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Three-Dimensional Stress Concentration Around a Cylindrical Hole in a Semi-Infinite Elastic Body

Youngdahl, C. K. and Sternberg, E. (1966) Three-Dimensional Stress Concentration Around a Cylindrical Hole in a Semi-Infinite Elastic Body. Journal of Applied Mechanics, 33 (4). pp. 855-865. ISSN 0021-8936. doi:10.1115/1.3625193.

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This paper contains a three-dimensional solution, exact within classical elastostatics, for the stresses and deformations arising in a half-space with a semi-infinite transverse cylindrical hole, if the body—at infinite distances from its cylindrical boundary—is subjected to an arbitrary uniform plane field of stress that is parallel to the bounding plane. The solution presented is in integral form and is deduced with the aid of the Papkovich stress functions by means of an especially adapted, unconventional, integral-transform technique. Numerical results for the nonvanishing stresses along the boundary of the hole and for the normal displacement at the plane boundary, corresponding to several values of Poisson’s ratio, are also included. These results exhibit in detail the three-dimensional stress boundary layer that emerges near the edges of the hole in the analogous problem for a plate of finite thickness, as the ratio of the plate thickness to the diameter of the hole grows beyond bounds. The results obtained thus illustrate the limitations inherent in the two-dimensional plane-strain treatment of the spatial plane problem; in addition, they are relevant to failure considerations and of interest in connection with experimental stress analysis.

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Additional Information:Copyright © 1966 by ASME. Manuscript received by ASME Applied Mechanics Division, May 20, 1965; final draft, December 6, 1965. This investigation was carried out under the auspices of the United Stales Atomic Energy Commission and was supported in part by the Office of Naval Research under Contract Nonr-220(58). Presented at the Fifth U. S. National Congress of Applied Mechanics, University of Minnesota, Minneapolis, Minn., June 14-17, 1966.
Funding AgencyGrant Number
Atomic Energy CommissionUNSPECIFIED
Office of Naval Research (ONR)Nonr-220(58)
Subject Keywords: Stress concentration , Stress , Thickness , Deformation , Poisson ratio , Stress analysis (Engineering) , Boundary layers , Displacement , Elastic half space , Failure
Issue or Number:4
Record Number:CaltechAUTHORS:20151125-104606590
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:62428
Deposited On:25 Nov 2015 18:59
Last Modified:10 Nov 2021 23:02

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