ISBN: 3540672303
TITLE: Singular Integral Equations
AUTHOR: Ladopoulos, E.G.
TOC:

CHAPTER 1 - INTRODUCTION
1.1 Finite-part Singular Integral Equations 1
1.2 Multidimensional Singular Integral Equations 6
1.3 Non-linear Singular Integral Equations 12
CHAPTER 2 - FINITE-PART SINGULAR INTEGRAL EQUATIONS
2.1 Introduction 17
2.2 Finite-part Singular Integral Representation Analysis in L_p Spaces 18
2.3 Systems of Finite-Part Singular Integral Equations in L_p Spaces 30
2.4 Generalization of the Sokhotski-Plemelj formulae for the Solution of Finite-Part Singular Integrals 40
2.5 Singular Integral Approximation Methods in General Hilbert Spaces 50
2.6 Numerical Methods for Systems of Singular Integral Equations in General Hilbert Spaces 59
2.7 Numerical Integration Rules for Finite-Part Singular Integrals 70
2.8 Numerical Integration Rules for Finite-Part Singular Integrals and Integral Equations with Logarithmic Singularities 98
2.9 Finite-Part Singular Integro-differential Equations 105
2.10 Approximations of Singular Integral Equations on Lyapounov Contours in Banach Spaces 109
2.11 Finite-part Singular Integral Approximations in Hilbert Spaces 120
CHAPTER 3 - FINITE-PART SINGULAR INTEGRAL EQUATIONS IN ELASTICITY AND FRACTURE MECHANICS
3.1 Introduction 133
3.2 Non-Symmetric Cross-Shaped Crack in an Infinite Plane 134
3.3 Symmetric Cross-Shaped Crack in an Infinite Plane 136
3.4 Elastic Stress Analysis in a Circular Ring with Curvilinear Cracks 138
3.5 Cracks Normal to a Bimaterial Interface 145
3.6 Crack Parallel to the Free Boundary of an Elastic Isotropic Semiplane 150
3.7 Crack Parallel to the Free Boundary of an Isotropic Semi-Infinite Solid 152
3.8 Crack in a Bimaterial Infinite and Isotropic Solid under Antiplane Shear 157
3.9 Straight Crack in an Infinite, Isotropic Solid 161
3.10 Periodic Array of Cracks along a Straight Line in an Infinite and Isotropic Solid 165
3.11 Periodic Array of Parallel Straight Cracks in an Infinite and Isotropic Solid 167
CHAPTER 4 - SINGULAR INTEGRAL EQUATIONS IN AERODYNAMICS
4.1 Introduction 173
4.2 Planar Airfoils in Two-dimensional Aerodynamics 174
CHAPTER 5 - MULTIDIMENSIONAL SINGULAR INTEGRAL EQUATIONS
5.1 Introduction 187
5.2 Multidimensional Singular Integral Equations in Lebesque Spaces L_p 191
5.3 Two dimensional Singular Integral Equations Exact Solutions 197
5.4 Numerical Evaluation of the Two-dimensional Singular Integral Equations 203
5.5 Numerical Evaluation of the Three-dimensional Singular Integral Equations 212
CHAPTER 6 - MULTIDIMENSIONAL SINGULAR INTEGRAL EQUATIONS IN ELASTICITY AND FRACTURE MECHANICS OF ISOTROPIC SOLIDS
6.1 Introduction 219
6.2 Two-dimensional Elastic Stress Analysis of Isotropic Solids 220
6.3 Application to the Determination of the Stress Field in the Neighbourhood of a Circular Hole under Internal Pressure in an Infinite and Isotropic Solid 225
6.4 The-dimensional Elastic Stress Analysis of Isotropic Solids 227
6.5 Application to the determination of the Elastic Stress Analysis of a thick Cylinder Subjected to an Internal Pressure 231
6.6 Application to the Determination of the Stress Intensity Factors near the Edge of a Rectangular Crack under Tensile Pressure in an Isotropic Solid 238
6.7 Linear Viscoelasticity of Isotropic Solids 242
6.8 Application of Linear Viscoelasticity 244
CHAPTER 7 - MULTIDIMENSIONAL SINGULAR INTEGRAL EQUATIONS IN RELATIVISTIC ELASTIC STRESS ANALYSIS FOR MOVING FRAMES
7.1 Introduction 251
7.2 Relative Stress Tensor Formulation for Moving Frames 252
7.3 Elastic Stress Analysis for Stationary and Moving Frames 263
7.4 Relativistic Thermoelastic Stress Analysis for Moving Frames 269
CHAPTER 8 - MULTIDIMENSIONAL SINGULAR INTEGRAL EQUATIONS IN ELASTICITY AND FRACTURE MECHANICS OF ANISOTROPIC SOLIDS
8 1 Introduction 275
8.2 General Anisotropic Elastic Stress Analysis 277
8.3 Fundamemal Solutions of Anisotropic Stress Field Analysis 281
8.4 Three-Dimensional Singular Integral Approximation Method 288
8.5 Application to the Determination of the Fracture Behaviour of a Circular Hole subjected to a Uniform Boundary Shear Traction in an Infinite and Orthotropic Solid 290
8.6 Application to the Determination of the Fracture Behaviour of a Circular Hole in the Centre of a Rectangular Orthotropic Plate, subjected to Deformation by Tangential Forces 294
8.7 Stress Field near the Crack Tip in an Anisotropic Solid 297
CHAPTER 9 - MULTIDIMENSIONAL SINGULAR INTEGRAL EQUATIONS IN PLASTICITY OF ISOTROPIC SOLIDS
9.1 Introduction 305
9.2 Two-dimensional Plastic Stress Analysis of Isotropic Solids 307
9.3 Application to the Determination of the Plastic Behaviour of a Perforated Tension Strip in Plane Stress 311
9.4 Application to the Determination of the Plastic Behaviour of a Thick Sphere and a Thick Cylinder in Plane Strain 314
9.5 Application of two-dimensional Plasticity in a Circular Rocky Tunnel 317
9.6 Application to the Determination of the Plastic Behaviour of a Square Block Compressed by two Opposite perfectly Rough Rigid Punches in Plane Strain 319
9.7 Three-dimensional Plastic Stress Analysis of Isotropic Solids 321
9.8 Fracture Behaviour of Double Notched Tensile Specimen 328
9.9 Three-dimensional Thermoelastoplastic Stress Analysis of Isotropic Solids 331
9.10 Thermoelastic Stress Analysis Application for a Hollow Cylinder 334
CHAPTER 10 - NON-LINEAR SINGULAR INTEGRAL EQUATIONS
10.1 Introduction 343
10.2 Existence and Uniqueness Theorems for Non-Linear Singular Integral Equations over Finite Sets of Contours in Banach Spaces 344
10.3 Existence and Uniqueness Theorems for Non-Linear Singular Integral Equations over a System of Arcs in Banach Spaces 353
10.4 Non-linear Finite-part Singular Integral Equations Uniqueness Theorems in Banach Spaces 367
10.5 Non-bar Singular Integrodifferential Equations Existence Theory 375
CHAPTER 11 - NUMERICAL EVALUATION METHODS FOR NON-LINEAR SINGULAR INTEGRAL EQUATIONS
11.1 Introduction 381
11.2 Approximation Methods for Non-linear Programming Problems 382
11.3 Non-linear Singular Integral Approximations in Banach Spaces by the Collocation Method 388
11.4 Non-linear Singular Integral Approximations in Banach Spaces by the Quadrature Method 394
11.5 Non-linear Singular Integrodifferential Approximation Theory by the Collocation Method 3 97
CHAPTER 12 - NON-LINEAR SINGULAR INTEGRAL EQUATIONS IN FLUID MECHANICS
12.1 Introduction 409
12.2 Profiles of Turbomachines in Steady Flow of Incompressible Fluids 410
12.3 Non-linear Unsteady Inviscid Flowfields Analysis 415
12.4 Velocity and Pressure Coefficient Field for Linear Vortex Distribution 419
12.5 Velocity and Pressure Coefficient Field for Linear Source Distribution 425
12.6 Velocity and Pressure Coefficient Field for Constant Vortex Distribution 429
12.7 Velocity and Pressure Coefficient Field for Constant Source Distribution 433
12.8 Lists of Computer Programs for Fluid Mechanics (airfoil without velocity) 437
12.9 Unsteady Cascade Aeroelasticity applied in Turbomachines 446
12.10 Non-linear Unsteady Inviscid Aerodynamic Analysis 453
12.11 Velocity and Pressure Coefficient Field for Linear Vortex Distribution (Airfoil with Velocity) 460
12.12 Velocity and Pressure Coefficient Field for Linear Source Distribution (Airfoil with Velocity) 464
12.13 Velocity and Pressure Coefficient Field for Constant Vortex Distribution (Airfoil with Velocity) 469
12.14 Velocity and Pressure Coefficient Field for Constant Source Distribution (Airfoil with Velocity) 473
12.15 Lists of Computer Programs for Aerodynamics (Airfoil with Velocity) 477
CHAPTER 13 - NON-LINEAR INTEGRO-DIFFERENTIAL EQUATIONS IN STRUCTURAL ANALYSIS
13.1 Introduction 491
13.2 Non-linear Integro-differential Equations used in Orthotropic Shallow Spherical Shell Analysis 491
13.3 Non-linear Integro-differential Equations in Sandwich Plates Stress Analysis 499
CHAPTER 14 - NON-LINEAR SINGULAR INTEGRAL EQUATIONS IN ELASTODYNAMICS
14.1 Introduction 509
14.2 Seismic Wave Equations Analysis by Hilbert Transformations 510
14.3 Non-linear Stationary and Dynamic Viiasticity 517
14.4 Application to the Determination of the Limit Load for a Rigidly Plastic Solid 528
CHAPTER 15 - CONCLUSIONS 533
APPENDIX - MATHEMATICAL DEFINITIONS 535
SUBJECT INDEX 539
AUTHOR INDEX 547
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