Bending Deformation of Multilayered One-Dimensional Quasicrystal Nanoplates Based on the Modified Couple Stress Theory

Abstract

The modified couple stress theory has been applied in many nanomaterials except for nano-quasicrystals. In this paper, the modified couple stress theory is firstly adopted to analyze the static bending deformation of multilayered one-dimensional (1D) hexagonal quasicrystal (QC) nanoplates under surface loadings. The general solutions for the extended displacement and traction vectors in a simply supported and homogeneous QC nanoplate are derived by solving an eigenvalue problem reduced from the governing equations. Utilizing the propagator matrix method, the analytical solutions of multilayered 1D QC nanoplates are then obtained by assuming that the layer interfaces are continuous. Numerical examples for some kinds of nanoplates made up of QC and crystal ($$\hbox {BaTiO}_{3}$$) are provided to illustrate the effects of the material length parameter, the number of layers and the stacking sequence of nanoplates on the phonon and phason fields, which is helpful for the application of QCs to surface coating and solar energy selective absorber.