Ebook: Singular Integral Equations: Linear and Non-linear Theory and its Applications in Science and Engineering

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.

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The book includes the latest high technology on solving very important theoretical and practical problems on solid mechanics, fracture mechanics, structural analysis, elastodynamics, fluid mechanis and aerodynamics, by using linear and non-linear singular integral equation methods. Analytical theories and numerical evaluation methods are investigated and introduced for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations with a very important use in a wide field of engineering mechanics. The proposed Singular Interal Operator Method in many cases offers important advantages over "domain" type solutions, like finite elements and finite difference, as well as analytical methods, such as complex variable methods.

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The book includes the latest high technology on solving very important theoretical and practical problems on solid mechanics, fracture mechanics, structural analysis, elastodynamics, fluid mechanis and aerodynamics, by using linear and non-linear singular integral equation methods. Analytical theories and numerical evaluation methods are investigated and introduced for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations with a very important use in a wide field of engineering mechanics. The proposed Singular Interal Operator Method in many cases offers important advantages over "domain" type solutions, like finite elements and finite difference, as well as analytical methods, such as complex variable methods.
Content:
Front Matter....Pages I-XXV
Introduction....Pages 1-15
Finite-Part Singular Integral Equations....Pages 17-132
Finite-Part Singular Integral Equations in Elasticity and Fracture Mechanics....Pages 133-171
Singular Integral Equations in Aerodynamics....Pages 173-185
Multidimensional Singular Integral Equations....Pages 187-218
Multidimensional Singular Integral Equations in Elasticity and Fracture Mechanics of Isotropic Solids....Pages 219-250
Multidimensional Singular Integral Equations in Relativistic Elastic Stress Analysis for Moving Frames....Pages 251-274
Multidimensional Singular Integral Equations in Elasticity and Fracture Mechanics of Anisotropic Solids....Pages 275-304
Multidimensional Singular Integral Equations in Plasticity of Isotropic Solids....Pages 305-342
Non-Linear Singular Integral Equations....Pages 343-380
Numerical Evaluation Methods for Nonlinear Singular Integral Equations....Pages 381-407
Non-Linear Singular Integral Equations In Fluid Mechanics....Pages 409-489
Non-Linear Integro-Differential Equations in Structural Analysis....Pages 491-507
Non-Linear Singular Integral Equations in Elastodynamics....Pages 509-532
Conclusions....Pages 533-534
Back Matter....Pages 535-551

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The book includes the latest high technology on solving very important theoretical and practical problems on solid mechanics, fracture mechanics, structural analysis, elastodynamics, fluid mechanis and aerodynamics, by using linear and non-linear singular integral equation methods. Analytical theories and numerical evaluation methods are investigated and introduced for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations with a very important use in a wide field of engineering mechanics. The proposed Singular Interal Operator Method in many cases offers important advantages over "domain" type solutions, like finite elements and finite difference, as well as analytical methods, such as complex variable methods.
Content:
Front Matter....Pages I-XXV
Introduction....Pages 1-15
Finite-Part Singular Integral Equations....Pages 17-132
Finite-Part Singular Integral Equations in Elasticity and Fracture Mechanics....Pages 133-171
Singular Integral Equations in Aerodynamics....Pages 173-185
Multidimensional Singular Integral Equations....Pages 187-218
Multidimensional Singular Integral Equations in Elasticity and Fracture Mechanics of Isotropic Solids....Pages 219-250
Multidimensional Singular Integral Equations in Relativistic Elastic Stress Analysis for Moving Frames....Pages 251-274
Multidimensional Singular Integral Equations in Elasticity and Fracture Mechanics of Anisotropic Solids....Pages 275-304
Multidimensional Singular Integral Equations in Plasticity of Isotropic Solids....Pages 305-342
Non-Linear Singular Integral Equations....Pages 343-380
Numerical Evaluation Methods for Nonlinear Singular Integral Equations....Pages 381-407
Non-Linear Singular Integral Equations In Fluid Mechanics....Pages 409-489
Non-Linear Integro-Differential Equations in Structural Analysis....Pages 491-507
Non-Linear Singular Integral Equations in Elastodynamics....Pages 509-532
Conclusions....Pages 533-534
Back Matter....Pages 535-551
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