Green's function expansion for exponentially graded elasticity |
| |
| Authors: | Omar M Sallah L J Gray M A Amer M S Matbuly |
| |
| Affiliation: | 1. Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig, Egypt;2. Computer Science and Mathematics Division, Oak Ridge National Laboratory Oak Ridge, TN 37831‐6367, U.S.A.;3. The contributions of Omar M. Sallah and L. J. Gray to this article were prepared as part of their official duties as United States Federal Government employees.;4. Department of Mathematics, Faculty of Engineering, German University, Cairo, Egypt |
| |
| 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. |
| |
| Keywords: | functionally graded materials Green's function boundary integral equation Galerkin boundary element method |
|
|
