Green's function expansion for exponentially graded elasticity

✍ Scribed by Omar M. Sallah; L. J. Gray; M. A. Amer; M. S. Matbuly

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 156 KB
• Volume: 82
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.2786

✦ Synopsis

Abstract

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 © 2009 John Wiley & Sons, Ltd.