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Evaluation of Green's function derivatives for exponentially graded elasticity
Faculty
Science
Year:
2010
Type of Publication:
Article
Pages:
693-708
Authors:
Sallah, Omar M, Gray, L. J, Fata, S. Nintcheu
DOI:
10.1002/nme.2851
Journal:
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING JOHN WILEY \& SONS LTD
Volume:
83
Research Area:
Engineering; Mathematics
ISSN
ISI:000280695400002
Keywords :
functionally graded materials, Green's function, boundary integral equation
Abstract:
Effective formulas for computing Green's function of an exponentially graded three-dimensional material have been derived in previous work. The expansion approach for evaluating Green's function has been extended to develop corresponding algorithms for its first- and second-order derivatives. The resulting formulas are again obtained as a relatively simple analytic term plus a single double integral, the integrand involving only elementary functions. A primary benefit of the expansion procedure is the ability to compute the second-order derivatives needed for fracture analysis. Moreover, as all singular terms in this hypersingular kernel are contained in the analytic expression, these expressions are readily implemented in a boundary integral equation calculation. The computational formulas for the first derivative are tested by comparing with results of finite difference approximations involving Green's function. In turn, the second derivatives are then validated by comparing with finite difference quotients using the first derivatives. Published in 2010 by John Wiley \& Sons, Ltd.
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