| Quasicrystal elasticity theory is a research hotspot in modern engineer. Because of the intrinsic brittleness, the fracture problems of the quasicrystalline materials are studied systemalically. The anti-plane problems of one-dimensional hexagonal quasicrystals with cracks are investigated by using the boundary collocation method.There are five chapters in this thesis. In the first chapter, the boundary collocation method is an effective means to solve the problem of one-dimensional hexagonal quasicrystals with cracks by using an overview of numerical methods, the briefly introduction for the function of quasicrystalline materials and the main contents of this thesis are introduced. In the second chapter, the formulas of stress intensity factor is obtained under some fundamental assumptions on the basis of one-dimensional hexagonal quasicrystal elasticity theory. The anti-plane problems of one-dimensional hexagonal quasicrystals with two symmetrical and single cracks are investigated in the third chapter. In the fourth chapter, the anti-plane problems of one-dimensional hexagonal quasicrystals with an interface centerl crack are investigated under two-way loading and the one-way loading cases separately. In the fifth chapter, the main contents of this thesis are summarized and analyzed. The future work is outlooked by analyzing the inadequacies of the dissertation.The stress functions can be expressed by selecting the appropriate displacement function under the boundary conditions on the basis of the properties of analytic function. Then, the related stress intensity factor in the phonon and quantum fields can be obtained from the stress functions. It can be shown that only the plate boundary conditions are needed to be satisfied approximatively when used the boundary collocation method on the half rectangle by considering symmetry. The influence of the stress intensity factor is discussed by using the numerical example. |
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