准晶数学弹性理论及应用9787030474292
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广东广州
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作者范天佑
出版社科学出版社
ISBN9787030474292
出版时间2016-07
装帧精装
开本其他
定价198元
货号8932542
上书时间2024-12-23
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目录
Contents
1 Crystals1
1.1 Periodicity of Crystal Structure， Crystal Cell 1
1.2 Three-Dimensional LatticeTypes2
1.3 Symmetry and Point Groups 2
1.4 Reciprocal Lattice 5
1.5 Appendix of Chapter 1：Some Basic Concepts6
1.5.1 ConceptofPhonon6
1.5.2 Incommensurate Crystals 10
1.5.3 Glassy Structure 11
1.5.4 Mathematical Aspect of Group 11
References 12
2 Framework of Crystal Elasticity13
2.1 Review on Some Basic Concepts13
2.1.1 Vector13
2.1.2 Coordinate Frame 14
2.1.3 Coordinate Transformation 14
2.1.4 Tensor16
2.1.5 Algebraic Operation of Tensor 16
2.2 Basic Assumptions of Theory of Elasticity17
2.3 Displacement and Deformation17
2.4 Stress Analysis 19
2.5 Generalized Hooke’sLaw20
2.6 Elastodynamics， Wave Motion 24
2.7 Summary25
References 26
3 Quasicrystal and Its Properties27
3.1 Discovery of Quasicrystal 27
3.2 Structure and Symmetry of Quasicrystals 29
3.3 A Brief Introduction on Physical Properties of Quasicrystals 31
3.4 One-， Two-and Three-Dimensional Quasicrystals 32
3.5 Two-Dimensional Quasicrystals and Planar Quasicrystals 32
References 33
4 The Physical Basis of Elasticity of Solid Quasicrystals37
4.1 Physical Basis of Elasticity of Quasicrystals 37
4.2 Deformation Tensors38
4.3 Stress Tensors and Equations of Motion 40
4.4 Free Energy Density and Elastic Constants 42
4.5 Generalized Hooke’sLaw44
4.6 Boundary Conditions and Initial Conditions 44
4.7 A Brief Introduction on Relevant Material Constants of Solid Quasicrystals 46
4.8 Summary and Mathematical Solvability of Boundary Value or Initial-Boundary Value Problem47
4.9 Appendix of Chapter 4：Description on Physical Basis of Elasticity of Quasicrystals Based on the Landau Density WaveTheory48
References 53
5 Elasticity Theory of One-Dimensional Quasicrystals and Simplification 55
5.1 Elasticity of Hexagonal Quasicrystals55
5.2 Decomposition of the Elasticity into a Superposition of Plane and Anti-plane Elasticity58
5.3 Elasticity of Monoclinic Quasicrystals61
5.4 Elasticity of Orthorhombic Quasicrystals64
5.5 Tetragonal Quasicrystals 65
5.6 The Space Elasticity of Hexagonal Quasicrystals 66
5.7 Other Results of Elasticity of One-Dimensional Quasicrystals 68
References 68
6 Elasticity of Two-Dimensional Quasicrystals and Simplification 71
6.1 Basic Equations of Plane Elasticity of Two-Dimensional Quasicrystals：Point Groups 5m and 10mm in Five-and TenfoldSymmetries75
6.2 Simplification of the Basic Equation Set：Displacement Potential Function Method81
6.3 Simplification of Basic Equations Set：Stress Potential Function Method 83
6.4 Plane Elasticity of Point Group 5， 5 and 10， 10 Pentagonal and Decagonal Quasicrystals85
6.5 Plane Elasticity of Point Group 12mm of Dodecagonal Quasicrystals 89
6.6 Plane Elasticity of Point Group8mm of Octagonal Quasicrystals， Displacement Potential93
6.7 Stress Potential of Point Group5；5 Pentagonal and Point Group 10；10 Decagonal Quasicrystals98
6.8 Stress Potential ofPointGroup8mm Octagonal Quasicrystals 100
6.9 Engineering and Mathematical Elasticity of Quasicrystals 103 References 106
7 Application I-Some Dislocation and Interface Problems and Solutions in One-and Two-Dimensional Quasicrystals109
7.1 Dislocations in One-Dimensional Hexagonal Quasicrystals 110
7.2 Dislocations in Quasicrystals with Point Groups 5m and 10 mm Symmetries112
7.3 Dislocations in Quasicrystals with Point Groups 5；5 Fivefold and 10，10 Tenfold Symmetries 119
7.4 Dislocations in Quasicrystals with Eightfold Symmetry124
7.4.1 Fourier Transform Method 125
7.4.2 Complex Variable Function Method 127
7.5 Dislocations in Dodecagonal Quasicrystals 128
7.6 Interface Between Quasicrystal and Crystal 129
7.7 Dislocation Pile up， Dislocation Group and Plastic Zone133
7.8 Discussions and Conclusions134
References 134
8Application II-Solutions of Notch and Crack Problems of One-and Two-Dimensional Quasicrystals137
8.1 Crack Problem and Solution of One-Dimensional Quasicrystals 138
8.1.1 GriffithCrack138
8.1.2 Brittle Fracture Theory 143
8.2 Crack Problem in Finite-Sized One-Dimensional Quasicrystals 145
8.2.1 Cracked Quasicrystal Strip with Finite Height 145
8.2.2 Finite Strip with Two Cracks 149
8.3 Griffith Crack Problems in Point Groups5m and 10mm Quasicrystal Based on Displacement Potential Function Method150
8.4 Stress Potential Function Formulation and Complex Analysis Method for Solving Notch/Crack Problem of Quasicrystals of Point Groups5，5and10；10155
8.4.1 Complex Analysis Method 156
8.4.2 The Complex Representation of Stresses and Displacements 156
8.4.3 Elliptic Notch Problem158
8.4.4 Elastic Field Caused by a Griffith Crack 162
8.5 Solutions of Crack/Notch Problems of Two-Dimensional Octagonal Quasicrystals 163
8.6 Approximate Analytic Solutions of Notch/Crack of Two-Dimen
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本书介绍了固体准晶弹性和软物质准晶弹性-流体动力学理论好应用，为靠前外靠前本该领域的专著，为原始创新成就。内容包括晶体，经典弹性基础，固体准晶及其性质，固体准晶弹性的物理基础，一维准晶弹性和化简，二维准晶弹性与化简，应用之一——一维和二维准晶的位错和界面问题及解，应用之二——一维和二维准晶的缺口和裂纹问题及解，三维准晶弹性和应用，准晶弹性与缺陷动力学，准晶弹性和缺陷的复分析，准晶弹性的变分原理和数值解，准晶弹性解的若干数学原理，固体准晶的非线性，固体准晶的断裂理论，可能的7次和14次固体准晶，可能的9次和18次固体准晶，准晶流体动力学，软物质准晶的弹性-流体动力学及其应用。
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