Analysis of One-Dimensional Hexagonal Quasicrystal Elastic Layer Under Surface Loads

This study aims to develop an elastic solution for a two-dimensional, surface-loaded layer made of a one-dimensional (1D) hexagonal quasicrystal (QC) resting on either a rigid or an elastic substrate. The governing equations, in terms of phonon and phason displacements, for both the layer and the substrate are derived from the linear elasticity theory for a 1D-hexagonal QC material and then solved by the method of Fourier transform and the direct stiffness technique. An efficient and accurate numerical quadrature is then implemented to evaluate all involved integrals resulting from Fourier transform inversion. After being verified with benchmark cases, the derived solutions are utilized to investigate the influence of the coating thickness and type of substrate on the mechanical behavior of the medium, including the coated object and the 1D-hexagonal QC coating layer.