The Study Of Defect Problem In One-Dimensional Orthorhombic Quasicrystals By Generalized Complex Variable Function Method

QCs are both a new structure of solids and a kind of novel materials, which were discovered in recent two decades. Elasticity problem of QCs is complex compared with the conventional crystals. What result in it is that a theoretical description of the state of QCs requires a combined consideration both of phonon field and phason field. The motion of lattices is described by the phonon field in physical and quasiperiodic arrangement of atoms by the phason describes in the complementary orthogonal space. Owing to the structure of 1D hexagonal QCs is simple relatively, the elasticity problem of 1D hexagonal QCs is discussed widely. Compared with 1D hexagonal, the structure and the elasticity problem of 1D orthorhombic QCs are more complex. The elasticity problem of 1D orthorhombic QCs is studied by using generalized complex variable function method in this paper. The main contributions of this paper are as follows.First, by introducing the generalized conformal transformation and using the complex variable function method , the analytic solution of the plane elasticity problem of an elliptical hole in one-dimensional (1D) orthorhombic quasicrystals (QCs) was obtained.Complex representation of stress was also derived. In special case, the elliptical hole can be reduced to the Griffith crack and the stress intensity factors (SIFs) at the crack tip were obtained. Under conditions of more symmetry, the plane elasticity problem of an elliptical hole in 1D orthorhombic QCs can degenerate to that of 1D tetragonal QCs and the corresponding analytic solution of stress was given. Similarly, the elliptical hole can be also reduced to the Griffith crack and the SIFs at the crack tip also be obtained. The part of content is discussed in the second chapter.nSecond, using generalized complex variable function method,the problem variable which parallel for quasi-periodical direction in 1D orthorhombic QCs is investigated and its exact analytic solution are obtained,then,using these basic solutions,the problem of interaction of dislocation are solved. The part of content is discussed in the third chapter.