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

Abstract

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.

Electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal circular plates with simply supported or clamped boundary conditions

“…Focusing on the QC cylinder, Guo and Pan [14] used the Laurent expansion technique to investigate the physical characteristics of 1D piezoelectric QC composite cylinder models. Hosseiniu et al [15] analyzed the elastodynamic responses of a hollow cylinder with decagonal QC properties via meshless approximation. In addition, the shear fracture [16], micromechanics [17], and the static response [18] in QC cylindrical composites have been analyzed.…”

Quo Vadis Quasicrystals?

“…By adopting a systematic tutorial approach, a variety of fundamental problems such as screw dislocation motion and crack propagation are described and properly illustrated with suitable application examples including decagonal, dodecagonal, and icosahedral QCs. Along the same vein, Mahmoud Hosseini, Jan Sladek, and Vladimir Sladek discuss the dynamical response of a cylinder made of materials with decagonal QC properties by considering both phonon and phason stress fields [46]. In this contribution, special attention is paid to the coupling between both fields in terms of waves propagating with a finite speed, making use of a methodology which can be easily extended to QCs exhibiting other structural symmetries.…”