Journal ArticleDOI
General solutions of equilibrium equations for 1D hexagonal quasicrystals
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TLDR
Wang et al. as mentioned in this paper presented three general solutions for the coupled equilibrium equations in one-dimensional (1D) hexagonal quasicrystals (QCs) expressed in terms of two displacement functions, which satisfy a quasi-harmonic equation and a sixth-order partial differential equation, respectively, as well as the theory of differential operator matrix developed by Wang.About:
This article is published in Mechanics Research Communications.The article was published on 2009-04-01. It has received 13 citations till now. The article focuses on the topics: Partial differential equation & Differential operator.read more
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Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect
TL;DR: In this paper, a set of 3D general solutions to static problems of 1D hexagonal piezoelectric quasicrystals is obtained by introducing two displacement functions and utilizing the rigorous operator theory.
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Elastic field in an infinite medium of one-dimensional hexagonal quasicrystal with a planar crack
TL;DR: In this paper, the authors considered planar cracks embedded in an infinite space of one-dimensional hexagonal quasicrystals, and derived analytical solutions of crack will not only play an important role in understanding the phonon-phason coupling behavior in quasics, but also serve as benchmarks for future numerical studies and simplified analyses.
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General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics
TL;DR: In this article, the plane piezoelasticity theory of onedimensional (1D) quasicrystals with all point groups is investigated systematically, including monoclinic, orthorhombic, tetragonal and hexagonal QCs, and closed-form solutions of the phonon, phason, and electric fields near the crack tip are obtained.
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An exact closed-form solution for a multilayered one-dimensional orthorhombic quasicrystal plate
TL;DR: By extending the pseudo-Stroh formalism to multilayered one-dimensional orthorhombic quasicrystal plates, an exact closed-form solution for simply supported plates under surface loadings was derived in this article.
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Fundamental thermo-electro-elastic solutions for 1D hexagonal QC
TL;DR: In this paper, the fundamental solutions for an inite/half-in-nite space of 1D hexagonal quasicrystals (QCs) were derived with the help of rigorous operator theory and generalized Almansi's theorem.
References
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Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
TL;DR: In this article, a metallic solid with long-range orientational order, but with icosahedral point group symmetry, which is inconsistent with lattice translations, was observed and its diffraction spots are as sharp as those of crystals but cannot be indexed to any Bravais lattice.
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Generalized elasticity theory of quasicrystals.
TL;DR: The classical theory of elasticity describing three- and lower-dimensional systems is generalized to higher-dimensional spaces and the elastic properties of quasicrystals can be derived from this theory, appropriately.
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Direct evidence for plastic deformation of quasicrystals by means of a dislocation mechanism
TL;DR: It was found that upon deformation the dislocation density increases by about 2 orders of magnitude, providing the first direct evidence for quasicrystal deformation by a dislocation mechanism.
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Simple octagonal and dodecagonal quasicrystals.
TL;DR: Penrose tilings have become the canonical model for quasicrystal structure, primarily because of their simplicity in comparison with other decagonally symmetric quasiperiodic tilings of the plane.
Related Papers (5)
On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies
W. Q. Chen,Y.L. Ma,H. J. Ding +2 more