准晶数学的弹性理论及应用

PrefaceChapter1 Crystals1.1 Periodicity of crystal structure, crystal cell1.2 Three-dimensional lattice types1.3 Symmetry and point groups1.4 Reciprocal lattice1.5 Appendix of Chapter1: Some basic conceptsReferencesChapter 2 Framework of the classical theory of elasticity2.1 Review on some basic concepts2.2 Basic assumptions of theory of elasticity2.3 Displacement and deformation2.4 Stress analysis and equations of motion2.5 Generalized Hooke's law2.6 Elastodynamics, wave motion2.7 SummaryReferencesChapter 3 Quasicrystal and its properties3.1 Discovery of quasicrystal3.2 Structure and symmetry of quasicrystals3.3 A brief introduction on physical properties of quasicrystals3.4 One-, two- and three-dimensional quasicrystals3.5 Two-dimensional quasicrystals and planar quasicrystalsReferencesChapter 4 The physical basis of elasticity of quasicrystals4.1 Physical basis of elasticity of quasicrystals4.2 Deformation tensors4.3 Stress tensors and the equations of motion4.4 Free energy and elastic constants4.5 Generalized Hooke's law4.6 Boundary conditions and initial conditions4.7 A brief introduction on relevant material constants of quasicrystals4.8 Summary and mathematical solvability of boundary value or initial- boundary value problem4.9 Appendix of Chapter 4: Description on physical basis of elasticity of quasicrystals based on the Landau density wave theoryReferencesChapter 5 Elasticity theory of one-dimensional quasicrystals and simplification5.1 Elasticity of hexagonal quasicrystals5.2 Decomposition of the problem into plane and anti-plane problems5.3 Elasticity of monoclinic quasicrystals5.4 Elasticity of orthorhombic quasicrystals5.5 Tetragonal quasicrystals5.6 The space elasticity of hexagonal quasicrystals5.7 Other results of elasticity of one-dimensional quasicrystalsReferencesChapter 6 Elasticity of two-dimensional quasicrystals and simplification6.1 Basic equations of plane elasticity of two-dimensional quasicrystals: point groups 5m and10mm in five- and ten-fold symmetries6.2 Simplification of the basic equation set: displacement potential function method6.3 Simplification of the basic equations set: stress potential function method6.4 Plane elasticity of point group 5, pentagonal and point group10, decagonal quasicrystals6.5 Plane elasticity of point group12mm of dodecagonal quasicrystals6.6 Plane elasticity of point group 8mm of octagonal quasicrystals, displacement potential6.7 Stress potential of point group 5, pentagonal and point group10, decagonal quasicrystals6.8 Stress potential of point group 8mm octagonal quasicrystals6.9 Engineering and mathematical elasticity of quasicrystalsReferencesChapter 7 Application I: Some dislocation and interface problems and solutions in one- and two,dimensional quasicrystals7.1 Dislocations in one-dimensional hexagonal quasicrystals7.2 Dislocations in quasicrystals with point groups 5m and10mm symmetries7.3 Dislocations in quasicrystals with point groups 5, five-fold and10, ten-fold symmetries7.4 Dislocations in quasicrystals with eight-fold symmetry7.5 Dislocations in dodecagonal quasicrystals7.6 Interface between quasicrystal and crystal7.7 Conclusion and discussionReferencesChapter 8 Application II: Solutions of notch and crack problems of one-and two-dimensional quasicrystals8.1 Crack problem and solution of one-dimensional quasicrystals8.2 Crack problem in finite-sized one-dimensional quasicrystals8.3 Griffith crack problems in point groups 5m and10mm quasicrystals based on displacement potential function method8.4 Stress potential function formulation and complex variable function method for solving notch and crack problems of quasicrystals of point groups 5, and10, 8.5 Solutions of crack/notch problems of two-dimensional octagonal quasicrystals8.6 Other solutions of crack problems in one-and two-dimensional quasicrystals8.7 Appendix of Chapter 8: Derivation of solution of Section 8.1ReferencesChapter 9 Theory of elasticity of three-dimensional quasicrystals and its a