An exact solution for a functionally graded multilayered one-dimensional orthorhombic quasicrystal plate

Abstract

This paper investigates the problem of a functionally graded multilayered one-dimensional orthorhombic quasicrystal plate with simply supported edge conditions. Assuming that the functionally graded material properties vary exponentially along the thickness direction, a solution for a functionally graded plate subjected to top surface loading is obtained by using the pseudo-Stroh formalism. The propagator matrix method is utilized to get the solution for the corresponding multilayered case. The exact solution is applied to a multilayered plate made of quasicrystals and crystals. The influences of the exponential factor, load form, and stacking sequence on physical quantities are studied in numerical examples. The exact solution can be used to design a functionally graded multilayered plate composed of one-dimensional quasicrystals and crystals. The numerical results can also serve as a basis for other numerical methods, such as finite element and boundary element methods.