
ACKNOWLEDGEMENT 115
REFERENCES 115
CHAPTER 11. A NUMERICAL METHOD FOR COUPLING OF 3–D ELASTOPLASTIC AND ELASTO–VISCOPLASTIC FINITE ELEMENTS 
116 
ABSTRACT 116
INTRODUCTION 116
SOME NUMERICAL PROBLEMS IN COUPLING F M AND BEM 116
COUPLING OF ELASTOPLASTIC FINITE ELEMENTSTO ELASTIC BOUNDARY ELEMENTS 119
COUPLING OF ELASTO-VISCOPLASTIC FINITE ELMSNTSTO ELASTIC BOUNDARY ELEMENTS 120
REFERENCES 124
CHAPTER 12. GENERALIZED BOUNDARY ANALYSIS OF NONLINEAR PROBLEMS 126
ABSTRACT 126
KEYWORDS 126
INTRODUCTION 126
GENERALIZED BOUNDARY ELEMENT METHOD 127
APPLICATIONS 128
CONCLUSIONS 135
REFERENCES 135
Part 5: Elastostatics 136
CHAPTER 13. BOUNDARY ELEMENT ANALYSIS OF A BONDED DISSIMILAR ELASTIC ROD 
138 
ABSTRACT 138
KEYWORDS 138
INTRODUCTION 138
BOUNDARY INTEGRAL EQUATIONS 139
DISPLACEMENTS AND STRESSES 142
NUMERICAL EXAMPLES 143
CONCLUDING REMARKS 146
REFRENCES 146
CHAPTER 14. BOUNDARY ELEMENT METHOD APPLIED TO 3– 
148 
ABSTRACT 148
KEYWORDS 148
INTRODUCTION 148
EQUATION OF CONTACT PROBLEMS 149
DISCUSSION 152
EXAMPLES 154
CONCLUSION 154
REFERENCES 156
CHAPTER 15. ELASTOSTATIC ANALYSIS OF SPATIAL FRAME STRUCTURES 
158 
ABSTRACT 158
KEYWORDS 158
INTRODUCTION 158
ELASTIC DEFORMATION OF A STRAIGHT BAR 159
METHOD OF ANALYSIS FOR SPATIAL FRAME STRUCTURES 161
NUMERICAL RESULTS AND DISCUSSION 163
CONCLUSION 166
REFERENCES 167
CHAPTER 16. BOUNDARY ELEMENT ANALYSIS OF AN UNDERGROUND CAVERN 168
ABSTRACT 168
KEYWORDS 168
INTRODUCTION 168
EVALUATION OF INITIAL STRESSES 169
ANALYSIS OF A CAVERN 174
AN ALGORITHM FOR VECTOR PROCESSOR 175
CONCLUDING REMARKS 177
ACKNOWLEDGMENTS 177
REFERENCES 177
Part 6: Crack Analysis II 178
CHAPTER 17. BIEM FOR SOLVING THE SCATTERING PROBLEM BY A CRACK WITH 
180 
ABSTRACT 180
KEYWORDS 180
INTRODUCTION 180
PROBLEM 181
BOUNDARY INTEGRAL EQUATION 182
CONTACT CONDITIONS ON A CRACK SURFACE 183
SYSTEM OF INTEGRAL EQUATIONS 183
NUMERICAL IMPLEMENTATION 184
NUMERICAL EXAMPLES 185
CONCLUDING REMARKS 188
REFERENCES 188
CHAPTER 18. A BIE METHOD FOR ELASTODYNAMIC CRACK ANALYSIS 
190 
ABSTRACT 190
KEYWORDS 190
INTRODUCTION 190
DERIVATION OF THE BIE 191
NUMERICAL SOLUTION OF THE BIE 193
ACKNOWLEDGMENT 196
REFERENCES 196
CHAPTER 19. NON-HYPERSINGULAR TIME-DOMAIN BIE 
198 
ABSTRACT 198
KEYWORDS 198
INTRODUCTION 198
THE CONVENTIONAL BIE FORMULATION 199
NON-HYPERSINGULAR BIE FORMULATION 200
NUMERICAL EXAMPLE 202
ACKNOWLEDGMENT 204
REFERENCES 204
Part 7: Elastodynamics II 206
CHAPTER 20. THE STUDY ON SOME PROBLEMS IN ELASTODYNAMICS 
208 
ABSTRACT 208
KEYWORDS 208
BOUNDARY INTEGRAL EQUATION OF THE STEADY-STATE ELASTODYNAMICS 208
RESPONSE OF THE ELASTIC STRUCTURES UNDER THE HARMONICLOADS 209
HYDRODYNAMIC PRESSURE ANALYSIS FOR COMPRESSIBLE FLUID 214
CONCLUSIONS 216
REFERENCES 216
CHAPTER 21. BEMTBY–THE BOUNDARY ELEMENT ANALYSIS PROGRAM FOR 3– 
218 
ABSTRACT 218
KEYWORD 218
INTRODUCTION 218
THE DISCRETE MODEL OF DYNAMIC BOUNDARY INTEGRAL EQUATION 219
THE TREATMENT OF SINGULAR KERNEL FUNCTION 220
THE NUMERICAL INVERSION OF LAPLACE TRANSFORM 221
COMPUTER PROGREM AND NUMERICAL STUDY 222
REFERENCE 226
CHAPTER 22. A Time Marching Boundary Element Method in Scattering Problems 
228 
ABSTRACT 228
KEYWORDS 228
INTRODUCTION 228
TIME MARCHING BOUNDARY ELEMENT METHOD 229
SPRING CONTACT MODEL 230
BEM FOR SPRING CONTACTED INCLUSION 231
NUMERICAL EXAMPLES 232
CONCLUSIONS 233
REFERENCES 233
CHAPTER 23. APPLICATION OF THE BOUNDARY ELEMENT METHOD 
238 
ABSTRACT 238
KEYWORDS 238
INTRODUCTION 238
FIELD EQUATIONS 239
INTEGRAL REPRESENTATION USING THE LAPLACE TRANSFORM 242
NUMERICAL EXAMPLES 244
CONCLUSIONS 247
REFERENCES 247
Part 8: Fluid Flows II 248
CHAPTER 24. NONLINEAR FREE SURFACE FLOW PROBLEMS BY BOUNDARY ELEMENT– 
250 
ABSTRACT 250
KEYWORDS 250
INTRODUCTION 250
FORMULATION 251
NUMERICAL SOLUTION PROCEDURE 252
NUMERICAL RESULTS 253
CONCLUSIONS 259
REFERENCES 259
CHAPTER 25. UNSTEADY MOVING BOUNDARY FLOW BY BEM AND 
260 
ABSTRACT 260
KEYWORDS 260
INTRODUCTION 260
FEM MODEL FOR TANK STRUCTURE 264
NUMERICAL RESULTS 265
CONCLUSION 266
ACKNOWLEDGEMENT 
266 
REFERENCES 266
CHAPTER 26. INTEGRAL EQUATION ANALYSES OF UNSTEADY VISCOUS FLOW PROBLEMS 
270 
ABSTRACT 270
KEYWORDS 270
INTRODUCTION 270
STATEMENT OF THE PROBLEMS 271
INTEGRAL EQUATION APPROACH 272
NUMERICAL EXAMPLES 274
CONCLUSIONS 279
REFERENCES 279
Part 9: Plates and Shells I 280
CHAPTER 27. BOUNDARY ELEMENT ANALYSIS FOR SHALLOW SPHERICAL SHELL BENDING PROBLEM 
282 
ABSTRACT 282
KEYWORDS 282
INTRODUCTION 282
BOUNDARY INTEGRAL EQUATION FORMULATION 283
FUNDAMENTAL SOLUTION 285
BOUNDARY ELEMENT DISCRETIZATION 287
NUMERICAL EXAMPLES AND RESULTS 287
CONCLUSIONS 290
ACKNOWLEDGMENTS 290
REFERENCES 290
CHAPTER 28. A SORT OF RING ELEMENT FOR SHELLS OF REVOLUTION 
292 
ABSTRACT 292
KEYWORDS 292
INTRODUCTION 292
THE BOUNDARY INTEGRAL EQUATIONS FOR ELASTIC BODIES OF REVOLUTION(AXISYMMETRIC PROBLEM 293
THE STIFFNESS MATRIX AND LOAD VECTOR OF A RING ELEMENTFOR SHELLS OF REVOLUTION BY BEM (SCHEME I) 295
THE STIFFNESS MATRIX AND LOAD VECTOR OF A RING ELEMENTFOR SHELLS OF REVOLUTION BY BEM (SCHEME II) 298
ACm)WLEDGEMENT 301
REFERENCES 301
CHAPTER 29. AN INTEGRAL EQUATION FORMULATION FOR GEOMETRICALLY NONLINEAR PROBLEM 
302 
ABSTRACT 302
KEYWORDS 302
INTRODUCTION 302
FUNDAMENTAL EQUATION 303
INTEGRAL EQUATION FORMULATION 305
FUNDAMENTAL SOLUTION 306
DISCRETIZATION SCHEME 307
CONCLUSIONS 308
REFERENCES 308
CHAPTER 30. OPTIMIZATION FOR ELASTIC THIN PLATE STRUCTURES 
310 
ABSTRACT 310
KEYWORDS 310
INTRODUCTION 310
THE THREE-EQUATION SCHEHE OF BENDING OF THIN PLATE 311
ACKNOWLEDGEMENT 316
REFERENCE 316
Part 10: Inverse Problems 318
CHAPTER 31. SHAPE OPTIMIZATION FOR STRESS CONCENTRATION PROBLEMS IN 
320 
ABSTRACT 320
KEYWORDS 320
INTRODUCTION 320
BOUNDARY ELEMENT METHOD ANALYSIS FOR ORTHOTROPIC MATERIALS 321
OPTIMIZATION FORMULATION 323
NUMERICAL RESULTS 325
CONCLUSIONS 330
REFERENCES 330
CHAPTER 32. DEFECT SHAPE IDENTIFICATION BY BOUNDARY ELEMENT METHOD COMBINED WITH METHOD OF MULTIPLE FORCE APPLICATIONS (IN CASE OF PLURAL DEFECTS) 
332 
ABSTRACT 332
KEYWORDS 332
INTRODUCTION 332
BOUNDARY ELEMENT ANALYSIS OF ELASTODYNAMIC PROBLEMS 333
APPLICATION OF OPTIMIZATION TECHNIQUE 334
IDENTIFICATION PROCEDURE 335
NUMERICAL RESULTS AND DISCUSSION 336
CONCLUSIONS 341
ACKNOWLEDGEMENT 341
REFERENCES 341
CHAPTER 33. OPTIMIZATION OF CATHODIC PROTECTION BY USING 
342 
ABSTRACT 342
KEYWORDS 342
INTRODUCTION 342
GOVERNING EQUATIONS 343
NUMERICAL METHOD 345
NUMERICAL EXAMPLES 346
CONCLUSIONS 351
ACKNOWLEDGMENTS 351
REFERENCES 351
CHAPTER 34. APPLICATION OF BEM TO GALVANIC CORROSION PROBLEMS AND THE QUASI– 
352 
ABSTRACT 352
KEYWORDS 352
FUNDAMENTAL EQUATIONS AND DISCRETIZATION 352
QUASI-LINEAR SOLUTION OF NON-LINEAR EQUATIONS 353
ANALYTICAL REPRESENTATION OF THE 3-D COEFFICIENT MATRIX 354
NUMERICAL EXAMPLES 356
REFERENCES 357
Part 11: Electromagnetics 362
CHAPTER 35. ANALYSIS OF ION FLOW FIELDSBY COMBINATION OF BEM WITH MOC 364
ABSTRACT 364
KEYWORDS 364
INTRODUCTION 364
FORMULATION 365
SOLUTION PROCEDURE 366
NUMERICAL RESULTS 367
CONCLUSIONS 373
REFERENCES 373
CHAPTER 36. SPLINE BOUNDARY ELEMENT METHOD OF TIME– 
374 
ABSTRACT 374
KEYWORDS 374
INTRODUCTION 374
BASIC EQUATIONS 375
SBEM OF STEADY STATE ELECTRO-MAGNETIC FIELDPROBLEMS 375
SBEM OF TRANSIENT ELECTRO-MAGNETIC FIELDPROBLEMS 378
PROBLEM OF WAVEGUIDES 380
CONCLUSIONS 383
REFERENCES 383
CHAPTER 37. NUMERICAL ANALYSIS OF STRIP ANTENNA 
384 
ABSTRACT 384
KEYWORDS 384
INTRODUCTION 384
THEORY 386
NUMERICAL RESULTS 389
CONCLUSION 393
REFERENCES 395
Part 12: Plates and Shells II 396
CHAPTER 38. POST–BUCKLING ANALYSIS 
398 
ABSTRACT 398
KEYWORDS 398
INTRODUCTION 398
BASIC EQUATIONS AND THEIR FUNDAMENTAL SOLUTION 399
INTEGRAL EQUATION FORMULATION 401
ITERATIVE SOLUTION 402
NUMERICAL EXAMPLES 403
CONCLUDING REMARKS 405
REFERENCES 405
CHAPTER 39. SPLINE INTEGRAL EQUATION METHOD FOR THE ANALYSIS OFSHALLOW SHELLS BY COUPLING THE BENDING PLATE ANDTHE PLANE-STRESS SHEET 406
ABSTRACT 406
KEYWORDS 406
INTRODUCTION 407
THE GOVERNING EQUATION OF SHALLOW SHELL OF MODERATE THICKNESS 407
THE GOVERNING EQUATIONS OF THIN SHALLOW SHELL 409
THE GOVERNING EQUATIONS OF THE VARIABLE THICKNESS PLATE 410
SPLINE INTEGRAL EQUATION METHOD 411
NUMERICAL EXAMPLES 412
DISCUSSION 416
REFERENCES 416
CHAPTER 40. NONLINEAR BIFURCATION ANALYSIS OF SHALLOW ARCH 
418 
ABSTRACT 418
KEYWORDS 418
INTRODUCTION 418
FORMULATION 419
NUMERICAL SOLUTION PROCEDURE 420
CONCLUSIONS 427
REFERENCES 427
Author Index 428

Produkt-Details

• Erscheint lt. Verlag: 23.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 1-4832-9794-2 / 1483297942
• ISBN-13: 978-1-4832-9794-1 / 9781483297941