# Weight function for an elliptic crack in an infinite medium. I. Normal loading

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### Cites background from "Weight function for an elliptic cra..."

...Several attempts have been made to derive the weight functions for embedded elliptical crack by solving the problem analytically, see recent development in [13,14]....

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^{1}, Jacob D. Hochhalter

^{2}, Paul A. Wawrzynek

^{3}, Gerd Heber

^{2}+1 more•Institutions (3)

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##### References

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### "Weight function for an elliptic cra..." refers background or methods in this paper

...Rice (1972) independently showed that weight functions could be determined by differentiating known elastic displacement field solutions with respect to crack length....

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...Foundations of the three dimensional weight function theory were given independently by Rice (1972) in the Appendix of that publication and by Bueckner (1973) in a review....

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834 citations

### "Weight function for an elliptic cra..." refers background in this paper

...The concept was first introduced by Bueckner (1970) for two-dimensional cracked bodies....

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829 citations

### "Weight function for an elliptic cra..." refers background or methods in this paper

...Now using the following relations (see Gradshteyn and Ryzhik, 1980 )...

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...Here it may be noted that the only contributing term in the weight function is W 0 0 . All other terms contribute zero either due to the orthogonal property of sine and cosine functions, or due to orthogonality of Jacobi’s polynomials or due to the relation ( Gradshteyn and Ryzhik, 1980 )...

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...respect to between 0 and 1, one obtains after making use of the orthogonality property (see Gradshteyn and Ryzhik, 1980 ):...

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