Three dimensional elastodynamics of 2D quasicrystals: The derivation of the time-dependent fundamental solution


Yakhno V. G., Yaslan H. C.

APPLIED MATHEMATICAL MODELLING, vol.35, no.6, pp.3092-3110, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 6
  • Publication Date: 2011
  • Doi Number: 10.1016/j.apm.2010.12.019
  • Journal Name: APPLIED MATHEMATICAL MODELLING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3092-3110
  • Keywords: Anisotropic dynamic elasticity (3D), Two-dimensional quasicrystals, Fundamental solution, Simulation, PLANE ELASTICITY PROBLEMS, FINAL GOVERNING EQUATION, GENERAL-SOLUTIONS, DIFFUSE-SCATTERING, DISLOCATIONS, POINT
  • Dokuz Eylül University Affiliated: Yes

Abstract

The time-dependent differential equations of elasticity for 20 quasicrystals with general structure of anisotropy (dodecagonal, octagonal, decagonal, pentagonal, hexagonal, triclinic) are considered in the paper. These equations are written in the form of a vector partial differential equation of the second order with symmetric matrix coefficients. The fundamental solution (matrix) is defined for this vector partial differential equation. A new method of the numerical computation of values of the fundamental solution is suggested. This method consists of the following: the Fourier transform with respect to space variables is applied to vector equation for the fundamental solution. The obtained vector ordinary differential equation has matrix coefficients depending on Fourier parameters. Using the matrix computations a solution of the vector ordinary differential equation is numerically computed. Finally, applying the inverse Fourier transform numerically we find the values of the fundamental solution. Computational examples confirm the robustness of the suggested method for 2D quasicrystals with arbitrary type of anisotropy. (C) 2010 Elsevier Inc. All rights reserved.