Mathematical Theory of Elasticity of Quasicrystals and Its Applications

1. Crystals
Tianyou Fan

2. Framework of the classical theory of elasticity
Tianyou Fan

3. Quasicrystal and its properties
Tianyou Fan

4. The physical basis of elasticity of quasicrystals
Tianyou Fan

5. Elasticity theory of one-dimensional quasicrystals and simplification
Tianyou Fan

6. Elasticity of two-dimensional quasicrystals and simplification
Tianyou Fan

7. Application I—Some dislocation and interface problems and solutions in one- and two-dimensional quasicrystals
Tianyou Fan

8. Application II: Solutions of notch and crack problems of one-and two-dimensional quasicrystals
Tianyou Fan

9. Theory of elasticity of three-dimensional quasicrystals and its applications
Tianyou Fan

10. Dynamics of elasticity and defects of quasicrystals
Tianyou Fan

11. Complex variable function method for elasticity of quasicrystals
Tianyou Fan

12. Variational principle of elasticity of quasicrystals, numerical analysis and applications
Tianyou Fan

13. Some mathematical principles on solutions of elasticity of quasicrystals
Tianyou Fan

14. Nonlinear behaviour of quasicrystals
Tianyou Fan

15. Fracture theory of quasicrystals
Tianyou Fan

16. Remarkable Conclusion
Tianyou Fan

Keywords: Engineering, Continuum Mechanics and Mechanics of Materials, Condensed Matter Physics, Applications of Mathematics