Computational Recipes of Linear and Non-Linear Singular Integral Equations and Relativistic Mechanics in Engineering and Applied Science. Volume II

Evangelos G. Ladopoulos
Civil Engineer, Mechanical Engineer, Interpaper Research Organization, Athens, Greece

Series: Computational Mathematics and Analysis
BISAC: SCI040000

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Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick

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The present book deals with the computational recipes of the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are widely used in many fields of engineering mechanics and mathematical physics with an applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, elastodynamics, fluid mechanics, potential flows, hydraulics and aerodynamics. Such types of linear and non-linear singular integral equations form the latest technology of very important problems of solid and fluid mechanics, which should be given special attention by the reader. The Singular Integral Operators Method (S.I.O.M.) is introduced and investigated for the numerical evaluation of the multidimensional singular integral equations.

This approximation 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. Additionally, a special field of applied mechanics is introduced, named as Relativistic Mechanics, which is a combination of the classical theory of elasticity and general relativity. Relativistic Mechanics has two main branches: Relativistic Elasticity and Relativistic Thermo-Elasticity and according to the above theory, the relative stress tensor for moving structures has been formulated and a formula has been given between the relative stress tensor and the absolute stress tensor of the stationary frame. This leads to the Universal Equation of Elasticity and the Universal Equation of Thermo-Elasticity. (Imprint: Nova)

Preface

Chapter 10 - Coupling of Singular Integral Equations and Finite Elements in Elasticity

Chapter 11 - Plate Bending Analysis by Multidimensional Singular Integral Equations

Chapter 12 - Multidimensional Singular Integral Equations in Potential Flows and Hydraulics

Chapter 13 - Computational Recipies of Hypersingular Integral Equations

Chapter 14 - General Computer Program Codes for Elastostatics and Potential Problems

Chapter 15 - Computational Recipies of Non-Linear Singular Integral Equations

Chapter 16 - Fluid Mechanics by Non-Linear Singular Integral Equations

Chapter 17 - Structural Analysis by Non-Linear Integro-Differential Equations

Chapter 18 - Elastodynamics by Non-Linear Singular Integral Equations

Chapter 19 - Conclusions

Appendix - Mathematical Definitions

Index

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