Green's function for a two-dimensional exponentially graded elastic medium

Youn Sha Chan, L. J. Gray, T. Kaplan, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

Abstract

The free-space Green function for a two-dimensional exponentially graded elastic medium is derived. The shear modulus μ is assumed to be an exponential function of the Cartesian coordinates (x,y), i.e. μ ≡ μ(x,y) = μ0e2(β1x+β2y) where μ0, β1, and β2 are material constants, and the Poisson ratio is assumed constant. The Green function is shown to consist of a singular part, involving modified Bessel functions, and a non-singular term. The non-singular component is expressed in terms of one-dimensional Fourier-type integrals that can be computed by the fast Fourier transform.

Original languageEnglish (US)
Pages (from-to)1689-1706
Number of pages18
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume460
Issue number2046
DOIs
StatePublished - Jun 8 2004
Externally publishedYes

Keywords

  • Boundary-element methods
  • Functionally graded materials
  • Green's function

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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