Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-19T20:10:56.655Z Has data issue: false hasContentIssue false
  • English
  • Français

Some dual series equations with an application in the theory of elasticity

Published online by Cambridge University Press:  14 November 2011

J. Tweed
J. Tweed
Affiliation:
Department of Mathematical Sciences, Old Dominion University, Norfolk, Va 23508, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper the author investigates a system of simultaneous dual trigonometric series equations. A closed form solution is obtained by reducing the dual series to singular integral equations of Carleman type. The use of these equations is then illustrated by their application to a crack problem in the theory of elasticity.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 3-4 , 1982 , pp. 241 - 251
Copyright
Copyright © Royal Society of Edinburgh 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Parihar, K. S.. Some triple trigonometrical series equations and their applications. Proc. Roy. Soc. Edinburgh Sect. A 69 (1970), 255–265.Google Scholar
2Tricomi, F. G.. On the finite Hilbert transformation. Quart. J. Math. 2 (1951) 199–211.CrossRefGoogle Scholar
3Michell, J. H.. The stress in a rotating lamina. Proc. London Math. Soc. 31 (1900), 100–124.Google Scholar
4Sokolnikoff, I. S.. Mathematical Theory of Elasticity (New York: McGraw-Hill, 1956).Google Scholar
5Savin, G. N.. Stress Distribution Around Holes (Trans). NASATTF-607, (1970).Google Scholar
6Rooke, D. P. and Cartwright, D. J.. Compendium of Stress Intensity Factors (London: HMSO, 1976).Google Scholar