CLC number: TH113
On-line Access: 2019-01-29
Received: 2018-08-14
Revision Accepted: 2018-11-16
Crosschecked: 2018-12-26
Cited: 0
Clicked: 5594
Yun-zhi Huang, Yang Li, Lian-zhi Yang, Yang Gao. Static response of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal plates using the state vector approach[J]. Journal of Zhejiang University Science A, 2019, 20(2): 133-147.
@article{title="Static response of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal plates using the state vector approach",
author="Yun-zhi Huang, Yang Li, Lian-zhi Yang, Yang Gao",
journal="Journal of Zhejiang University Science A",
volume="20",
number="2",
pages="133-147",
year="2019",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1800472"
}
%0 Journal Article
%T Static response of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal plates using the state vector approach
%A Yun-zhi Huang
%A Yang Li
%A Lian-zhi Yang
%A Yang Gao
%J Journal of Zhejiang University SCIENCE A
%V 20
%N 2
%P 133-147
%@ 1673-565X
%D 2019
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1800472
TY - JOUR
T1 - Static response of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal plates using the state vector approach
A1 - Yun-zhi Huang
A1 - Yang Li
A1 - Lian-zhi Yang
A1 - Yang Gao
J0 - Journal of Zhejiang University Science A
VL - 20
IS - 2
SP - 133
EP - 147
%@ 1673-565X
Y1 - 2019
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1800472
Abstract: The effect of the non-homogeneity of material properties has been considered the important variation mechanism in the static responses of quasicrystal structures, but the existing theoretical model for it is unable to simulate the material change format beyond the exponential function. In this paper, we create a new model of functionally graded multilayered 1D piezoelectric quasicrystal plates using the state vector approach, in which varying functionally graded electro-elastic properties can be extended from exponential to linear and higher order in the thickness direction. Based on the state equations, an analytical solution for a single plate has been derived, and the result for the corresponding multilayered case is obtained utilizing the propagator matrix method. The present study shows, in particular, that coefficient orders of two varying functions (the power function and the exponential function) of the material gradient provide the ability to tailor the mechanical behaviors in the system’s phonon, phason, and electric fields. Moreover, the insensitive points of phonon stress and electric potential under functionally graded effects in the quasicrystal layer are observed. In addition, the influences of stacking sequences and discontinuity of horizontal stress are explored in the simulation by the new model. The results are very useful for the design and understanding of the characterization of functionally graded piezoelectric quasicrystal materials in their applications to multilayered systems.
The authors applied the state vector method to study static response of FG multilayered piezoelectric plates. Although the state vector method is not new, however, there is original engineering interests in the problem presented in this paper, particularly quasicrystal material properties and multilayered effects.
[1]Alibeigloo A, 2018. Thermo elasticity solution of functionally graded, solid, circular, and annular plates integrated with piezoelectric layers using the differential quadrature method. Mechanics of Advanced Materials and Structures, 25(9):766-784.
[2]Altay G, Dökmeci MC, 2012. On the fundamental equations of piezoelasticity of quasicrystal media. International Journal of Solids and Structures, 49(23-24):3255-3262.
[3]Chan KC, Qu NS, Zhu D, 2002. Fabrication of graded nickel-quasicrystal composite by electrodeposition. Transactions of the IMF, 80(6):210-213.
[4]Chen WQ, Lee KY, 2003. Alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates. International Journal of Solids and Structures, 40(21):5689-5705.
[5]Ding DH, Yang WG, Hu CZ, et al., 1993. Generalized elasticity theory of quasicrystals. Physical Review B, 48(10):7003-7010.
[6]Dubois JM, 2005. Useful Quasicrystals. World Scientific, Singapore, Singapore, p.45-56.
[7]Fan TY, 2010. Mathematical Theory of Elasticity of Quasicrystals and Its Applications. Science Press, Beijing, China, p.118-120 (in Chinese).
[8]Fan TY, 2013. Mathematical theory and methods of mechanics of quasicrystalline materials. Engineering, 5(4):407-448.
[9]Fujiwara T, de Laissardière GT, Yamamoto S, 1994. Electronic structure and electron transport in quasicrystals. Materials Science Forum, 150-151:387-394.
[10]Gao Y, Zhao BS, 2009. General solutions of three-dimensional problems for two-dimensional quasicrystals. Applied Mathematical Modelling, 33(8):3382-3391.
[11]Guo JH, Chen JY, Pan EN, 2016. Size-dependent behavior of functionally graded anisotropic composite plates. International Journal of Engineering Science, 106:110-124.
[12]Hu CZ, Wang RH, Ding DH, et al., 1997. Piezoelectric effects in quasicrystals. Physical Review B, 56(5):2463-2468.
[13]Hu WF, Liu YH, 2015. A new state space solution for rectangular thick laminates with clamped edges. Chinese Journal of Theoretical and Applied Mechanics, 47(5):762-771 (in Chinese).
[14]Levinson M, Cooke DW, 1983. Thick rectangular plates—I: the generalized Navier solution. International Journal of Mechanical Sciences, 25(3):199-205.
[15]Li LH, Liu GT, 2012. Stroh formalism for icosahedral quasicrystal and its application. Physics Letters A, 376(8-9):987-990.
[16]Li XF, Xie LY, Fan TY, 2013. Elasticity and dislocations in quasicrystals with 18-fold symmetry. Physics Letters A, 377(39):2810-2814.
[17]Li XY, Ding HJ, Chen WQ, 2006. Pure bending of simply supported circular plate of transversely isotropic functionally graded material. Journal of Zhejiang University SCIENCE A, 7(8):1324-1328.
[18]Li XY, Li PD, Wu TH, et al., 2014. Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Physics Letters A, 378(10):826-834.
[19]Li Y, Yang LZ, Gao Y, 2017. An exact solution for a functionally graded multilayered one-dimensional orthorhombic quasicrystal plate. Acta Mechanica, in press.
[20]Louzguine-Luzgin DV, Inoue A, 2008. Formation and properties of quasicrystals. Annual Review of Materials Research, 38:403-423.
[21]Mikaeeli S, Behjat B, 2016. Three-dimensional analysis of thick functionally graded piezoelectric plate using EFG method. Composite Structures, 154:591-599.
[22]Móricz F, 1989. On Λ2-strong convergence of numerical sequences and Fourier series. Acta Mathematica Hungarica, 54(3-4):319-327.
[23]Pan E, Han F, 2005. Exact solution for functionally graded and layered magneto-electro-elastic plates. International Journal of Engineering Science, 43(3-4):321-339.
[24]Qing GH, Wang L, Zhang XH, 2017. Analytical solution of composite laminates with two opposite sides clamped and other sides free boundary. Machinery Design & Manufacture, (2):161-164 (in Chinese).
[25]Shechtman D, Blech I, Gratias D, et al., 1984. Metallic phase with long-range orientational order and no translational symmetry. Physical Review Letters, 53(20):1951-1953.
[26]Sheng HY, Wang H, Ye JQ, 2007. State space solution for thick laminated piezoelectric plates with clamped and electric open-circuited boundary conditions. International Journal of Mechanical Sciences, 49(7):806-818.
[27]Sladek J, Sladek V, Pan E, 2013. Bending analyses of 1D orthorhombic quasicrystal plates. International Journal of Solids and Structures, 50(24):3975-3983.
[28]Sun TY, Guo JH, Zhang XY, 2018. Static deformation of a multilayered one-dimensional hexagonal quasicrystal plate with piezoelectric effect. Applied Mathematics and Mechanics (English Edition), 39(3):335-352.
[29]Suresh S, Mortensen A, 1998. Fundamentals of Functionally Graded Materials: Processing and Thermomechanical Behavior of Graded Metals and Metal-ceramic Composites. IOM Communications, London, UK, p.156-163.
[30]Timoshenko SP, Goodier JN, 1970. Theory of Elasticity. McGraw-Hill, New York, USA, p.78-82.
[31]Wang JG, Chen LF, Fang SS, 2003. State vector approach to analysis of multilayered magneto-electro-elastic plates. International Journal of Solids and Structures, 40(7):1669-1680.
[32]Wang X, Zhang JQ, Guo XM, 2005. Two kinds of contact problems in decagonal quasicrystalline materials of point group 10 mm. Acta Mechanica Sinica, 37(2):169-174 (in Chinese).
[33]Xu WS, Wu D, Gao Y, 2017. Fundamental elastic field in an infinite plane of two-dimensional piezoelectric quasicrystal subjected to multi-physics loads. Applied Mathematical Modelling, 52:186-196.
[34]Yang B, Ding HJ, Chen WQ, 2012. Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported. Applied Mathematical Modelling, 36(1):488-503.
[35]Yang LZ, Gao Y, Pan EN, et al., 2015. An exact closed-form solution for a multilayered one-dimensional orthorhombic quasicrystal plate. Acta Mechanica, 226(11):3611-3621.
[36]Yaslan HÇ, 2013. Equations of anisotropic elastodynamics in 3D quasicrystals as a symmetric hyperbolic system: deriving the time-dependent fundamental solutions. Applied Mathematical Modelling, 37(18-19):8409-8418.
[37]Ying J, Lü CF, Lim CW, 2009. 3D thermoelasticity solutions for functionally graded thick plates. Journal of Zhejiang University SCIENCE A, 10(3):327-336.
[38]Zhao MH, Dang HY, Fan CY, et al., 2017. Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 1: theoretical solution. Engineering Fracture Mechanics, 179:59-78.
[39]Zhao MH, Li Y, Fan CY, et al., 2018. Analysis of arbitrarily shaped planar cracks in two-dimensional hexagonal quasicrystals with thermal effects. Part I: theoretical solutions. Applied Mathematical Modelling, 57:583-602.
[40]Zhou YB, Li XF, 2018. Two collinear mode-III cracks in one-dimensional hexagonal piezoelectric quasicrystal strip. Engineering Fracture Mechanics, 189:133-147.
Open peer comments: Debate/Discuss/Question/Opinion
<1>