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Singular Integral Equations : Linear and Non-Linear Theory and Its Applications in Science and Engineering - E.G. Ladopoulos

Singular Integral Equations

Linear and Non-Linear Theory and Its Applications in Science and Engineering

Hardcover Published: 6th June 2000
ISBN: 9783540672302
Number Of Pages: 552

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The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Introduction
Finite-part Singular Integral Equationsp. 1
Multidimensional Singular Integral Equationsp. 6
Non-linear Singular Integral Equationsp. 12
Finite-Part Singular Integral Equations
Introductionp. 17
Finite-part Singular Integral Representation Analysis in Lp Spacesp. 18
Systems of Finite-Part Singular Integral Equations in Lp Spacesp. 30
Generalization of the Sokhotski-Plemelj formulae for the Solution of Finite-Part Singular Integralsp. 40
Singular Integral Approximation Methods in General Hilbert Spacesp. 50
Numerical Methods for Systems of Singular Integral Equations inGeneral Hilbert Spacesp. 59
Numerical Integration Rules for Finite-Part Singular Integralsp. 70
Numerical Integration Rules for Finite-Part Singular Integrals andIntegral Equations with Logarithmic Singularitiesp. 98
Finite-Part Singular Integro-differential Equationsp. 105
Approximations of Singular Integral Equations on Lyapounov Contours in Banach Spacesp. 109
Finite-part Singular Integral Approximations in Hilbert Spacesp. 120
Finite-Part Singular Integral Equations Inelasticity and Fracture Mechanics
Introductionp. 133
Non-Symmetric Cross-Shaped Crack in an Infinite Planep. 134
Symmetric Cross-Shaped Crack in an Infinite Planep. 136
Elastic Stress Analysis in a Circular Ring with Curvilinear Cracksp. 138
Cracks Normal to a Bimaterial Interfacep. 145
Crack Parallel to the Free Boundary of an Elastic Isotropic Semiplanep. 150
Crack Parallel to the Free Boundary of an Isotropic Semi-Infinite Solidp. 152
Crack in a Bimaterial Infinite and Isotropie Solid under Antiplane Shearp. 157
Straight Crack in an Infinite, Isotropie Solidp. 161
Periodic Array of Cracks along a Straight Line in an Infinite and Isotropic Solidp. 165
Periodic Array of Parallel Straight Cracks in an Infinite and Isotropic Solidp. 167
Singular Integral Equations In Aerodynamics
Introductionp. 173
Planar Airfoils in Two-dimensional Aerodynamicsp. 174
Multidimensional Singular Integralequations
Introductionp. 187
Multidimensional Singular Integral Equations in Lebesque Spaces Lp.p. 191
Two dimensional Singular Integral Equations Exact Solutionsp. 197
Numerical Evaluation of the Two-dimensional Singular Integral Equationsp. 203
Numerical Evaluation of the Three-dimensional Singular Integral Equationsp. 212
Multidimensional Singular Integralequations in Elasticity and Fracture Mechanics of Isotropic Solids
Introductionp. 219
Two-dimensional Elastic Stress Analysis of Isotropic Solidsp. 220
Application to the Determination of the Stress Field in the Neighbourhood of a Circular Hole under Internal Pressure in an Infinite and Isotropic Solidp. 225
Three-dimensional Elastic Stress Analysis of Isotropic Solidsp. 227
Application to the determination of the Elastic Stress Analysis of athick Cylinder Subjected to an Internal Pressurep. 231
Application to the Determination of the Stress Intensity Factors nearthe Edge of a Rectangular Crack under Tensile Pressure in anIsotropic Solidp. 238
Linear Viscoelasticity of Isotropic Solidsp. 242
Application of Linear Viscoelasticityp. 244
Multidimensional Singular Integral Equations in Relativistic Elastic Stress Analysis for Moving Frames
Introductionp. 251
Relative Stress Tensor Formulation for Moving Framesp. 252
Elastic Stress Analysis for Stationary and Moving Framesp. 263
Relativistic Thermoelastic Stress Analysis for Moving Framesp. 269
Multidimensional Singular Integralequations in Elasticity and Fracture Mechanics of Anisotropic Solids
Introductionp. 275
General Anisotropic Elastic Stress Analysisp. 277
Fundamental Solutions of Anisotropic Stress Field Analysisp. 281
Three-Dimensional Singular Integral Approximation Methodp. 288
Application to the Detennination of the Fracture Behaviour of aCircular Hole subjected to a Uniform Boundary Shear Traction in anInfinite and Qrthotropic Solidp. 290
Application to the Determination of the Fracture Behaviour of aCircular Hole in the Centre of a Rectangular Orthotropic Plate,subjected to Deformation by Tangential Forcesp. 294
Stress Field near the Crack Tip in an Anisotropic Solidp. 297
Multidimensional Singular Integralequations in Plasticity of Isotropic Solids
Introductionp. 305
Two-dimensional Plastic Stress Analysis of Isotropic Solidsp. 307
Application to the Determination of the Plastic Behaviour of aPerforated Tension Strip in Plane Stressp. 311
Application to the Determination of the Plastic Behaviour of a ThickSphere and a Thick Cylinder in Plane Strainp. 314
Application of two-dimensional Plasticity in a Circular Rocky Tunnelp. 317
Application to the Determination of the Plastic Behaviour of a SquareBlock Compressed by two Opposite Perfectly Rough Rigid Punches in Plane Strainp. 319
Three-dimensional Plastic Stress Analysis of Isotropic Solidsp. 321
Fracture Behaviour of Double Notched Tensile Specimenp. 328
Three-dimensional Thermoelastoplastic Stress Analysis of Isotropic Solidsp. 331
Thermoelastic Stress Analysis Application for a Hollow Cylinderp. 334
Non-Linear Singular Integral Equations
Introductionp. 343
Existence and Uniqueness Theorems for Non-Linear Singular IntegralEquations over Finite Sets of Contours in Banach Spacesp. 344
Existence and Uniqueness Theorems for Non-Linear Singular Integral Equations over a System of Arcs in Banach Spacesp. 353
Non-linear Finite-part Singular Integral Equations Uniqueness Theorems in Banach Spacesp. 367
Non-linear Singular Integrodifferential Equations Existence Theoryp. 375
Numerical Evaluation Methods for Non-Linear Singular Integral Equations
Introductionp. 381
Approximation Methods for Non-linear Programming Problemsp. 382
Non-linear Singular Integral Approximations in Banach Spaces by theCollocation Methodp. 388
Non-linear Singular Integral Approximations in Banach Spaces by theQuadrature Methodp. 394
Non-linear Singular Integrodifferential Approximation Theory by the Collocation Methodp. 397
Non-Linear Singular Integral Equations In Fluid Mechanics
Introductionp. 409
Profiles of Turbomachines in Steady Flow of Incompressible Fluidsp. 410
Non-linear Unsteady Inviscid Flowfields Analysisp. 415
Velocity and Pressure Coefficient Field for Linear Vortex Distributionp. 419
Velocity and Pressure Coefficient Field for Linear Source Distributionp. 425
Velocity and Pressure Coefficient Field for Constant Vortex Distributionp. 429
Velocity and Pressure Coefficient Field for Constant Source Distributionp. 433
Lists of Computer Programs for Fluid Mechanics (airfoil without velocity)p. 437
Unsteady Cascade Aeroelasticity applied in Turbomachinesp. 446
Non-linear Unsteady Inviscid Aerodynamic Analysisp. 453
Velocity and Pressure Coefficient Field for Linear Vortex Distribution (Airfoil with Velocity)p. 460
Velocity and Pressure Coefficient Field for Linear Source Distribution (Airfoil with Velocity)p. 464
Velocity and Pressure Coefficient Field for Constant Vortex Distribution (Airfoil with Velocity)p. 469
Velocity and Pressure Coefficient Field for Constant Source Distribution (Airfoil with Velocity)p. 473
Lists of Computer Programs for Aerodynamics (Airfoil with Velocity)p. 477
Non-Linear Integro-Differential Equations in Structural Analysis
Introductionp. 491
Non-linear Integro-differential Equations used in Orthotropic Shallow Spherical Shell Analysisp. 491
Non-linear Integro-differential Equations in Sandwich Plates Stress Analysisp. 499
Non-Linear Singular Integral Equations Inelastodynamics
Introductionp. 509
Seismic Wave Equations Analysis by Hubert Transformationsp. 510
Non-linear Stationary and Dynamic Viscoplasticityp. 517
Application to the Determination of the Limit Load for a Rigidly Plastic Solidp. 528
Conclusionsp. 533
Appendix - Mathematical Definitionsp. 535
Subject Indexp. 539
Author Indexp. 547
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540672302
ISBN-10: 3540672303
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 552
Published: 6th June 2000
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 3.18
Weight (kg): 0.99

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