Semi-analytical solutions for functionally graded cubic quasicrystal laminates with mixed boundary conditions

Tremendous attention of researchers has been attracted by the unusual properties of quasicrystals. In this paper, the static solution of functionally gradient multilayered cubic quasicrystal plates on an elastic foundation with mixed boundary conditions is presented based on the linear elastic theory of quasicrystals. The quasicrystal material properties are assumed to have an exponent-law variation along the thickness direction. The elastic foundation is taken as the Winkler-Pasternak model, which is utilized to simulate the interaction between the plate and the elastic medium. The multilayered quasicrystal structures with two opposite edges simply supported and simply/clamped/free supported boundary conditions at other edges are considered. The semi-analytical method, which makes use of the state-space method in the z-direction, the one-dimensional differential quadrature method in the x-direction, and the series solution in the y-direction, is adopted to convert the system of governing partial differential equations into the ordinary one. From the propagator matrix, the static solution can be derived by imposing the boundary conditions on the top and bottom surfaces of the multilayered plates. Finally, typical numerical examples are presented to verify the effectiveness of this method and illustrate the influence of different boundary conditions, stacking sequence, foundation parameters, and functionally gradient exponential factors on the phonon and phason variables.