New Method for Solving Elasticity Problems of Some Planar Quasicrystals and Solutions

A new method for solving elasticity problems of some planar quasicrystals is presented. The set of partial differential equations for the phonon and phason displacement components is reduced to a single higher-order equation by introducing a displacement function. A general solution formulation is suggested. As an example, the elastic field caused by a dislocation in planar quasicrystals of point groups 5 m , 10, and 10mm is calculated.