ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
An exact expression is derived for the general finite-part integral over an inclined ellipticaldomain Ω. r denotes the distance of a point in Ω to the singular point \documentclass{article}\pagestyle{empty}\begin{document}$\left({x,y} \right).f = x_{^0 }^i y_0^j \sqrt {Z\left({x_{0,} y_0 }\right)}$\end{document} is a general function of the Cartesian co-ordinates x0,y0. The boundary of the region Ω represents the equation Z(x0, y0)=O. These integrals appear during the numerical solution of plane crack problems in three-dimensional elasticity where they are the dominant part of a hypersingular integral equation. The availability of exact expressions for the integrals with arbitrary integers i and j will increase the accuracy of the numerical results and, simultaneously, lead to quicker numerical results.The considered finite-part integral can be expressed in closed form as function of complete elliptical integrals or Gauss hypergeometric functions, respectively.Formuias for special cases and some i, j values and their numerical verification are given in Appendices II and III.
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620330509
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