网站首页  软件下载  游戏下载  翻译软件  电子书下载  电影下载  电视剧下载  教程攻略

请输入您要查询的图书:

 

书名 准晶数学的弹性理论及应用(精)
分类 科学技术-自然科学-数学
作者 Chen Yuzhuo
出版社 科学出版社
下载
简介
编辑推荐

This monograph is devoted to the development of a mathematical theory of elasticity of quasicrystals and its applications. Some results on elastodynamics and plasticity of quasicrystais are also included to document preliminary advances in recent years.

As this book is focused on the mathematical theory of elasticity of quasicrystals, it does not include in-depth discussions on the physics of the phason degrees of freedom and the physical nature of the phason variables. These research subjects are important to the quasicrystal study.

内容推荐

This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter phvsics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed.

目录

Preface

Chapter 1 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 Chapter 1: Some basic concepts

 References

Chapter 2 Framework of the classical theory of elasticity

 2.1 Review on some basic concepts

 2.2 Basic assumptions of theory of elasticity

 2.3 Displacement and deformation

 2.4 Stress analysis and equations 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 equations of motion

 4.4 Free energy and elastic constants

 4.5 Generalized Hooke's law

 4.6 Boundary conditions and initial conditions

 4.7 A brief introduction on relevant material constants 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 equations of plane elasticity of two-dimensional quasicrystals:

point groups 5m and 10mm in five- and ten-fold symmetries

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

 6.3 Simplification of the basic equations set: stress potential function method

 6.4 Plane elasticity of point group 5, ■ pentagonal and point group 10, ■ decagonal quasicrystals

 6.5 Plane elasticity of point group 12mm 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 group 10, ■ 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 solutions in one- and two,dimensional quasicrystals

 7.1 Dislocations in one-dimensional hexagonal quasicrystals

 7.2 Dislocations in quasicrystals with point groups 5m and 10mm symmetries

 7.3 Dislocations in quasicrystals with point groups 5, ■ five-fold and 10, ■ ten-fold symmetries

 7.4 Dislocations in quasicrystals with eight-fold symmetry

 7.5 Dislocations in dodecagonal quasicrystals

 7.6 Interface between quasicrystal and crystal

 7.7 Conclusion and discussion

 References

Chapter 8 Application II: Solutions 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 and 10mm 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, ■ and 10, ■

 8.5 Solutions of crack/notch problems of two-dimensional octagonal quasicrystals

 8.6 Other solutions 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 applications

 9.1 Basic equations 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 screw 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 analytic

solution for moving screw dislocation in anti-plane elasticity

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

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

 10.8 Appendix of Chapter 10: The detail of finite difference scheme

 References

Chapter 11 Complex variable function method for elasticity of quasicrystals

 11.1 Harmonic and quasi-biharmonic equations in anti-plane elasticity of one-dimensional quasicrystals

 11.2 Biharmonic equations in plane elasticity of point group 12mm two-dimensional quasicrystals

 11.3 The complex variable function method of quadruple harmonic

equations and applications in two-dimensional quasicrystals

 11.4 Complex variable function method for sextuple harmonic equation

and applications to icosahedral quasicrystals

 11.5 Complex analysis and solution of quadruple quasiharmonic equation

 11.6 Conclusion and discussion

 References

Chapter 12 Variational principle of elasticity of quasicrystals

numerical analysis and applications

 12.1 Basic relations of plane elasticity of two-dimensional quasicrystals

 12.2 Generalized variational principle for static elasticity ofquasicrystals

 12.3 Finite element method

 12.4 Numerical examples

 References

Chapter 13 Some mathematical principles on solutions of elasticity of quasicrystals

 13.1 Uniqueness of solution of elasticity of quasicrystals

 13.2 Generalized Lax-Milgram theorem

 13.3 Matrix expression of elasticity of three-dimensional qnasicrystals

 13.4 The weak solution of boundary value problem of elasticity of quasicrystals

 13.5 The uniqueness of weak solution

 13.6 Conclusion and discussion

 References

Chapter 14 Nonlinear behaviour of quasicrystals

 14.1 Macroscopic behaviour of plastic deformation of quasicrystals

 14.2 Possible scheme of plastic constitutive equations

 14.3 Nonlinear elasticity and its formulation

 14.4 Nonlinear solutions based on simple models

 14.5 Nonlinear analysis based on the generalized Eshelby theory

 14.6 Nonlinear analysis based on the dislocation model

 14.7 Conclusion and discussion

 14.8 Appendix of Chapter 14: Some mathematical details

 References

Chapter 15 Fracture theory of quasicrystals

 15.1 Linear fracture theory of quasicrystals

 15.2 Measurement of GIC

 15.3 Nonlinear fracture mechanics

 15.4 Dynamic fracture

 15.5 Measurement of fracture toughness and relevant mechanical

parameters of quasicrystalline material

 References

Chapter 16 Remarkable conclusion

 References

Major Appendix: On some mathematical materials

 Appendix I Outline of complex variable functions and some additional calculations

A.I.1 Complex functions, analytic functions

A.I.2 Cauchy's formula

A.I.3 Poles

A.I.4 Residue theorem

A.I.5 Analytic extension

A.I.6 Conformal mapping

A.I.7 Additional derivation of solution (8.2-19)

A.I.8 Additional derivation of solution (11.3-53)

A.I.9 Detail of complex analysis of generalized cohesive force model for plane

 elasticity of two-dimensional point groups 5m, 10mm and 10, 10 quasicrystals

A.I.10 On the calculation of integral (9.2-14)

 Appendix II Dual integral equations and some additional calculations.

A.II.1 Dual integral equations

A.II.2 Additional derivation on the solution of dual integral equations(8.3-8)

A.II.3 Additional derivation on the solution of dual integral equations(9.8-8)

 References

Index

随便看

 

霍普软件下载网电子书栏目提供海量电子书在线免费阅读及下载。

 

Copyright © 2002-2024 101bt.net All Rights Reserved
更新时间:2025/4/8 2:13:33