Barber Contact Mechanics

1. Auflage 2018
ISBN: 978-3-319-70939-0
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 250, 592 Seiten

Reihe: Solid Mechanics and Its Applications

This book describes the solution of contact problems with an emphasis on idealized (mainly linear) elastic problems that can be treated with elementary analytical methods. General physical and mathematical features of these solutions are highlighted. Topics covered include the contact of rough surfaces and problems involving adhesive (e.g. van der Waals) forces. 
The author is a well-known researcher in the subject with hands-on experience of the topics covered and a reputation for lucid explanations. The target readership for the book includes researchers who encounter contact problems but whose primary focus is not contact mechanics. Coverage is also suitable for a graduate course in contact mechanics and end-of-chapter problems are included.

James Richard Barber graduated in Mechanical Sciences from the University of Cambridge in 1963. He then joined British Rail, who later sponsored his research at Cambridge between 1965 and 1968 on the subject of thermal effects in braking systems. In 1969 he became a Lecturer and later Reader in Solid Mechanics at the University of Newcastle upon Tyne, U.K.  He moved to the University of Michigan, Department of Mechanical Engineering in 1981. His current research interests are in solid mechanics with particular reference to thermoelasticity, contact mechanics and tribology. He is a Chartered Engineer in the U.K., a Fellow of the Institution of Mechanical Engineers and has engaged extensively in consulting work in the field of stress analysis for engineering design. Dr. Barber is author of two books and numerous articles in the fields of Elasticity, Thermoelasticity, Contact Mechanics, Tribology, Heat Conduction and Elastodynamics and he is a member of the editorial boards of the International Journal of Mechanical Sciences and the Journal of Thermal Stresses. 

Autoren/Hrsg.

Barber, J. R.

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;1 Kinematics of Contact;19
3.1;1.1 Reference Frame and the Initial Gap Function;20
3.2;1.2 Establishment of a Contact Region;21
3.2.1;1.2.1 Definition of Contact;22
3.2.2;1.2.2 The Boundary Value Problem;22
3.2.3;1.2.3 Signorini Problems;23
3.2.4;1.2.4 Asymptotic Arguments;23
3.2.5;1.2.5 The Discrete Problem;25
3.3;1.3 Nonlinear Kinematics;26
3.4;1.4 Almost Conformal Contact;27
4;2 Three-Dimensional Frictionless Elastic Problems;30
4.1;2.1 The Half-Space Approximation;30
4.2;2.2 Normal Loading of the Half-Space;31
4.2.1;2.2.1 The Point Force Solution;32
4.2.2;2.2.2 Similarity, Equilibrium and Anisotropy;33
4.2.3;2.2.3 The Composite Elastic Modulus;34
4.3;2.3 Integral Equation Formulation;35
4.3.1;2.3.1 Field-Point Integration;37
4.3.2;2.3.2 Indentation by a Flat Elliptical Punch;37
4.4;2.4 Galin's Theorem;40
4.4.1;2.4.1 A Special Case;41
4.5;2.5 Interior Stress Fields;42
4.5.1;2.5.1 In-Plane Stress Components Near the Surface;42
5;3 Hertzian Contact;45
5.1;3.1 Transformation of Coordinates;45
5.1.1;3.1.1 Cylinders and Spheres;47
5.1.2;3.1.2 More General Cases;48
5.2;3.2 Hertzian Pressure Distribution;49
5.3;3.3 Strategy for Hertzian Contact Calculations;50
5.3.1;3.3.1 Eccentricity of the Contact Area;50
5.3.2;3.3.2 Dimensions of the Contact Area;51
5.3.3;3.3.3 Highly Elliptical Contacts;54
5.4;3.4 First Yield;55
6;4 More General Problems for the Half-Space;58
6.1;4.1 The Electrical--Mechanical Analogy;59
6.1.1;4.1.1 Other Mathematical Analogies;61
6.1.2;4.1.2 Boyer's Approximation;63
6.1.3;4.1.3 Fabrikant's Approximation;64
6.2;4.2 General Theorems for Frictionless Contact;66
6.3;4.3 Superposition by Differentiation;70
6.4;4.4 The Force--Displacement Relation;72
6.4.1;4.4.1 Non-conformal Contact Problems;73
7;5 Axisymmetric Contact Problems;77
7.1;5.1 Green and Collins Solution;77
7.1.1;5.1.1 The Flat Punch Solution;79
7.2;5.2 Non-conformal Contact Problems;80
7.3;5.3 Annular Contact Regions;82
7.4;5.4 The Non-axisymmetric Cylindrical Punch;83
7.5;5.5 The Method of Dimensionality Reduction (MDR);84
8;6 Two-Dimensional Frictionless Contact Problems;90
8.1;6.1 The Line Force Solution;91
8.2;6.2 Integral Equation Formulation;93
8.2.1;6.2.1 Edge Conditions;94
8.3;6.3 Incremental Solution of Non-conformal Contact Problems;98
8.3.1;6.3.1 Symmetric Problems;98
8.3.2;6.3.2 Bounded-Singular Problems;99
8.4;6.4 Solution by Fourier Series;99
8.4.1;6.4.1 Rigid-Body Rotation;100
8.4.2;6.4.2 Galin's Theorem, Chebyshev Polynomials and Recurrence Relations;102
8.5;6.5 Periodic Contact Problems;104
8.5.1;6.5.1 Sinusoidal Contact Pressure;104
8.5.2;6.5.2 Fourier Series Methods;105
8.5.3;6.5.3 The Periodic Green's Function;106
8.5.4;6.5.4 The Cotangent Transform;106
8.5.5;6.5.5 Manners' Solution;107
8.5.6;6.5.6 Westergaard's Problem;109
8.6;6.6 The Smirnov--Sobolev Transform;110
8.6.1;6.6.1 Inversion of the Transform;111
8.6.2;6.6.2 Example: Uniform Loading Over the Circle;111
8.6.3;6.6.3 Anisotropic Problems;112
8.7;6.7 Displacements in Two-Dimensional Problems;113
8.7.1;6.7.1 Kalker's Line Contact Theory;115
9;7 Tangential Loading;121
9.1;7.1 Kinematics;121
9.1.1;7.1.1 Gross Slip and Microslip;122
9.2;7.2 Green's Functions for Tangential Forces and Displacements;123
9.2.1;7.2.1 Three-Dimensional [point] Loading;123
9.2.2;7.2.2 Two-Dimensional [line] Loading;125
9.2.3;7.2.3 Normal-Tangential Coupling;126
9.3;7.3 Two-Dimensional Flat Rigid Punch with No Slip;127
9.3.1;7.3.1 Uncoupled Problem;129
9.3.2;7.3.2 Oscillatory Singularities;129
9.4;7.4 Axisymmetric Flat Rigid Punch with No Slip;131
9.5;7.5 The `Goodman' Approximation;133
9.6;7.6 Uniform Tangential Displacement in a Prescribed Area;135
9.6.1;7.6.1 Tangential Loading over a Circular Area;135
9.6.2;7.6.2 Tangential Loading over an Elliptical Area;136
9.6.3;7.6.3 Two Conjectures;138
9.7;7.7 Non-conformal Contact Problems with No Slip;139
9.7.1;7.7.1 Uncoupled Hertzian Contact with Tangential Loading;140
9.7.2;7.7.2 The Coupled Axisymmetric Problem under Purely Normal Loading;141
9.7.3;7.7.3 The Coupled Two-Dimensional Problem;142
9.7.4;7.7.4 Relaxation Damping;144
10;8 Friction Laws;149
10.1;8.1 Amontons' Law;149
10.1.1;8.1.1 Continuum Problems;150
10.1.2;8.1.2 Two-Dimensional Problems;151
10.1.3;8.1.3 Existence and Uniqueness Theorems;151
10.2;8.2 The Klarbring Model;152
10.2.1;8.2.1 General Loading Scenarios;154
10.2.2;8.2.2 The Critical Coefficient of Friction;154
10.2.3;8.2.3 Wedging;155
10.3;8.3 Multinode Systems;156
10.3.1;8.3.1 The Evolution and Rate Problems;157
10.3.2;8.3.2 Algorithms for Two-Dimensional Problems with Time-Varying Forces;157
10.3.3;8.3.3 History-Dependence and Memory;158
10.3.4;8.3.4 Klarbring's P-Matrix Criterion;159
10.4;8.4 Periodic Loading;160
10.4.1;8.4.1 A Uniqueness Proof for Uncoupled Systems;161
10.4.2;8.4.2 Shakedown;163
10.4.3;8.4.3 Coupled Systems;163
10.4.4;8.4.4 Asymptotic Approach to a Steady State;163
10.5;8.5 A Simple Continuum Frictional System;164
10.5.1;8.5.1 Unloading;167
10.5.2;8.5.2 Periodic Loading;168
10.5.3;8.5.3 Discrete Model of the Strip Problem;169
10.5.4;8.5.4 The Inverse Problem;169
10.6;8.6 More Complex Friction Laws;170
10.6.1;8.6.1 Instabilities During Steady Sliding;171
10.6.2;8.6.2 Velocity-Dependent Friction Coefficient;171
10.6.3;8.6.3 Stick-Slip Vibrations;173
10.6.4;8.6.4 Slip-Weakening Laws;174
10.6.5;8.6.5 Rate-State Laws;175
11;9 Frictional Problems Involving Half-Spaces;181
11.1;9.1 Cattaneo's Problem;181
11.2;9.2 The Ciavarella--Jäger Theorem;184
11.2.1;9.2.1 Three-Dimensional Problems;186
11.3;9.3 More General Loading Scenarios;187
11.3.1;9.3.1 Constant Normal Force;187
11.3.2;9.3.2 Variable Normal Force;188
11.3.3;9.3.3 Memory and `Advancing Stick';190
11.4;9.4 The Effect of Bulk Stress;191
11.4.1;9.4.1 Hertz Problem with Superposed Bulk Stress;191
11.4.2;9.4.2 Combined Bulk Stress and Tangential Force;193
11.5;9.5 Coupled Problems;196
11.5.1;9.5.1 Indentation by a Two-Dimensional Flat Rigid Punch;196
11.5.2;9.5.2 Normal Loading for More General Geometries;199
11.5.3;9.5.3 Combined Normal and Tangential Loading;201
11.5.4;9.5.4 Unloading;201
11.5.5;9.5.5 Periodic Loading;202
12;10 Asymptotic Methods;206
12.1;10.1 Indentation by a Frictionless Rigid Punch;206
12.1.1;10.1.1 Eigenfunction Series;208
12.1.2;10.1.2 More General Frictionless Indentation Problems;209
12.1.3;10.1.3 Non-conformal Problems;210
12.1.4;10.1.4 Both Materials Deformable;211
12.2;10.2 No-Slip Conditions;212
12.3;10.3 Frictional Slip;213
12.3.1;10.3.1 Slip-Separation Transition;214
12.3.2;10.3.2 Slip--Stick Transition;215
12.4;10.4 Indentation by an Elastic Wedge;216
12.4.1;10.4.1 Right-Angle Wedge of the Same Material;217
12.4.2;10.4.2 A Slipping Interface;218
12.5;10.5 Local Fields;219
12.5.1;10.5.1 The Flat and Rounded Indenter;220
12.5.2;10.5.2 Fretting in Non-conformal Contact;222
12.5.3;10.5.3 Edge Slip Zones with a Rigid Punch;223
12.5.4;10.5.4 Slip Zones in Conformal Contact;225
13;11 Receding Contact;232
13.1;11.1 Characteristics of Receding Contact;233
13.1.1;11.1.1 Examples of Receding Contact;234
13.2;11.2 Frictional Problems;237
13.2.1;11.2.1 Frictional Unloading;237
13.3;11.3 Thermoelastic Problems;239
13.4;11.4 Almost Conformal Contact Problems;240
14;12 Adhesive Forces;244
14.1;12.1 Adhesion Between Rigid Bodies;247
14.2;12.2 The JKR Theory;248
14.2.1;12.2.1 Axisymmetric Problems;249
14.2.2;12.2.2 Indentation by a Sphere;250
14.2.3;12.2.3 Energetic Considerations and Stability;252
14.2.4;12.2.4 Hysteretic Energy Dissipation;254
14.2.5;12.2.5 JKR Solution for More General Axisymmetric Bodies;254
14.2.6;12.2.6 Guduru's Problem;256
14.3;12.3 The Tabor Parameter;257
14.3.1;12.3.1 An Adhesive Length Scale;259
14.3.2;12.3.2 Limitations on the JKR Solution;260
14.4;12.4 Solutions for Finite Tabor Parameter;261
14.4.1;12.4.1 Jump-In at Large Tabor Parameter;262
14.4.2;12.4.2 Simplified Force Laws;263
14.4.3;12.4.3 Maugis' Solution;264
14.4.4;12.4.4 The `double-Hertz' Approximation;267
14.4.5;12.4.5 More General Axisymmetric Geometries;269
14.5;12.5 Other Geometries;269
14.5.1;12.5.1 Two-Dimensional Problems;269
14.5.2;12.5.2 Elliptical Contact Area;270
14.5.3;12.5.3 General Three-Dimensional Geometries;271
15;13 Beams, Plates, Membranes and Shells;274
15.1;13.1 Contact of Beams;274
15.1.1;13.1.1 A Heavy Beam Lifted from the Ground;276
15.1.2;13.1.2 Adhesive Forces;277
15.1.3;13.1.3 Piston Ring in a Cylinder;278
15.1.4;13.1.4 Two and Three-Dimensional Effects;281
15.1.5;13.1.5 Matched Asymptotic Expansions;282
15.2;13.2 Contact of Plates;285
15.2.1;13.2.1 Displacement Due to a Concentrated Point Force;286
15.2.2;13.2.2 Indentation by a Rigid Sphere;286
15.3;13.3 Membrane Effects;288
15.3.1;13.3.1 `Membrane Only' Solutions;289
15.4;13.4 Contact of Shells;292
15.5;13.5 Implications for Finite Element Solutions;296
16;14 Layered Bodies;300
16.1;14.1 Esll El: Plate on an Elastic Foundation;301
16.1.1;14.1.1 Choice of Foundation Modulus;302
16.1.2;14.1.2 Two-Dimensional Problems;302
16.1.3;14.1.3 Three-Dimensional Problems;305
16.2;14.2 Esgg El: Layer on a Rigid Foundation;306
16.2.1;14.2.1 Frictionless Unbonded Layer;307
16.2.2;14.2.2 Bonded Compressible Layer;309
16.2.3;14.2.3 Bonded Incompressible Layer;309
16.2.4;14.2.4 Flat Punch Problems;314
16.2.5;14.2.5 Frictional Problems;315
16.2.6;14.2.6 Effect of Adhesive Forces;315
16.3;14.3 Winkler Layer on an Elastic Foundation;318
16.3.1;14.3.1 Nonlinear Layers;319
16.4;14.4 Fourier Transform Methods;320
16.4.1;14.4.1 Elastic Layer Bonded to a Rigid Foundation;320
16.4.2;14.4.2 Multilayered Bodies;324
16.5;14.5 Functionally Graded Materials;324
16.5.1;14.5.1 Exponential Variation of Modulus;325
16.5.2;14.5.2 Power-Law Grading;326
16.5.3;14.5.3 Linear Variation of Modulus;329
17;15 Indentation Problems;333
17.1;15.1 The Hardness Test;333
17.2;15.2 Power-Law Material;334
17.2.1;15.2.1 Graded Materials;336
17.3;15.3 Other Constitutive Laws;337
18;16 Contact of Rough Surfaces;339
18.1;16.1 Bowden and Tabor's Theory of Friction;339
18.1.1;16.1.1 The Ploughing Force;340
18.1.2;16.1.2 Plastic Deformation at an Actual Contact;341
18.1.3;16.1.3 The Effect of Surface Films;342
18.2;16.2 Profilometry;343
18.2.1;16.2.1 The Bearing Area Curve;344
18.2.2;16.2.2 The Contact Problem;346
18.3;16.3 Asperity Model Theories;347
18.3.1;16.3.1 The Exponential Distribution;349
18.3.2;16.3.2 The Gaussian Distribution;350
18.3.3;16.3.3 The Plasticity Index;352
18.4;16.4 Statistical Models of Surfaces;353
18.4.1;16.4.1 Discrete Models;353
18.4.2;16.4.2 Random Process Models;355
18.4.3;16.4.3 Determining Asperity Parameters;361
18.5;16.5 Fractal Surfaces;362
18.5.1;16.5.1 Archard's Model;362
18.5.2;16.5.2 Self-affine Fractals and the Fractal Dimension;362
18.5.3;16.5.3 The Weierstrass Function;364
18.5.4;16.5.4 Generating Realizations of Fractal Profiles and Surfaces;366
18.6;16.6 Contact of Fractal Surfaces;369
18.6.1;16.6.1 Majumdar and Bhushan's Theory;369
18.6.2;16.6.2 Elastic Contact for a Fractal Surface;370
18.6.3;16.6.3 The Weierstrass Profile;372
18.6.4;16.6.4 Persson's Theory;374
18.6.5;16.6.5 Implications for Coulomb's Law of Friction;378
18.7;16.7 Adhesive Forces;379
18.7.1;16.7.1 Asperity Model Predictions;380
18.7.2;16.7.2 The Sinusoidal Profile;381
18.7.3;16.7.3 Adhesion of Random Rough Surfaces;384
18.8;16.8 Incremental Stiffness and Contact Resistance;385
18.8.1;16.8.1 Asperity Model Predictions;386
18.8.2;16.8.2 Clustering of Actual Contacts;387
18.8.3;16.8.3 Bounds on Incremental Stiffness;388
18.8.4;16.8.4 Persson's Theory of Incremental Stiffness;390
18.8.5;16.8.5 Gaps and Fluid Leakage;391
18.9;16.9 Finite-Size Effects;392
18.9.1;16.9.1 Integral Equation Formulation;393
18.9.2;16.9.2 Unit Cells and the Constriction Alleviation Factor;396
18.9.3;16.9.3 Contact of Rough Spheres;397
19;17 Thermoelastic Contact;405
19.1;17.1 Thermoelastic Deformation;406
19.1.1;17.1.1 Fourier Transform Solutions;406
19.1.2;17.1.2 Steady-State Temperature;407
19.1.3;17.1.3 Thermoelastic Distortion Due to a Point Heat Source;408
19.1.4;17.1.4 Dundurs' Theorem;409
19.1.5;17.1.5 Moving Heat Sources;410
19.2;17.2 The Axisymmetric Thermoelastic Hertz Problem;411
19.2.1;17.2.1 The Heat Conduction Problem;412
19.2.2;17.2.2 Thermoelastic Distortion;413
19.2.3;17.2.3 Solution of the Contact Problem;413
19.3;17.3 Existence and Uniqueness;415
19.3.1;17.3.1 A One-Dimensional Model;416
19.3.2;17.3.2 Effect of a Thermal Interface Resistance;417
19.3.3;17.3.3 Imperfect Thermal Contact;419
19.3.4;17.3.4 The Hertz Problem Revisited;420
19.3.5;17.3.5 Stability;420
19.3.6;17.3.6 Contact of Dissimilar Materials;423
19.3.7;17.3.7 Two-Dimensional Stability Problems;423
19.4;17.4 Solidification Problems;425
19.5;17.5 Frictional Heating;427
19.5.1;17.5.1 The Rod Model;429
19.5.2;17.5.2 Burton's Stability Analysis;430
19.5.3;17.5.3 Out-of-Plane Sliding;431
19.5.4;17.5.4 In-Plane Sliding;433
19.5.5;17.5.5 Limiting Configurations;435
19.5.6;17.5.6 Effect of Geometry;437
19.5.7;17.5.7 Numerical Solutions;439
20;18 Rolling and Sliding Contact;443
20.1;18.1 Rigid-Body Kinematics;443
20.1.1;18.1.1 Three-Dimensional Motions;445
20.2;18.2 Johnson's Belt Drive Problem;448
20.3;18.3 Tractive Rolling of Elastic Cylinders;451
20.3.1;18.3.1 Dissimilar Materials;455
20.3.2;18.3.2 Antiplane Loading;456
20.3.3;18.3.3 Rolling of Misaligned Cylinders;456
20.3.4;18.3.4 Three-Dimensional Rolling Contact Problems;457
20.3.5;18.3.5 Kalker's Strip Theory;458
20.3.6;18.3.6 The Incipient Sliding Solution;460
20.3.7;18.3.7 Transient Problems;460
20.3.8;18.3.8 Rail Corrugations;461
20.4;18.4 Steady Sliding;462
20.4.1;18.4.1 Two-Dimensional Problems;462
20.4.2;18.4.2 Three-Dimensional Problems;464
20.5;18.5 Wear;465
20.5.1;18.5.1 Archard's Wear Law;465
20.5.2;18.5.2 Long-Time Solution;466
20.5.3;18.5.3 Transient Problems;467
20.5.4;18.5.4 Galin's Eigenfunction Method;469
20.5.5;18.5.5 Non-conformal Contact Problems;471
20.6;18.6 Sliding of Rough Surfaces;472
20.6.1;18.6.1 Flash Temperatures;473
20.6.2;18.6.2 Bulk Temperatures;478
20.6.3;18.6.3 Transient Asperity Interactions;479
21;19 Elastodynamic Contact Problems;484
21.1;19.1 Wave Speeds;485
21.1.1;19.1.1 Rayleigh Waves;486
21.2;19.2 Moving Contact Problems;487
21.2.1;19.2.1 The Moving Line Force;487
21.2.2;19.2.2 Integral Equation Formulation;488
21.2.3;19.2.3 The Subsonic Problem;489
21.2.4;19.2.4 The Speed Range cRc1;494
21.2.8;19.2.8 Three-Dimensional Problems;496
21.3;19.3 Interaction of a Bulk Wave with an Interface;499
21.3.1;19.3.1 SH-Waves Transmitted Across a Frictional Interface;499
21.3.2;19.3.2 In-Plane Waves;505
21.4;19.4 Interface Waves;507
21.4.1;19.4.1 Slip Waves;508
21.4.2;19.4.2 Slip Waves at a Sliding Interface;509
21.4.3;19.4.3 Slip--Stick Waves;510
21.5;19.5 Stability of Frictional Sliding;512
21.6;19.6 Transient Elastodynamic Contact Problems;513
21.6.1;19.6.1 Impulsive Line Force;513
21.6.2;19.6.2 A Uniform Pressure Suddenly Applied;513
21.6.3;19.6.3 Integral Equation Formulation of the Transient Contact Problem;514
21.6.4;19.6.4 Normal Indentation by a Rigid Body;515
21.6.5;19.6.5 Superseismic Indentation;516
21.6.6;19.6.6 Self-Similar Indentation Problems;517
21.6.7;19.6.7 Three-Dimensional Transient Problems;518
22;20 Impact;522
22.1;20.1 Hertz' Theory of Impact;523
22.1.1;20.1.1 Duration of the Impact;524
22.1.2;20.1.2 Homogeneous Sphere;526
22.1.3;20.1.3 Range of Validity of the Theory;526
22.1.4;20.1.4 The Superseismic Phase;527
22.2;20.2 Impact of a Cylinder;528
22.3;20.3 Oblique Impact;530
22.3.1;20.3.1 The Equation of Motion;531
22.3.2;20.3.2 The Tangential Contact Problem;532
22.3.3;20.3.3 Complete Stick;532
22.3.4;20.3.4 Gross Slip;535
22.3.5;20.3.5 Partial Slip;535
22.3.6;20.3.6 The Complete Trajectory;536
22.3.7;20.3.7 Rebound Conditions;537
22.4;20.4 One-Dimensional Bar Problems;538
22.4.1;20.4.1 The Semi-infinite Bar;539
22.4.2;20.4.2 The Infinite Bar;540
22.4.3;20.4.3 Reflections;541
22.4.4;20.4.4 The Impact Problem;542
22.4.5;20.4.5 A Rigid Mass Impacting an Elastic Bar;542
22.4.6;20.4.6 Frictional Problems;545
22.4.7;20.4.7 Continuous Frictional Supports;547
23;Appendix A Potential Function Solutions for Elasticity Problems;551
23.1;A.1 Frictionless Problems;551
23.2;A.2 Problems with Tangential Tractions;552
23.3;A.3 Two-Dimensional Problems;554
24;Appendix B Integrals over Elliptical Domains;555
24.1;B.1 Mathematical Preliminaries;556
24.1.1;B.1.1 The Singular Field n=0;557
24.1.2;B.1.2 The Hertzian Field n=1;557
24.2;B.2 Applications;558
24.2.1;B.2.1 Normal Loading of an Isotropic Half-Space;558
24.2.2;B.2.2 The Anisotropic Half-Space;559
24.2.3;B.2.3 Tangential Loading of an Isotropic Half-Space;559
24.3;B.3 Evaluation of Integrals;561
25;Appendix C Cauchy Singular Integral Equations;562
25.1;C.1 Integral Equations of the First Kind;562
25.2;C.2 Integral Equations of the Second Kind;564
26;Appendix D Dundurs' Bimaterial Constants;566
27;References;568
28;Index;588