Research On Plane Elasticity Of Cubic Quasicrystals

Cubic quasicrystals are an important kind of three-dimensional quasicrystals,which have the symmetry of cubic crystals,but the atomic arrangement is quasi-periodic.Describing the elasticity of cubic quasicrystals requires the interaction of phonon field and phase field,and cubic quasicrystals have nine independent elastic constants,which increase the complexity of elastic research of cubic quasicrystals.However,its special structure and performance still make the study of its elasticity of great theoretical and practical significance.This thesis mainly studies the plane elasticity of cubic quasicrystals.The main works are as follows:(1)An elastic analysis of a solid rotating disk composed of cubic quasicrystal is made.Firstly,basic equations for rotating cubic quasicrystal disk in a polar coordinate system are given.Then by solving equilibrium equations,the stress distribution and displacements can be derived with use of basic equations and the boundary conditions.An exact analytic solution is determined finally and explicit expressions for the displacement and stress fields are given.Numerical examples show that the existence of phonon-phase coupling field will not change the stresses distribution of phonon field,but will affect the displacement components of phonon field.(2)An analytical method is studied to calculate the thermal stress of cubic quasicrystal disk with thermal effect.The semi-inversion method is extended to seek explicit expressions for the thermal stresses,strains,and displacements in the phonon and phason fields.It is found that the phonon and phason stresses are axisymmetrically distributed,whereas the strains and displacements are not axisymmetric,and depend on the angle.Numerical examples are given to illustrate the influence of phonon-phase coupling field on stresses and strains.(3)The Flamant problem of cubic quasicrystal half-plane is solved,and the semi-infinite plane is considered to be subjected to surface concentrated force system.Using the generalized Almansi’s theorem and the Fourier transform technique,we obtain fundamental solutions.Explicit expressions for the phonon and phason stresses and strains are derived.Comparing cubic quasicrystals with cubic crystals in numerical examples,it is found that the deformation of cubic quasicrystals is smaller.26 figures,1 table,110 references in total...