准晶数学弹性理论及应用(英文版) pdf kindle caj 下载 azw3 umd 电子版 夸克云

This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter phyics and partial differential equati*** discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applicati*** by setting up new partial differential equati*** of higher order and their soluti*** under complicated boundary value and initial value conditi***. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equati*** involving elasticity are reduced to a single or a few partial differential equati*** of higher order. Systematical and direct methods of mathematical physics and complex variable functi*** are developed to solve the equati*** under appropriate boundary value and initial value conditi***, and many exact ***ytical soluti*** are c***tructed.

Preface

Chapter1 Crystals

　1.1 Periodicity of crystal structure, crystal cell

　1.2 Three-dimensional lattice types

　1.3 Symmetry and point groups

　1.4 Reciprocal lattice

　1.5 Appendix of Chapter1: Some basic concepts

　References　

Chapter 2 Framework of the classical theory of elasticity

　2.1 Review on some basic concepts

　2.2 Basic assumpti*** of theory of elasticity

　2.3 Displacement and deformation

　2.4 Stress ***ysis and equati*** of motion

　2.5 Generalized Hooke's law

　2.6 Elastodynamics, wave motion

　2.7 Summary

　References　

Chapter 3 Quasicrystal and its properties

　3.1 Discovery of quasicrystal

　3.2 Structure and symmetry of quasicrystals

　3.3 A brief introduction on physical properties of quasicrystals

　3.4 One-, two- and three-dimensional quasicrystals

　3.5 Two-dimensional quasicrystals and planar quasicrystals

　References　

Chapter 4 The physical basis of elasticity of quasicrystals

　4.1 Physical basis of elasticity of quasicrystals

　4.2 Deformation tensors

　4.3 Stress tensors and the equati*** of motion

　4.4 Free energy and elastic c***tants

　4.5 Generalized Hooke's law

　4.6 Boundary conditi*** and initial conditi***

　4.7 A brief introduction on relevant material c***tants of quasicrystals

　4.8 Summary and mathematical solvability of boundary value or initial- boundary value problem

　4.9 Appendix of Chapter 4: Description on physical basis of elasticity of quasicrystals based on the Landau density wave theory

　References

Chapter 5 Elasticity theory of one-dimensional quasicrystals and simplification

　5.1 Elasticity of hexagonal quasicrystals

　5.2 Decomposition of the problem into plane and anti-plane problems

　5.3 Elasticity of monoclinic quasicrystals

　5.4 Elasticity of orthorhombic quasicrystals

　5.5 Tetragonal quasicrystals

　5.6 The space elasticity of hexagonal quasicrystals

　5.7 Other results of elasticity of one-dimensional quasicrystals

　References　

Chapter 6 Elasticity of two-dimensional quasicrystals and simplification

　6.1 Basic equati*** of plane elasticity of two-dimensional quasicrystals: point groups 5m and10mm in five- and ten-fold symmetries

　6.2 Simplification of the basic equation set: displacement potential function method

　6.3 Simplification of the basic equati*** set: stress potential function method

　*** Plane elasticity of point group 5, pentagonal and point group10, decagonal quasicrystals

　6.5 Plane elasticity of point group12mm of dodecagonal quasicrystals

　6.6 Plane elasticity of point group 8mm of octagonal quasicrystals, displacement potential

　6.7 Stress potential of point group 5, pentagonal and point group10, decagonal quasicrystals

　6.8 Stress potential of point group 8mm octagonal quasicrystals

　6.9 Engineering and mathematical elasticity of quasicrystals

　References　

Chapter 7 Application I: Some dislocation and interface problems and soluti*** in one- and two,dimensional quasicrystals

　7.1 Dislocati*** in one-dimensional hexagonal quasicrystals

　7.2 Dislocati*** in quasicrystals with point groups 5m and10mm symmetries

　7.3 Dislocati*** in quasicrystals with point groups 5, five-fold and10, ten-fold symmetries

　7.4 Dislocati*** in quasicrystals with eight-fold symmetry

　7.5 Dislocati*** in dodecagonal quasicrystals

　7.6 Interface between quasicrystal and crystal

　7.7 Conclusion and discussion

　References　

Chapter 8 Application II: Soluti*** of notch and crack problems of one-and two-dimensional quasicrystals

　8.1 Crack problem and solution of one-dimensional quasicrystals

　8.2 Crack problem in finite-sized one-dimensional quasicrystals

　8.3 Griffith crack problems in point groups 5m and10mm quasicrystals based on displacement potential function method

　8.4 Stress potential function formulation and complex variable function method for solving notch and crack problems of quasicrystals of point groups 5, and10,

　8.5 Soluti*** of crack/notch problems of two-dimensional octagonal quasicrystals

　8.6 Other soluti*** of crack problems in one-and two-dimensional quasicrystals

　8.7 Appendix of Chapter 8: Derivation of solution of Section 8.1

　References　

Chapter 9 Theory of elasticity of three-dimensional quasicrystals and its applicati***

　9.1 Basic equati*** of elasticity of icosahedral quasicrystals

　9.2 Anti-plane elasticity of icosahedral quasicrystals and problem of interface between quasicrystal and crystal

　9.3 Phonon-phason decoupled plane elasticity of icosahedral quasicrystals

　9.4 Phonon-phason coupled plane elasticity of icosahedral quasicrystals displacement potential formulation

　9.5 Phonon-phason coupled plane elasticity of icosahedral quasicrystals stress potential formulation

　9.6 A straight dislocation in an icosahedral quasicrystal

　9.7 An elliptic notch/Griffith crack in an icosahedral quasicrystal

　9.8 Elasticity of cubic quasicrystals——the anti-plane and axisymmetric deformation

　References　

Chapter 10 Dynamics of elasticity and defects of quasicrystals

　10.1 Elastodynamics of quasicrystals followed the Bak's argument

　10.2 Elastodynamics of anti-plane elasticity for some quasicrystals

　10.3 Moving *** dislocation in anti-plane elasticity

　10.4 Mode III moving Griftith crack in anti-plane elasticity

　10.5 Elast0-/hydro-dynamics of quasicrystals and approximate ***ytic solution for moving *** dislocation in anti-plane elasticity

　10.6 Elasto-/hydro-dynamics and soluti*** of two-dimensional decagonal quasicrystals

　10.7 Elasto-/hydro-dynamics and applicati*** to fracture dynamics of icosahedral quasicrystals

　10.8 Appendix of Chapter10: The detail of finite difference scheme

　References　

Chapter 11 Complex variable function method for elasticity of quasicrystals

Chapter 12 Variational principle of elasticity of quasicrystals

Chapter 13 Some mathematical principles on soluti*** of elasticity of quasicrystals

Chapter 14 Nonlinear behaviour of quasicrystals

Chapter 15 Fracture theory of quasicrystals

Chapter 16 Remarkable conclusion

References

Major Appendix: On some mathematical materials

Appendix I Outline of complex variable functi*** and some additional calculati***

Appendix II Dual integral equati*** and some additional calculati***.

A

References

Index

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书籍介绍

《准晶数学的弹性理论及应用(英文版)》内容简介：This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter phyics and partial differential equati*** discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applicati*** by setting up new partial differential equati*** of higher order and their soluti*** under complicated boundary value and initial value conditi***. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equati*** involving elasticity are reduced to a single or a few partial differential equati*** of higher order. Systematical and direct methods of mathematical physics and complex variable functi*** are developed to solve the equati*** under appropriate boundary value and initial value conditi***, and many exact ***ytical soluti*** are c***tructed.