Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-19T10:00:07.692Z Has data issue: false hasContentIssue false
  • English
  • Français

Plane elastostatic boundary value problems (III). Stresses in a parabolic mound

Published online by Cambridge University Press:  26 February 2010

V. T. Buchwald
V. T. Buchwald
Affiliation:
Dept. of Applied Mathematics, The University of Sydney.
Get access

Summary

The first and second boundary value problems of plane elastostatics are solved for the interior of a parabola. A conformal transformation is used to map the interior of the parabola onto an infinite strip. An analytic continuation technique reduces the boundary value problem to the solution of a form of differential-difference equation. This is solved by a Fourier integral method. The resulting integrals are evaluated by residues to give eigenfunction expansions for the complex potentials.

Type
Research Article
Information
Mathematika , Volume 10 , Issue 1 , June 1963 , pp. 35 - 42
Copyright
Copyright © University College London 1963

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

1. Buchwald, V. T., “Plane elastostatic boundary value problems (I)”, Mathematika, 10 (1963), 25–28.CrossRefGoogle Scholar
2. Muskhelishvili, N. I., Some basic problems of the mathematical theory of elasticity, translated by Radok, J. B. M. (Nordhoff, Groningen, 1953), 244.Google Scholar
3. Buchwald, V. T. and Davies, G. A. o., Quart. J. Mech. App. Math., in the press.Google Scholar
4. Tiffen, R., Quart. J. Mech. App. Math., 5 (1952), 352.CrossRefGoogle Scholar
5. Titchmarsh, E. C., Introduction to the theory of Fourier integrals (Oxford, 1937), Chap. X.Google Scholar
6. Green, A. E. and Zerna, W., Theoretical elasticity (Oxford, 1954), 254.Google Scholar
7. Lighthill, M. J., Fourier analysis and generalized functions (Cambridge, 1958).Google Scholar
8. Buchwald, V. T., Lecture to the Australian Math. Soc., to be published.Google Scholar
9. Filon, L. N. G., Phil. Trans. Boy. Soc. A., 201 (1903), 63.Google Scholar
10. Sneddon, I. N., Fourier transforms (McGraw Hill, 1951), 476.Google Scholar
11. Hardy, G. H., Mess, of Math., 31 (1902), 161.Google Scholar
12. Hillman, A. P. and Salzer, H. E., Phil. Mag. (7), 34 (1943), 5.CrossRefGoogle Scholar
13. Ricci, L., Tavola di Radicci, Publ. 1st. Applic. Calcola, No. 296 (Rome, 1951).Google Scholar