[Volume. 1]----------
CONTENTS
0 BOUNDARY INTEGRAL FORMULATIONS = 1
0.1 Fundamentals of Functional Analysis = 1
0.2 Generalized Green's Formula = 3
0.3 Variational Formulation = 5
0.4 Weighted Residual Scheme = 7
0.5 Boundary Integral Formulation of Poisson's Equation = 10
0.6 Boundary Integral Formulation of Navier Equations = 10
0.7 Final Remarks = 11
Bibliography = 11
1 A REVIEW OF THE THEORY = 13
1.1 Historical Introduction = 13
1.2 Potential Theory : Green's Formula = 14
1.3 Boundary Integral Equations = 21
1.4 Vector Potential Theory : Somigliana's Formula = 27
1.5 Indirect Vector Formulations = 30
1.6 Two-Dimensional Potential Theory = 33
References = 38
2 APPLICATIONS IN TRANSIENT HEAT CONDUCTION = 41
2.1 Introduction = 41
2.2 Integral Formulation of Heat Conduction Problems = 42
2.3 Numerical Solution of the Integral Equations = 46
2.4 Time-Marching Procedures = 50
2.5 Examples and Conclusions = 52
References = 57
Notation = 58
3 FRACTURE MECHANICS APPLICATION IN THERMOELASTIC STATES = 59
3.1 Introduction = 59
3.2 Integral Equation Formulation = 59
3.3 Computational Scheme = 62
3.3.1 Transient Heat Conduction Problems = 62
3.3.2 Thermoelastic Problems = 65
3.4 Numerical Results and Discussion = 67
3.4.1 Transient Heat Conduction = 67
3.4.2 Stress Intensity Factor Computation = 67
3.5 Some Considerations on Numerical Accuracy = 75
3.6 Concluding Remarks = 77
References = 77
4 APPLICATIONS OF BOUNDARY ELEMENT METHODS TO FLUID MECHANICS = 78
4.1 Introduction = 78
4.2 History = 78
4.3 Aerodynamics and Hydrodynamics = 80
4.4 Porous Media Flow = 83
4.5 Free Boundary Problems = 86
4.6 Unsteady Free Boundaries - Water Waves = 88
4.7 Linear Waves = 90
4.8 Stoke's Flow = 91
4.9 Porous-Elasticity = 92
4.10 Concluding Remarks = 92
References = 93
5 WATER WAVES ANALYSIS = 97
5.1 Introduction = 97
5.2 Basic Theory = 97
5.3 Boundary Element Formulation = 99
5.4 Special Structural Types = 102
5.5 Equations of Motion for the Structure = 110
5.6 Numerical Examples = 110
5.7 Conclusions = 121
References = 122
6 INTERELEMENT CONTINUITY IN THE BOUNDARY ELEMENT METHOD = 123
6.1 Introduction = 123
6.2 Continuous Elements = 124
6.3 Planar Discontinuous Elements = 128
6.4 Discontinuous Elements for Three Dimensional Analysis = 135
6.5 Closure = 140
References = 140
7 APPLICATIONS IN GEOMECHANICS = 142
7.1 Introduction = 142
7.2 Basic Formulation = 143
7.3 No-Tension and Discontinuity Problems = 149
7.4 Viscoplasticity = 156
7.5 Conclusions = 167
Appendix : Fundamental Solutions and Other Tensor Forms = 167
References = 168
8 APPLICATIONS IN MINING = 170
8.1 Introduction = 170
8.2 Review of the Development and Application of Boundary Element Formulations in Mining = 172
8.3 Displacement Discontinuity Formulation = 174
8.4 The Boundary Element Formulation = 177
8.5 Elasto-plastic Material Behaviour = 185
8.6 Combination of BEM with Other Techniques = 187
8.7 Summary and Future Outlook = 195
Appendix A : Equation Solvers = 196
Appendix B : Fundamental Solutions = 198
References = 201
9 FINITE DEFLECTIONS OF PLATES = 204
9.1 Introduction = 204
9.2 Geometrically Nonlinear Governing Equations = 204
9.3 Integral Equation Formulation for von Karman-type Equations = 207
9.4 The Approximate Berger Equation = 210
9.5 Integral Formulation for the Berger Equation = 212
9.6 Numerical Examples = 213
9.7 Nonlinear Shallow Shell and Sandwich Plate／Shell Problems = 216
9.8 Concluding Remarks = 221
References = 222
Appendices = 222
10 TREFFTZ METHOD = 225
10.1 Introduction = 225
10.2 Scope = 226
10.3 Green's Formulas = 235
10.4 Illustration of Green's Formulas = 242
10.5 Green's Formulas in Discontinuous Fields = 244
10.6 T-Complete Systems = 248
10.7 Hilbert-Space Formulation = 249
10.8 Representation of Solutions = 250
References = 251
SUBJECT INDEX = 255
[Volume. 2]----------
CONTENTS
1 FUNDAMENTALS OF BOUNDARY INTEGRAL EQUATION METHODS IN ELASTODYNAMICS = 1
1.1 Introduction = 1
1.2 Elastodynamic Problems = 3
1.2.1 Basic Equations = 3
1.2.2 Elastodynarnic Problems = 5
1.2.3 Reciprocal Theorem = 6
1.3 BIE Formulations in Time-Space Domain = 8
1.3.1 Integral Representation and Fundamental Solutions = 8
1.3.2 Two-Dimensional Representation = 11
1.3.3 Boundary Integral Equations = 12
1.4 BIE Formulations in the Transformed Domain of Integral Transforms = 15
1.4.1 Fourier Transformed Problems of Elastodynamics = 15
1.4.2 BIE Formulations of Transformed Problems = 17
1.4.3 Laplace Transformed Domain BIE = 23
1.5 Integral Equation Formulations for Inhomogeneous Domain = 25
1.5.1 Basic Equations = 25
1.5.2 Integral Equation Formulations = 26
1.6 Eigenfrequency Problems = 29
1.7 Some Remarks on Inherent Problems of BIEM in Elastodynamics = 30
1.7.1 Fictitious Eigenfrequencies in the Time-Harmonic Elastodynamics = 30
1.7.2 Half-Plane Problems = 32
1.7.3 Treatment of Singularities = 36
1.7.4 BIE-FE Hybrid Method = 38
1.7.5 Miscellaneous in Numerical Treatment = 40
1.8 Application Examples = 41
1.8.1 Transient Response Analysis by the Time-Space Domain BIEM = 41
1.8.2 Applications of Integral Transformed Domain BIEM = 45
1.9 Concluding Remarks = 49
References = 49
2 ELASTIC POTENTIALS IN BIE FORMULATIONS = 55
2.1 Introduction = 55
2.2 Elastodynamic Formulations = 56
2.3 Elastostatic Formulations = 58
2.4 Solution Methods = 60
2.5 Comments and Suggestions = 61
References = 61
3 TIME DEPENDENT NON-LINEAR POTENTIAL PROBLEMS = 63
3.1 Introduction = 63
3.2 Governing Equations = 64
3.3 Homogeneous Parabolic Equation = 66
3.4 Constant and Linear Time Interpolation = 69
3.5 Non-Linear Boundary Conditions for the Case of Constant Conductivity = 75
3.6 Non-Linear Boundary Conditions for the Case of Temperature Dependent Conductivity = 77
3.7 Applications = 78
3.8 Conclusions = 86
References = 86
4 FURTHER DEVELOPMENTS ON THE SOLUTION OF THE TRANSIENT SCALAR WAVE EQUATION = 87
4.1 Introduction = 87
4.2 The Boundary Initial Value Problem = 88
4.3 Dirac Delta and Heaviside Functions = 89
4.4 Fundamental Solution in Three Dimensions = 90
4.5 Kirchhoff Integral Representation = 91
4.6 Two-Dimensional Boundary Integral Equation = 96
4.7 Additional Transformations to Volterra's Integral Representation = 98
4.8 Numerical Implementation = 102
4.8.1 Boundary Integrals = 103
4.8.2 Domain Integrals = 107
4.8.3 Double Nodes = 110
4.9 Examples = 111
4.9.1 One-Dimensional Rod under a Heaviside Type Forcing Function = 112
4.9.2 One-Dimensional Rod under Prescribed Initial Velocity and Displacement = 118
4.9.3 Square Membrane under Prescribed Initial Velocity = 120
References = 121
5 TRANSIENT ELASTODYNAMICS = 124
5.1 Introduction = 124
5.2 Basic Theory = 125
5.3 The Initial Value Problem of Elastodynamics = 129
5.4 One-Dimensional Motions = 130
5.5 Plane Motions = 132
5.6 Fundamental Solutions for Transient Elastodynamics = 134
5.7 Time Domain Elastodynamic Boundary Integral Representation = 136
5.8 Additional Transformations to the Two-Dimensional Boundary Integral Equation of Elastodynamics = 140
5.9 Numerical Implementation for Two Dimensions = 142
5.10 Examples - Two-Dimensional Elastodynamics = 146
5.11 Conclusions = 153
References = 154
6 PROPAGATION OF SURFACE WAVES = 156
6.1 Introduction = 156
6.2 Three-Dimensional Formulation = 156
6.2.1 Particular Fundamental Solutions = 160
6.2.2 Numerical and Computational Aspects = 162
6.3 Floating Bodies = 164
6.4 Vertical Axisymmetric Bodies = 166
6.5 Vertical Cylinders of Arbitrary Section = 169
6.6 Horizontal Cyclinders of Arbitrary Section = 172
6.6.1 Obliquely Incident Waves = 177
6.7 Transient Problems = 180
6.8 Nonlinear Problems = 183
References = 188
7 BOUNDARY INTEGRAL FORMULATION OF MASS MATRICES FOR DYNAMIC ANALYSIS = 191
7.1 Introduction = 191
7.2 Formulation of the Dynamical Problem = 192
7.3 Various Boundary Integral Formulations = 193
7.4 Boundary Integral Formulation Using the Statical Fundamental Solution = 194
7.5 The Numerical Solution Procedure = 195
7.6 Derivation of Different Types of Dynamical Problems = 198
7.7 Two-Dimensional Formulation = 200
7.8 Computer Implementation = 202
7.9 Applications = 204
Conclusions = 207
References = 207
8 BOUNDARY ELEMENT METHOD FOR LAMINAR VISCOUS FLOW AND CONVECTIVE DIFFUSION PROBLEMS = 209
8.1 Introduction = 209
8.2 Governing Equations = 209
8.2.1 Field Equations = 210
8.2.2 Boundary Conditions = 210
8.3 Boundary Integral Equations = 213
8.3.1 BIE of the Stream Function = 213
8.3.2 BIE of the Vorticity = 214
8.3.3 BIE of the Temperature = 215
8.4 Boundary Element Approximation = 216
8.4.1 Discretization of the Stream Function = 217
8.4.2 Discretization on Vorticity and Temperature = 218
8.5 Computational Scheme = 220
8.6 Numerical Examples = 222
8.6.1 Isothermal Channel Flow = 222
8.6.2 Isothermal Flow Past a Cylinder = 223
8.6.3 Isothermal Driven-Cavity Flow = 225
8.6.4 Convection-Diffusion in Wind-Driven Flow = 226
8.6.5 Natural Convection in a Compartment = 227
8.6.6 Natural Convection around a Heated Cylinder = 227
8.7 Conclusion = 228
References = 229
9 ASYMPTOTIC ACCURACY AND CONVERGENCE FOR POINT COLLOCATION METHODS = 230
9.1 Introduction = 230
9.2 Examples of Boundary Integral Equations = 232
9.3 Standard Collocation for Two-Dimensional Problems = 238
9.4 Standard Collocation for Three-Dimensional Problems with Fredholm Boundary Integral Equations of the Second Kind = 245
References = 252
SUBJECT INDEX = 259
