Abstract
As mentioned in Chap. 4, there exist three one-, two- and three-dimensional quasicrystals. Each can be further divided into subclasses with respect to symmetry consideration.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Wang R H,Yang W G, Hu C Z and Ding D H, 1997, Point and space groups and elastic behaviour of one-dimensional quasicrystals, J. Phys.:Condens. Matter, 9(11), 2411-2422.
Fan T Y, 2000, Mathematical theory of elasticity and defects of quasicrystals, Advances in Mechanics (in Chinese), 30(2),161-174.
Fan T Y and Mai Y W, 2004, Elasticity theory, fracture mechanics and some relevant thermal properties of quasicrystalline materials, Appl. Mech. Rev., 57(5), 325-344.
Liu G T, Fan T Y and Guo R P, 2004,Governing equations and general solutions of plane elasticity of one-dimensional quasicrystals, Int. J. Solid and Structures, 41(14), 3949-3959.
Liu G T, 2004,The complex variable function method of the elastic theory of quasicrystals and defects and auxiliary equation method for solving some nonlinear evolution equations,, Dissertation (in Chinese), Beijing Institute of Technology.
Peng Y Z and Fan T Y, 2000, Elastic theory of 1-D quasiperiodic stacking 2-D crystals, J. Phys.:Condens. Matter, 12(45), 9381-9387.
Peng Y Z, 2001, Study on elastic three-dimensional problems of cracks for quasicrystals, Dissertation (in Chinese), Beijing Institute of Technology.
Fan T Y, Xie L Y, Fan L and Wang Q Z, 2011, Study on interface of quasicrystal-crystal, Chin Phys B, 20(7), 076102.
Chen W Q, Ma Y L and Ding H J, 2004, On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies, Mech. Res. Commun., 31(5), 633-641.
Wang X, 2006, The general solution of one-dimensional hexagonal quasicrystal, Appl. Math. Mech., 33(4), 576-580.
Gao Y, Zhao Y T and Zhao B S, 2007, Boundary value problems of holomorphic vector functions in one-dimensional hexagonal quasicrystals, Physica B, Vol.394(1), 56–61.
Li X Y, 2013, Fundamental solutions of a penny shaped embedded crack and half-infinite plane crack in infinite space of one-dimensional hexagonal quasicrystals under thermal loading, Proc Roy Soc A, 469, 20130023.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Science Press and Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Fan, TY. (2016). Elasticity Theory of One-Dimensional Quasicrystals and Simplification. In: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. Springer Series in Materials Science, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-10-1984-5_5
Download citation
DOI: https://doi.org/10.1007/978-981-10-1984-5_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-1982-1
Online ISBN: 978-981-10-1984-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)