Green's function expansion for exponentially graded elasticity

New computational forms are derived for Green's function of an exponentially graded elastic material in three dimensions. By suitably expanding a term in the defining inverse Fourier integral, the displacement tensor can be written as a relatively simple analytic term, plus a single double integral that must be evaluated numerically. The integration is over a fixed finite domain, the integrand involves only elementary functions, and only low-order Gauss quadrature is required for an accurate answer. Moreover, it is expected that this approach will allow a far simpler procedure for obtaining the first and second-order derivatives needed in a boundary integral analysis. The new Green's function expressions have been tested by comparing with results from an earlier algorithm. Copyright (C) 2009 John Wiley \& Sons, Ltd.