Static response of functionally graded multilayered two-dimensional quasicrystal plates with mixed boundary conditions

The unusual properties of quasicrystals (QCs) have attracted tremendous attention from researchers. In this paper, a semi-analytical solution is presented for the static response of a functionally graded (FG) multilayered two-dimensional (2D) decagonal QC rectangular plate with mixed boundary conditions. Based on the elastic theory of FG 2D QCs, the state-space method is used to derive the state equations composed of partial differential along the thickness direction. Besides, the Fourier series expansion and the differential quadrature technique are utilized to simulate the simply supported boundary conditions and the mixed boundary conditions, respectively. Then, the propagator matrix which connects the field variables at the upper interface to those at the lower interface of any homogeneous layer can be derived based on the state equations. Combined with the interface continuity condition, the static response can be obtained by imposing the sinusoidal load on the top surfaces of laminates. Finally, the numerical examples are presented to verify the effectiveness of this method, and the results are very useful for the design and understanding of the characterization of FG QC materials in their applications to multilayered systems.