Singular Integral Equations

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.

The author treats the theory of Singular Integral Equations thoroughly Applications - mostly in engineering mechanics - are widely described in connection to the treated theory The author is a well-known scientist in this field and made major contributions to the application of Singular Integral Equations in mechanics Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt
1 Introduction.- 2 Finite-Part Singular Integral Equations.- 3 Finite-Part Singular Integral Equations in Elasticity and Fracture Mechanics.- 4 Singular Integral Equations in Aerodynamics.- 5 Multidimensional Singular Integral Equations.- 6 Multidimensional Singular Integral Equations in Elasticity and Fracture Mechanics of Isotropic Solids.- 7 Multidimensional Singular Integral Equations in Relativistic Elastic Stress Analysis for Moving Frames.- 8 Multidimensional Singular Integral Equations in Elasticity and Fracture Mechanics of Anisotropic Solids.- 9 Multidimensional Singular Integral Equations in Plasticity of Isotropic Solids.- 10 Non-Linear Singular Integral Equations.- 11 Numerical Evaluation Methods for Non-Linear Singular Integral Equations.- 12 Non-Linear Singular Integral Equations in Fluid Mechanics.- 13 Non-Linear Integro-Differential Equations in Structural Analysis.- 14 Non-Linear Singular Integral Equations in Elastodynamics.- 15 Conclusions.- Appendix Mathematical Definitions.- Author Index.