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Crystals 2016, 6(8), 94; doi:10.3390/cryst6080094

Elastodynamic Analysis of a Hollow Cylinder with Decagonal Quasicrystal Properties: Meshless Implementation of Local Integral Equations

1
Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, 91775-1111 Mashhad, Iran
2
Department of Mechanics, Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia
*
Author to whom correspondence should be addressed.
Academic Editor: Enrique Maciá Barber
Received: 29 June 2016 / Revised: 4 August 2016 / Accepted: 5 August 2016 / Published: 17 August 2016
(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)
View Full-Text   |   Download PDF [2150 KB, uploaded 17 August 2016]   |  

Abstract

A meshless approximation and local integral equation (LIE) formulation are proposed for elastodynamic analysis of a hollow cylinder made of quasicrystal materials with decagonal quasicrystal properties. The cylinder is assumed to be under shock loading. Therefore, the general transient elastodynamic problem is considered for coupled phonon and phason displacements and stresses. The equations of motion in the theory of compatible elastodynamics of wave type for phonons and wave-telegraph type for phasons are employed and can be easily modified to the elasto-hydro dynamic equations for quasicrystals (QCs). The angular dependence of the tensor of phonon–phason coupling coefficients handicaps utilization of polar coordinates, when the governing equations would be given by partial differential equations with variable coefficients. Despite the symmetry of the geometrical shape, the local weak formulation and meshless approximation are developed in the Cartesian coordinate system. The response of the cylinder in terms of both phonon and phason stress fields is obtained and studied in detail. View Full-Text
Keywords: quasicrystals; phonon and phason fields; elastodynamic analysis; hollow cylinder; local integral equations; meshless approximation quasicrystals; phonon and phason fields; elastodynamic analysis; hollow cylinder; local integral equations; meshless approximation
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Hosseini, S.M.; Sladek, J.; Sladek, V. Elastodynamic Analysis of a Hollow Cylinder with Decagonal Quasicrystal Properties: Meshless Implementation of Local Integral Equations. Crystals 2016, 6, 94.

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