Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-17T18:24:47.640Z Has data issue: false hasContentIssue false

Stress Distribution in Rotating Discs with Non-Central Holes

Published online by Cambridge University Press:  07 June 2016

Get access

Summary

The stress distribution in rotating circular discs containing a central hole and a symmetrical array of non-central holes is determined by numerical solution of the equations of generalised plane stress. Particular attention is given to an annulus containing the holes and of width approximately eight hole diameters, in which the full two-dimensional equations are solved. The region outside this annulus is treated as radially symmetric and the stresses there are determined from a simpler one-dimensional model. Stress distributions are reported for uniform discs of fixed geometry containing 10, 20 and 45 holes. Results are also obtained for 20-hole discs of non-uniform thickness comprising a uniformly tapered disc, a disc with a thickened annulus containing the holes, and a uniform disc with each hole surrounded by thickened bosses. As a check on the numerical method, calculations have been carried out on a disc of identical geometry to one examined photoelastically bv Leist and Weber with good agreement. The effect of changing Poisson's ratio for this particular disc is also examined.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1964

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. Saito, H. Stresses in Rotating Discs with Non-Central Circular Holes. Tohoku University Technical Reports, Vol. 21, No. 2, p. 217, 1957.Google Scholar
2. Leist, K. and Weber, J. Optical Stress Distributions in Rotating Discs with Eccentric Holes. Report No. 57, Institute for Jet Propulsion: German Research Institute for Aeronautics, Aachen, 1956.Google Scholar
3. Fox, L. (Editor). Numerical Solution of Ordinary and Partial Differential Equations. Pergamon Press, 1962.Google Scholar
4. Fox, L. Mixed Boundary Conditions in the Relaxational Treatment of Biharmonic Problems (Plane Strain or Stress). Proc. Roy. Soc. A, Vol. 189, p. 535, 1947.Google Scholar
5. Forsythe, G. E. Difference Methods on a Digital Computer for Laplacian Boundary Value and Eigenvalue Problems. Communications in Pure and Applied Mathematics, Vol. 9, p. 425, 1956.CrossRefGoogle Scholar
6. Howland, R. C. J. Stresses in a Plate Containing an Infinite Row of Holes. Proc. Roy. Soc. A 148, p. 471, 1935.Google Scholar
7. Bicklev, W. G. The Distribution of Stress Round a Circular Hole in a Plate. Phil. Trans. Roy. Soc. A, Vol. 227, p. 383, 1928.Google Scholar