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

作　　者：Xin FENG Liangliang ZHANG Yuxuan WANG Jinming ZHANG Han ZHANG Yang GAO 

机构地区：[1]College of Engineering,China Agricultural University,Beijing 100083,China [2]College of Science,China Agricultural University,Beijing 100083,China [3]China State Key Laboratory of Acoustics,Institute of Acoustics,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2021年第11期1599-1618,共20页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11972354,11972365,12102458);the China Agricultural University Education Foundation(No.1101-2412001)。

摘　　要：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(2 D)decagonal QC rectangular plate with mixed boundary conditions.Based on the elastic theory of FG 2 D 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.

关 键 词：two-dimensional(2D)quasicrystal(QC)laminate functionally graded material(FGM) mixed boundary condition static response differential quadrature technique 

分 类 号：TB34[一般工业技术—材料科学与工程] O753.3[理学—晶体学]