Advanced methods for calculating Green's function and its derivatives for three-dimensional anisotropic elastic solids

Longtao Xie, Chyanbin Hwu, Chuanzeng Zhang

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Three advanced methods are presented for constructing and evaluating Green's function and its derivatives for three-dimensional anisotropic elastic solids. The first one is obtained from a line integral followed by Cauchy's residue theorem, and expressed in terms of Stroh's eigenvalues. The second one is obtained by using the explicit solutions of Stroh's eigenvector matrix available in two-dimensional anisotropic elasticity. Whereas the last one is derived from the solution obtained from 2D Radon transform, and expressed in terms of the fundamental elasticity matrix in vertical planes, which makes the derivatives simpler than those obtained from the line integral operated on an oblique plane. The novelty of the first two methods lies in the construction and computation of the first and second derivatives of the Green's function, though the Green's function itself in the first two methods is rather known. In contrast, the third method is quite new for both the Green's function itself and its first and second derivatives. The advantages and disadvantages of these three solution methods are investigated and discussed through their derivations and numerical implementations for isotropic, transversely isotropic, and fully anisotropic elastic solids. Good agreement between the results calculated by these three methods is shown in all numerical examples. Among these three methods, the last one is proved to be the most efficient one.

Original languageEnglish
Pages (from-to)261-273
Number of pages13
JournalInternational Journal of Solids and Structures
Volume80
DOIs
Publication statusPublished - 2016 Feb 1

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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