Discussion: “Finite Inflation of a Bonded Toroid” (Hsu, K. H., 1972, ASME J. Appl. Mech., 39, pp. 491–494)
Year: 1972
Type: article
Abstract: Professor Zak has provided a useful tool for handling problems of technical significance.In a number of applications, there has been clear evidence of a stress singularity but no means to evaluate it.In the absence of results of the sort presented in this paper, the analyst was obliged to use singularity behavior for planar situations, as developed by Williams [l], 3 and then hope that the effects of curvature were not adverse.The present paper begins to transcend the need for such approximation and is therefore most welcome.Viewing this work in the context of [1], however, leads to certain suggestions for its extension.It will be recalled that in [1] the minimum eigenvalue X was reported as a function of the wedge's extent ($ ma x -<f>min)-This had the advantage of permitting visual determination of whether a given geometry would generate a singularity so that one might decide whether a singularity analysis is needed.Further, such data were provided for several combinations of boundary conditions.Another suggestion for extension of this work derives from the numerical results given in [2].The cylinder's radius is taken as unity in the present work, and a transformation to localized coordinates is made (cf.equations ( 9) and (10), et seq.).If, however, dimensional coordinates are used, the transformation becomes p = y/[(Rr )t + 2 2] tan (f> = (ffi -r)/z than that pertinent to axisymmetry.(It seems less likely that X and in particular its minimum value will be affected by R.)Needed, then, to carry this line of investigation further is a bit of mathematical alchemy.Professor Zak has made an auspicious start, and we look forward to results for arbitrary wedge angles, for various boundary conditions, and for the influence of R.
Source: Journal of Applied Mechanics
DOI: 10.1115/1.3422865
Author: R. A. Harrington
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1975369963