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E-raamat: Static Green's Functions in Anisotropic Media

(Zhejiang University, China), (University of Akron, Ohio)
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  • Ilmumisaeg: 30-Apr-2015
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316236093
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Static Green's Functions in Anisotropic MediaSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 30-Apr-2015
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316236093
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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 presented including those in anisotropic and transversely isotropic piezoelectric and piezomagnetic media, and in purely anisotropic elastic, transversely isotropic elastic and isotropic elastic media. Problems include those in three-dimensional, (two-dimensional) infinite, half, and biomaterial spaces (planes). While the emphasis is on the Green's functions related to the line and point force, those corresponding to the important line and point dislocation are also provided and discussed. This book provides a comprehensive derivation and collection of the Green's functions in the concerned media, and as such, it is an ideal reference book for researchers and engineers, and a textbook for both students in engineering and applied mathematics.

Muu info

This book presents the theory on static Green's functions in anisotropic magnetoelectroelastic media and their detailed derivations via different methods.
Preface xv
Acknowledgments xvii
1 Introduction
1(28)
1.0 Introduction
1(1)
1.1 Definition of Green's Functions
1(5)
1.2 Green's Theorems and Identities
6(2)
1.3 Green's Functions of Potential Problems
8(14)
1.3.1 Primary on 2D and 3D Potential Green's Functions
8(1)
1.3.2 Potential Green's Functions in Bimaterial Planes
9(2)
1.3.3 Potential Green's Functions in Bimaterial Spaces
11(1)
1.3.4 Potential Green's Functions in an Anisotropic Plane or Space
12(1)
1.3.5 An Inhomogeneous Circle in a Full-Plane
13(1)
1.3.5.1 A Source in the Matrix
14(2)
1.3.5.2 A Source in the Circular Inhomogeneity
16(1)
1.3.6 An Inhomogeneous Sphere in a Full-Space
17(1)
1.3.6.1 A Source in the Sphere
17(4)
1.3.6.2 A Source in the Matrix
21(1)
1.4 Applications of Green's Theorems and Identities
22(2)
1.4.1 Integral Equations for Potential Problems
22(1)
1.4.2 Boundary Integral Equations for Potential Problems
23(1)
1.5 Summary and Mathematical Keys
24(1)
1.5.1 Summary
24(1)
1.5.2 Mathematical Keys
25(1)
1.6 Appendix A: Equivalence between Infinite Series Summation and Integral over the Image Line Source
25(2)
1.7 References
27(2)
2 Governing Equations
29(28)
2.0 Introduction
29(1)
2.1 General Anisotropic Magnetoelectroelastic Solids
29(3)
2.1.1 Equilibrium Equations Including Also Those Associated with the E- and H-Fields
30(1)
2.1.2 Constitutive Relations for the Fully Coupled MEE Solid
30(1)
2.1.3 Gradient Relations (i.e., Elastic Strain-Displacement, Electric Field-Potential, and Magnetic Field-Potential Relations)
30(2)
2.2 Special Case: Anisotropic Piezoelectric or Piezomagnetic Solids
32(1)
2.2.1 Piezoelectric Materials
32(1)
2.2.2 Piezomagnetic Materials
33(1)
2.3 Special Case: Anisotropic Elastic Solids
33(2)
2.4 Special Case: Transversely Isotropic MEE Solids
35(2)
2.5 Special Case: Transversely Isotropic Piezoelectric/Piezomagnetic Solids
37(1)
2.6 Special Case: Transversely Isotropic or Isotropic Elastic Solids
37(2)
2.7 Special Case: Cubic Elastic Solids
39(1)
2.8 Two-Dimensional Governing Equations
39(2)
2.9 Extended Betti's Reciprocal Theorem
41(1)
2.10 Applications of Betti's Reciprocal Theorem
41(5)
2.10.1 Relation between Extended Point Forces and Extended Point Dislocations
41(4)
2.10.2 Relation between Extended Line Forces and Extended Line Dislocations
45(1)
2.11 Basics of Eshelby Inclusion and Inhomogeneity
46(3)
2.11.1 The Eshelby Inclusion Problem
46(2)
2.11.2 The Eshelby Inhomogeneity Problem
48(1)
2.12 Summary and Mathematical Keys
49(1)
2.12.1 Summary
49(1)
2.12.2 Mathematical Keys
50(1)
2.13 Appendix A: Governing Equations from the Energy Point of View
50(1)
2.14 Appendix B: Transformation of MEE Material Properties from One Coordinate System to the Other
51(3)
2.15 Appendix C: Some Important Unit Relations
54(1)
2.16 References
54(3)
3 Green's Functions in Elastic Isotropic Full and Bimaterial Planes
57(54)
3.0 Introduction
57(1)
3.1 Antiplane vs. Plane-Strain Deformation
57(1)
3.2 Antiplane Solutions of Line Forces and Line Dislocations
58(2)
3.3 Plane Displacements in Terms of Complex Functions
60(2)
3.4 Plane-Strain Solutions of Line Forces and Line Dislocations
62(3)
3.4.1 Plane-Strain Solutions of Line Forces
62(1)
3.4.2 Plane-Strain Solutions of Line Dislocations
63(2)
3.5 Bimaterial Antiplane Solutions of a Line Force and a Line Dislocation
65(5)
3.5.1 Bimaterial Antiplane Solutions of a Line Force
65(2)
3.5.2 Bimaterial Antiplane Solutions of a Line Dislocation
67(3)
3.6 Bimaterial Plane-Strain Solutions of Line Forces and Line Dislocations
70(6)
3.7 Line Forces or Line Dislocations Interacting with a Circular Inhomogeneity
76(25)
3.7.1 Antiplane Solutions
76(1)
3.7.1.1 A Line Force Inside or Outside a Circular Inhomogeneity
76(4)
3.7.1.2 A Screw Dislocation Inside or Outside a Circular Inhomogeneity
80(4)
3.7.2 Plane-Strain Solutions
84(1)
3.7.2.1 Line Forces or Edge Dislocations Outside a Circular Inhomogeneity
84(9)
3.7.2.2 Line Forces or Edge Dislocations Inside a Circular Inhomogeneity
93(8)
3.8 Applications of Bimaterial Line Force/Dislocation Solutions
101(7)
3.8.1 Image Force of a Line Dislocation
101(1)
3.8.1.1 PK Force on a Screw Dislocation in a Bimaterial Plane
101(1)
3.8.1.2 PK Force on a Screw Dislocation Interacting with a Circular Inhomogeneity
102(1)
3.8.1.3 PK Force on an Edge Dislocation in a Bimaterial Plane
103(2)
3.8.1.4 PK Force on an Edge Dislocation Interacting with a Circular Inhomogeneity
105(2)
3.8.2 Image Work of Line Forces
107(1)
3.8.2.1 Image Work on an Antiplane Line Force in a Bimaterial Plane
108(1)
3.8.2.2 Image Work on an Antiplane Line Force Interacting with a Circular Inhomogeneity
108(1)
3.9 Summary and Mathematical Keys
108(2)
3.9.1 Summary
108(1)
3.9.2 Mathematical Keys
109(1)
3.10 References
110(1)
4 Green's Functions in Magnetoelectroelastic Full and Bimaterial Planes
111(29)
4.0 Introduction
111(1)
4.1 Generalized Plane-Strain Deformation
111(2)
4.2 Solutions of Line Forces and Line Dislocations in a 2D Full-Plane
113(4)
4.2.1 General Solutions of Line Forces and Line Dislocations
113(2)
4.2.2 Green's Functions of a Line Force
115(2)
4.2.3 Green's Functions of a Line Dislocation
117(1)
4.3 Green's Functions of Line Forces and Line Dislocations in a Half-Plane
117(6)
4.3.1 Green's Functions of a Line Force in a Half-Plane
118(1)
4.3.2 Green's Functions of a Line Dislocation in a Half-Plane
118(1)
4.3.3 Green's Functions of Line Forces and Line Dislocations in a Half-Plane under General Boundary Conditions
119(4)
4.4 Green's Functions of Line Forces and Line Dislocations in Bimaterial Planes
123(3)
4.4.1 General Green's Functions of Line Forces and Line Dislocations in Bimaterial Planes
123(1)
4.4.2 Green's Functions of Line Forces and Line Dislocations in Bimaterial Planes under Perfect Interface Conditions
124(2)
4.5 Green's Functions of Line Forces and Line Dislocations in Bimaterial Planes under General Interface Conditions
126(3)
4.6 Applications in Semiconductor Industry
129(7)
4.6.1 Basic Formulations of the Eshelby Inclusion and Quantum Wires
129(2)
4.6.2 Quantum Wires in a Piezoelectric Full Plane
131(1)
4.6.3 Quantum Wires in an MEE Half-Plane
132(3)
4.6.4 Quantum Wires in a Piezoelectric Bimaterial Plane
135(1)
4.7 Summary and Mathematical Keys
136(2)
4.7.1 Summary
136(2)
4.7.2 Mathematical Keys
138(1)
4.8 References
138(2)
5 Green's Functions in Elastic Isotropic Full and Bimaterial Spaces
140(36)
5.0 Introduction
140(1)
5.1 Green's Functions of Point Forces in an Elastic Isotropic Full-Space
140(3)
5.2 Papkovich Functions and Green's Representation
143(2)
5.3 Papkovich Functions in an Elastic Isotropic Bimaterial Space with Perfect Interface
145(10)
5.3.1 A Point Force Normal to the Interface Applied in Material 1
146(4)
5.3.2 A Point Force Parallel to the Interface Applied in Material 1
150(5)
5.4 Papkovich Functions in an Elastic Isotropic Bimaterial Space with Smooth Interface
155(1)
5.4.1 A Point Force Normal to the Interface Applied in Material 1
155(1)
5.4.2 A Point Force Parallel to the Interface Applied in Material 1
156(1)
5.5 Papkovich Functions for Both Perfect-Bonded and Smooth Interfaces of Bimaterial Spaces
156(2)
5.5.1 Papkovich Functions for a Vertical Point Force in Material 1
156(1)
5.5.2 Papkovich Functions for a Horizontal Point Force in Material 1
157(1)
5.6 Green's Displacements and Stresses in Elastic Isotropic Bimaterial Spaces
158(8)
5.6.1 Green's Displacements and Stresses in Bimaterial Spaces by a Vertical Point Force
158(3)
5.6.2 Green's Displacements and Stresses in Bimaterial Spaces by a Horizontal Point Force
161(5)
5.7 Brief Discussion on the Corresponding Dislocation Solution
166(1)
5.8 Applications: Uniform Loading over a Circular Area on the Surface of a Half-Space
166(6)
5.9 Summary and Mathematical Keys
172(1)
5.9.1 Summary
172(1)
5.9.2 Mathematical Keys
172(1)
5.10 Appendix A: Derivatives of Some Common Functions
172(1)
5.11 Appendix B: Displacements and Stresses in a Traction-Free Half-Space Due to a Point Force Applied on the Surface
173(1)
5.12 Appendix C: Displacements and Stresses in a Half Space Induced by a Point Force Applied on the Surface with Mixed Boundary Conditions
174(1)
5.13 References
175(1)
6 Green's Functions in a Transversely Isotropic Magnetoelectroelastic Full Space
176(44)
6.0 Introduction
176(1)
6.1 General Solutions in Terms of Potential Functions
176(7)
6.2 Solutions of a Vertical Point Force, a Negative Electric Charge or Negative Magnetic Charge
183(4)
6.3 Solutions of a Horizontal Point Force along x-Axis
187(4)
6.4 Various Decoupled Solutions
191(7)
6.4.1 Piezoelectric Green's Functions
191(2)
6.4.1.1 Solutions of a Vertical Point Force and a Negative Electric Charge
193(1)
6.4.1.2 Solutions of a Horizontal Point Force along x-Axis
194(1)
6.4.2 Elastic Green's Functions
195(1)
6.4.2.1 Solutions of a Vertical Point Force
196(1)
6.4.2.2 Solutions of a Horizontal Point Force along x-Axis
197(1)
6.5 Technical Applications
198(11)
6.5.1 Eshelby Inclusion Solution in Terms of the Green's Functions
198(3)
6.5.2 Elements of the Extended Eshelby Tensor
201(7)
6.5.3 Special Cases
208(1)
6.5.3.1 Special Geometric Cases
208(1)
6.5.3.2 Special Material Coupling Cases
209(1)
6.6 Summary and Mathematical Keys
209(1)
6.6.1 Summary
209(1)
6.6.2 Mathematical Keys
209(1)
6.7 Appendix A: The Extended Green's Functions and Their Derivatives
209(7)
6.7.1 The Extended Green's Displacements
209(2)
6.7.2 Derivatives of the Extended Green's Displacements
211(1)
6.7.2.1 Derivatives of the Extended Green's Displacements Due to the Point Source in K-direction (K = 3,4,5)
211(1)
6.7.2.2 Derivatives of the Extended Green's Displacements Due to the Point Source in x-direction
211(1)
6.7.2.3 Derivatives of the Extended Green's Displacements Due to the Point Source in y-direction
212(1)
6.7.3 The Scaled Green's Function Derivatives GKJi (l) in Terms of the Unit Vector l
213(1)
6.7.3.1 Due to the Point Source in K-direction (K = 3,4,5)
214(1)
6.7.3.2 Due to the Point Source in x-direction
214(1)
6.7.3.3 Due to the Point Source in y-direction
215(1)
6.8 Appendix B: Functions Involved in the Eshelby Inclusion Problem
216(2)
6.8.1 A Spheroidal Inclusion (b = a/c)
216(1)
6.8.2 Three Special Geometric Cases of Inclusion (b = a/e)
217(1)
6.9 References
218(2)
7 Green's Functions in a Transversely Isotropic Magnetoelectroelastic Bimaterial Space
220(40)
7.0 Introduction
220(1)
7.1 Problem Description
220(1)
7.2 Green's Functions in a Bimaterial Space Due to Extended Point Sources
221(9)
7.2.1 Solutions for a Vertical Point Force, a Negative Electric Charge, or a Negative Magnetic Charge
221(4)
7.2.2 Solutions for a Horizontal Point Force
225(5)
7.3 Reduced Bimaterial Spaces
230(7)
7.3.1 Green's Solutions for Piezoelectric Bimaterial Space
230(1)
7.3.1.1 Solutions for a Vertical Point Force and a Negative Electric Charge
230(2)
7.3.1.2 Solutions for a Horizontal Point Force
232(2)
7.3.2 Green's Solutions for an Elastic Bimaterial Space
234(1)
7.3.2.1 Solutions for a Vertical Point Force
234(1)
7.3.2.2 Solutions for a Horizontal Point Force
235(2)
7.4 Bimaterial Green's Functions for Other Interface Conditions
237(4)
7.4.1 Solutions for a Smoothly Contacting and Perfectly Conducting Interface
237(1)
7.4.2 Solutions for a Mechanically Perfect and Electromagnetically Insulating Interface
238(3)
7.5 Half-Space Green's Functions
241(5)
7.5.1 Green's Functions for an MEE Half-Space with Free Surface
241(1)
7.5.2 Green's Functions for an MEE Half-Space with Surface Electrode
242(1)
7.5.3 Surface Green's Functions
243(1)
7.5.3.1 Extended Boussinesq Solutions for a Vertical Point Force, Electric Charge, or Magnetic Charge
243(1)
7.5.3.2 Extended Cerruti Solutions for a Horizontal Point Force
244(2)
7.6 Technical Application: Indentation over an MEE Half-Space
246(11)
7.6.1 Theory of Indentation
246(3)
7.6.2 Indentation over an MEE Half-Space
249(8)
7.7 Summary and Mathematical Keys
257(1)
7.7.1 Summary
257(1)
7.7.2 Mathematical Keys
257(1)
7.8 References
257(3)
8 Green's Functions in an Anisotropic Magnetoelectroelastic Full-Space
260(33)
8.0 Introduction
260(1)
8.1 Basic Equations in 3D MEE Full-Space
260(1)
8.2 Green's Functions in Terms of Line Integrals
261(4)
8.3 Green's Functions in Terms of Stroh Eigenvalues
265(2)
8.4 Green's Functions Using 2D Fourier Transform Method
267(7)
8.5 Green's Functions in Terms of Radon Transform
274(1)
8.6 Green's Functions in Terms of Stroh Eigenvalues and Eigenvectors
275(6)
8.6.1 General Definitions
275(1)
8.6.2 Orthogonal Relations
276(1)
8.6.3 Variation and Integration of Stroh Quantities in the (m, n)-Plane and the Green's Functions
276(1)
8.6.4 Derivatives of Extended Green's Displacements
277(4)
8.7 Technical Applications of Point-Source Solutions
281(6)
8.7.1 Couple Force, Dipoles, and Moments
281(1)
8.7.2 Relations among Dislocation, Faulting, and Force Moments
282(3)
8.7.3 Equivalent Body Forces of Dislocations
285(2)
8.8 Numerical Examples of Dislocations
287(1)
8.9 Summary and Mathematical Keys
288(3)
8.9.1 Summary
288(2)
8.9.2 Mathematical Keys
290(1)
8.10 Appendix A: Some Basic Mathematical Formulations
291(1)
8.11 References
292(1)
9 Green's Functions in an Anisotropic Magnetoelectroelastic Bimaterial Space
293(36)
9.0 Introduction
293(1)
9.1 Problem Description
293(1)
9.2 Solutions in Fourier Domain for Forces in Material 1
294(2)
9.3 Solutions in Physical Domain for Forces in Material 1
296(3)
9.4 Solutions in Physical Domain for Forces in Material 1 with Imperfect Interface Conditions
299(3)
9.4.1 Imperfect Interface Type 1
299(1)
9.4.2 Imperfect Interface Type 2
300(2)
9.5 Special Case: Upper Half-Space under General Surface Conditions
302(2)
9.6 Bimaterial Space with Extended Point Forces in Material 2
304(2)
9.7 Special Case: Lower Half-Space under General Surface Conditions
306(1)
9.8 Technical Application: Quantum Dots in Anisotropic Piezoelectric Semiconductors
307(5)
9.8.1 Analytical Integral over Flat Triangle, the Anisotropic MEE Full-Space Case
308(3)
9.8.2 Analytical Integral over a Flat Triangle, the Anisotropic MEE Bimaterial Space Case
311(1)
9.9 Numerical Examples
312(14)
9.9.1 A Pyramidal QD in a Piezoelectric Full-Space
312(1)
9.9.2 QD Inclusion in a Piezoelectric Half-Space
313(11)
9.9.3 Triangular and Hexagonal Dislocation Loops in Elastic Bimaterial Space
324(2)
9.10 Summary and Mathematical Keys
326(1)
9.10.1 Summary
326(1)
9.10.2 Mathematical Keys
326(1)
9.11 References
327(2)
Index 329
Ernian Pan is a Professor of Civil Engineering at the University of Akron and a Fellow of both ASME and ASCE. He received his BS from Lanzhou University, his MS from Peking University, and his PhD from the University of Colorado, Boulder. His research interests are in computational mechanics with applications to anisotropic magnetoelectroelastic solids and nanostructures. As a well-recognized expert in anisotropic and multilayered Green's functions, he has pioneered various benchmark solutions for multiphase and multilayered composites with functionally graded materials and played various active roles in, and contributed to, Green's function research and education. He has published more than 250 journal articles. Weiqiu Chen is a Professor of Engineering Mechanics at Zhejiang University, China. He received his BS and PhD degrees from Zhejiang University in 1990 and 1996, respectively. He has engaged himself in the mechanics of smart materials/structures and vibrations/waves in structures for more than twenty years. He has co-authored more than 300 peer-reviewed journal articles, and he has published two books on the elasticity of transversely isotropic elastic and piezoelectric solids in 2006 and 2001, respectively. He has received numerous awards, including the National Science Fund for Excellent Young Scholars from the NSFC in 2007 and the Award of Science and Technology (the second grade) from the Ministry of Education, China, in 2012.
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