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On the Axisymmetrical Stress Concentration at an Eccentrically Reinforced Circular Hole in a Plate

Published online by Cambridge University Press:  07 June 2016

W. H. Wittrick
W. H. Wittrick*
Affiliation:
Department of Aeronautical Engineering, University of Sydney*
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Summary

This paper is concerned with the effectiveness of reinforcing a hole in a plate on one surface only. The particular problem considered is that of a circular hole in a plate of infinite extent, subjected to axially symmetrical tension at infinity, when the reinforcement consists of an annular plate on one surface. Because of the interaction between bending and stretching, the problem is highly non-linear and it has only been possible to solve it for certain limiting cases. The stress concentration factor depends on a dimensionless parameter proportional to the tension at infinity. It is shown that the stress concentration factor is increased, because of the eccentricity of the reinforcement, if the parameter is small, but for values of the parameter greater than a certain minimum the stress concentration factor is decreased. The results also make it quite clear that there is no possibility of obtaining reasonably accurate results by linearisation of the equations.

Type
Research Article
Information
Aeronautical Quarterly , Volume 16 , Issue 1 , February 1965 , pp. 15 - 32
Copyright
Copyright © Royal Aeronautical Society. 1965

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References

1. Gurney, C. On the Analysis of the Stresses in a Flat Plate with a Reinforced Circular Hole under Edge Forces. R. & M. 1834, 1938.Google Scholar
2. Savin, G. N. Stress Concentration around Holes. Pergamon Press, 1961.Google Scholar
3. Mansfield, E. H. Neutral Holes in Plane Sheets. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 6 p. 370, 1953.CrossRefGoogle Scholar
4. Wells, A. A. On the Plane Stress-Distribution in an Infinite Plate with a Rim-Stiffened Elliptical Opening. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 3 p. 23, 1950.Google Scholar
5. Hicks, R. Reinforced Elliptical Holes in Stressed Plates. Journal of the Royal Aeronautical Society, Vol. 61 p. 688, October 1957.CrossRefGoogle Scholar
6. Wittrick, W. H. Stresses around Reinforced Elliptical Holes, with Applications to Pressure Cabin Windows. Aeronautical Quarterly, Vol. X p. 373, November 1959.CrossRefGoogle Scholar
7. Wittrick, W. H. Analysis of Stress Concentrations at Reinforced Holes in Infinite Sheets. Aeronautical Quarterly, Vol. XI p. 233, August 1960.CrossRefGoogle Scholar
8. Wittrick, W. H. Stress Concentrations for a Family of Uniformly Reinforced Square Holes with Rounded Corners. Aeronautical Quarterly, Vol. XIII p. 223, August 1962.Google Scholar
9. Wittrick, W. H. Stress Concentrations for Uniformly Reinforced Equilateral Triangular Holes with Rounded Corners. Aeronautical Quarterly, Vol. XIV p. 254, August 1963.CrossRefGoogle Scholar
10. Hicks, R. Asymmetrically Ring-Reinforced Circular Hole in a Uniformly End-Loaded Plate, with Reference to Pressure Vessel Design. The Chartered Mechanical Engineer, Vol. 5, November 1958.Google Scholar
11. Hicks, R. Asymmetrically Plate-Reinforced Circular Hole in a Uniformly End-Loaded Flat Plate. Aeronautical Quarterly, Vol. X p. 183, May 1959.Google Scholar
12. Wittrick, W. H. Axisymmetrical Bending of a Highly Stretched Annular Plate. (To be published in the Quarterly Journal of Mechanics and Applied Mathematics.)Google Scholar
13. Watson, G. N. Theory of Bessel Functions. Cambridge University Press, 2nd Edition, 1958.Google Scholar
14. Tables of Bessel Functions of Fractional Order. Vol. 2. Columbia University Press, New York, 1959.Google Scholar
15. Bessel Functions. Part 1, Functions of Orders Zero and Unity. Cambridge University Press, 1950.Google Scholar
16. Bessel Functions. Part 2, Functions of Positive Integer Order. Cambridge University Press, 1952.Google Scholar
17. Comrie, L. J. Chambers Six-Figure Mathematical Tables. Vol. 2, Natural Values, p. 514. Chambers, London, 1949.Google Scholar
18. Morgan, S. P. Tables of Bessel Functions of Imaginary Order and Imaginary Argument. California Institute of Technology, Pasadena, 1947.Google Scholar