COMPLETE PLANE STRAIN PROBLEM OF A ONE DIMENSIONAL HEXAGONAL QUASICRYSTALS WITH A DOUBLY-PERIODIC SET OF CRACKS

The first fundamental complete plane strain (CPS) problem for an infinite onedimensional hexagonal quasi crystals body containing a doubly-periodic array of cracks in periodical and aperiodical plane is considered. Employing the superposition principle of force, the complete plane strain state, which is a special three-dimensional elastic system, is resolved into two linearly independent two-dimensional (plane) elastic systems, one is the generalized plane strain state, and another is the longitudinal displacement state. Using a technique that based on the complex potential function of Kolosov and Muskhelishvili, solving this problem are transferred into seeking analytic functions which fit certain boundary value problems. Furthermore, the general representation for the solution is constructed, under some general restrictions the boundary value problem is reduced to a normal type singular integral equation with a Weierstrass zeta kernel along the boundary of cracks, and the unique solvability of which is proved.