Introduction to finite and boundary element methods for engineers

목차 (Table of Contents)

• CONTENTS
• Preface = ⅸ
• Acknowledgements = xi
• 1 Introduction to finite and boundary element methods = 1
• 1.1 Background = 1
• 1.2 Computational steps = 3
• 1.3 Notation = 6
• 1.4 Concluding remarks = 8
• 1.5 Text books on the finite element method = 9
• 1.6 Text books on the boundary element method = 11
• 2 Solid modelling-finite and boundary elements = 13
• 2.1 Introduction = 13
• 2.2 One-dimensional elements = 14
• 2.3 Two-dimensional elements = 19
• 2.4 Three-dimensional elements = 27
• 2.5 Elements of infinite extent = 29
• 2.6 Description of physical quantities = 31
• 2.7 Coordinate transformation = 33
• 2.8 Differentia1 geometry = 34
• 2.9 Integration over elements = 37
• 2.10 Derivatives of shape functions = 37
• 2.11 Concluding remarks = 38
• 2.12 Exercises = 40
• 2.13 References = 41
• 3 Material modelling = 43
• 3.l Introduction = 43
• 3.2 Heat conduction and seepage = 44
• 3.3 Solid mechanics-stress and strain = 45
• 3.4 Elastic material = 50
• 3.5 Inelastic material = 53
• 3.6 Closure = 61
• 3.7 Exercises = 62
• 3.8 References = 62
• 4 Finite elements of a continuum = 63
• 4.l Introduction = 63
• 4.2 Derivation of element response matrices = 64
• 4.3 Derivation of continuum response-assembly = 77
• 4.4 Boundary conditions and applied loads = 80
• 4.5 Solution = 87
• 4.6 Examples-1 = 94
• 4.7 Examples-2 = 101
• 4.8 Concluding remarks = 105
• 4.9 Exercises = 108
• 4.10 References = 109
• 4.11 Recommended further reading = 110
• 5 Special finite elements : plate／shell element, joint element = 111
• 5.l Introduction = 111
• 5.2 Plate elements = 112
• 5.3 Shell elements = 114
• 5.4 Examples and applications of plate and shell elements = 117
• 5.5 Joint elements = 120
• 5.6 Examples and applications of joint elements = 134
• 5.7 Closure = 138
• 5.8 Exercises = 138
• 5.9 References = 140
• 5.10 Recommended further reading = 140
• 6 Boundary element methods-basic principles = 141
• 6.1 Introduction = 141
• 6.2 Fundamental solutions = 143
• 6.3 Trefftz methods = 148
• 6.4 The indirect boundary element method for Laplace's equation = 151
• 6.5 The indirect method for elasticity = 158
• 6.6 The direct boundary element method for Laplace's equation = 162
• 6.7 The direct method for elasticity = 166
• 6.8 The displacement discontinuity method for Laplace's equation = 169
• 6.9 The displacement discontinuity method for elasticity = 175
• 6.10 Body forces = 177
• 6.11 Infinite regions = 178
• 6.12 Summary and conclusions = 181
• 6.13 References = 184
• 7 Boundary element methods-practical implementation = 187
• 7.l Introduction = 187
• 7.2 Isoparametrice lements and discrete systems = 189
• 7.3 Infinite elements = 196
• 7.4 Integration schemes for two-dimensional analysis = 203
• 7.5 Integration schemes for three-dimensional analysis = 213
• 7.6 Assembly of discrete systems = 223
• 7.7 Subregions = 232
• 7.8 Simultaneous equation solution = 235
• 7.9 Post-processing = 248
• 7.10 Examples-1 = 253
• 7.11 Examples-2 = 263
• 7.12 Summary and conclusions = 275
• 7.13 Exercises = 278
• 7.14 References = 282
• 8 Coupled boundary element／finite element analysis = 283
• 8.l Introduction = 283
• 8.2 Coupling theory = 284
• 8.3 Examples-1 = 297
• 8.4 Examples-2 = 301
• 8.5 Concluding remarks = 304
• 8.6 Exercises = 305
• 8.7 References = 306
• 9 Non-linear problems = 307
• 9.l Introduction = 307
• 9.2 General solution procedures = 308
• 9.3 Non-linear material problems = 310
• 9.4 Examples = 321
• 9.5 Concluding remarks = 324
• 9.6 Exercises = 325
• 9.7 References = 327
• 9.8 Suggested further reading = 328
• 10 Mesh design and error analysis = 329
• 10.l Introduction = 329
• 10.2 Finite elements, boundary elements or both? = 330
• 10.3 Design of meshes = 333
• 10.4 Pitfalls = 334
• 10.5 Sources of errors = 336
• 10.6 Estimate of discretisation error = 340
• 10.7 Hierarchical elements and adaptive mesh refinement = 345
• 10.8 Conclusions = 354
• 10.9 Exercises = 354
• 10.10 References = 356
• 10.11 Suggested further reading = 356
• 11 Computer aided pre- and post-processing = 357
• 11.1 Introduction = 357
• 11.2 Pre-Processing = 359
• 11.3 Post-Processing = 370
• 11.4 Conclusions = 376
• 11.5 References = 377
• 11.6 Suggested further reading = 377
• Appendix A Porgram DEMON = 379
• Al Introduction = 379
• A2 Input data(file DEMON.DAT) = 381
• A3 Printable output(file DEMON.OUT) = 390
• A4 Plot file(DPLOT.PLT) = 392
• A5 Program DEMON source code = 394
• A6 Selected listings = 400
• Appendix B Program BOUND = 429
• B1 Introduction = 429
• B2 Input data(file BOUND.DAT) = 431
• B3 Printable output(file BOUND.OUT) = 442
• B4 Plot file(DPLOT.PLT) = 442
• B5 Program BOUND source code = 442
• B6 Selected listings = 449
• Appendix C Fundamental solutions = 485
• C1 Laplace equation-isotropic = 487
• C2 Elasticity-isotropic point load (KELVIN) solution = 488
• C3 Elasticity-isotropic displacement discontinuity solution = 490
• Appendix D Green's symmetric identity and the boundary integral equation of the direct method for Laplace's equation = 493
• Appendix E Betti's theorem and the boundary integralequation of the direct method for elasticity = 501
• Index = 507