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

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

doi:10.1098/rspa.2003.1220

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 journal › Article › peer-review

79 Scopus citations

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) = μ₀e^2(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 language	English (US)
Pages (from-to)	1689-1706
Number of pages	18
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	460
Issue number	2046
DOIs	https://doi.org/10.1098/rspa.2003.1220
State	Published - Jun 8 2004
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
General Engineering
General Physics and Astronomy

Keywords

Boundary-element methods
Functionally graded materials
Green's function

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10.1098/rspa.2003.1220

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title = "Green's function for a two-dimensional exponentially graded elastic medium",

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.",

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language = "English (US)",

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TY - JOUR

T1 - Green's function for a two-dimensional exponentially graded elastic medium

AU - Chan, Youn Sha

AU - Gray, L. J.

AU - Kaplan, T.

AU - Paulino, Glaucio H.

PY - 2004/6/8

Y1 - 2004/6/8

N2 - 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.

AB - 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.

KW - Boundary-element methods

KW - Functionally graded materials

KW - Green's function

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SP - 1689

EP - 1706

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2046

ER -

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

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