Research On Cracks In One Dimensional Hexagonal Quasicrystal Under Action Of SH Wave

As a new material,quasicrystal has been widely used in modern industrial production owning to its unique physical structure and superior mechanical properties.Due to its unique properties,such as non-stickiness,heat resistance,wear resistance,it can be covered on the surface of other materials in the form of coating or film,which is valued by automobile manufacturing and aviation industry.Despite the superior characteristics of quasicrystal materials,the effect of dynamic load will cause cracks in the material and cause material damage.Therefore,the defect problem of quasicrystal materials attract considerable attention in the literature.This paper studies the problem of cracks in one-dimensional hexagonal quasicrystals materials and the scattering of SH waves by cracks.Chapter 1 of the dissertation introduce the research background,structural classification,linear elastic theory and research status.Chapter 2 discusses the basic theory of one-dimensional hexagonal quasicrystal materials and the dual integral equation-Copson method.The anti-plane problem of cracks in a regular hexagonal hole in a one-dimensional hexagonal piezoelectric quasicrystals is discussed in Chapter 3.Based on the complex variable function method,the analytical solutions of the stress and displacement components at the crack tip are obtained under the electrically impermeable boundary conditions by constructing the conformal mapping function.Chapter 4 investigates the scattering of SH waves by straight cracks in the one-dimensional hexagonal quasicrystal.Using integral transformation technique,the problem is transformed into dual integral equations,which are solved by Copson method.The effects of crack length,incident wave direction,material width and wave number a?/csh on the dimensionless stress intensity factor at the crack tip are analyzed.Chapter 5 considers the piezoelectric effect of one-dimensional hexagonal quasicrystal.The integral transformation technique is used to study the scattering of SH waves by a crack in a one-dimensional hexagonal piezoelectric quasicrystal.The problem is transformed into a dual integral equation by Fourier transform,and the analytical solution of the stress component and displacement at the crack tip is obtained by Copson method.The effects of crack length,incident wave direction,material height and wave number a?/csh on the dimensionless stress intensity factor of crack tip are analyzed by numerical examples.