Proceedings of the Royal Society of London. A: Mathematical, Physical and Engineering Sciences. Vol. 460, No. 2046, pp.1689-1706, 2004
Y.S. Chan, L. J. Gray, T. Kaplan
Computer Science & Mathematics Division, Oak Ridge
National Laboratory, Oak Ridge, TN 37831-6367.
G.H. Paulino,
Department of Civil and Environmental Engineering, University of Illinois
at Urbana-Champaign, Newmark
Laboratory, 205 North Mathews Avenue, IL
61801-2352
Abstract
The free space Green's functions
for a two-dimensional exponentially graded elastic medium is derived. The shear
modulus m is assumed to be an exponential function of the Cartesian coordinates
(x,y), i.e. m=m(x,y)=m0e2(b1x+b2y),
where m0, b1,
and b2 are material
constants, and the Poisson's ratio is assumed constant. The Green's 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.
Key words: functionally graded materials, Green's
functions, boundary-element methods