Static Green's functions in anisotropic media / Ernian Pan, University of Akron, Weiqiu Chen, Zhejiang University.
This book presents basic theory on static Green's functions in general anisotropic magnetoelectroelastic media including detailed derivations based on the complex variable method, potential method, and integral transforms. Green's functions corresponding to the reduced cases are also prese...
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| Format: | Electronic eBook |
| Language: | English |
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New York NY :
Cambridge University Press,
2015.
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Table of Contents:
- Cover; Half-title; Title page; Copyright information; Epigraph; Table of contents; Preface; Acknowledgments; 1 Introduction; 1.0 Introduction; 1.1 Definition of Green's Function; 1.2 Green's Theorems and Identities; 1.3 Green's Functions of Potential Problems; 1.3.1 Primary on 2D and 3D Potential Green's Functions; 1.3.2 Potential Green's Functions in Bimaterial Planes; 1.3.3 Potential Green's Functions in Bimaterial Spaces; 1.3.4 Potential Green's Functions in an Anisotropic Plane or Space; 1.3.5 An Inhomogeneous Circle in a Full-Plane; 1.3.5.1 A Source in the Matrix.
- 1.3.5.2 A Source in the Circular Inhomogeneity1.3.6 An Inhomogeneous Sphere in a Full-Space; 1.3.6.1 A Source in the Sphere; 1.3.6.2 A Source in the Matrix; 1.4 Applications of Green's Theorems and Identities; 1.4.1 Integral Equations for Potential Problems; 1.4.2 Boundary Integral Equations for Potential Problems; 1.5 Summary and Mathematical Keys; 1.5.1 Summary; 1.5.2 Mathematical Keys; 1.6 Appendix A: Equivalence between Infinite Series Summation and Integral over the Image Line Source; 1.7 References; 2 Governing Equations; 2.0 Introduction.
- 2.1 General Anisotropic Magnetoelectroelastic Solids2.1.1 Equilibrium Equations Including Also Those Associated with the E- and H-Fields; 2.1.2 Constitutive Relations for the Fully Coupled MEE Solid; 2.1.3 Gradient Relations (i.e., Elastic Strain-Displacement, Electric Field-Potential, and Magnetic Field-Potential Relations); 2.2 Special Case: Anisotropic Piezoelectric or Piezomagnetic Solids; 2.2.1 Piezoelectric Materials; 2.2.2 Piezomagnetic Materials; 2.3 Special Case: Anisotropic Elastic Solids; 2.4 Special Case: Transversely Isotropic MEE Solids.
- 2.5 Special Case: Transversely Isotropic Piezoelectric/Piezomagnetic Solids2.6 Special Case: Transversely Isotropic or Isotropic Elastic Solids; 2.7 Special Case: Cubic Elastic Solids; 2.8 Two-Dimensional Governing Equations; 2.9 Extended Betti's Reciprocal Theorem; 2.10 Applications of Betti's Reciprocal Theorem; 2.10.1 Relation between Extended Point Forces and Extended Point Dislocations; 2.10.2 Relation between Extended Line Forces and Extended Line Dislocations; 2.11 Basics of Eshelby Inclusion and Inhomogeneity; 2.11.1 The Eshelby Inclusion Problem.
- 2.11.2 The Eshelby Inhomogeneity Problem2.12 Summary and Mathematical Keys; 2.12.1 Summary; 2.12.2 Mathematical Keys; 2.13 Appendix A: Governing Equations from the Energy Point of View; 2.14 Appendix B: Transformation of MEE Material Properties from One Coordinate System to the Other; 2.15 Appendix C: Some Important Unit Relations; 2.16 References; 3 Green's Functions in Elastic Isotropic Full and Bimaterial Planes; 3.0 Introduction; 3.1 Antiplane vs. Plane-Strain Deformation; 3.2 Antiplane Solutions of Line Forces and Line Dislocations; 3.3 Plane Displacements in Terms of Complex Functions.