Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T21:42:50.798Z Has data issue: false hasContentIssue false
  • English
  • Français

Some axially symmetric stress distributions in elastic solids containing penny-shaped cracks. II. Cracks in solids under torsion

Published online by Cambridge University Press:  26 February 2010

W. D. Collins
W. D. Collins
Affiliation:
King's College, Newcastle upon Tyne, The University, Manchester
Get access

Extract

This paper is a sequel to a previous paper [1] on axially symmetric torsion-free stress distributions in isotropic elastic solids and applies the methods used to investigate these distributions to distributions in solids under torsion. The basis of these methods is that in a solid of revolution containing a symmetrically located crack the stresses set up in the neighbourhood of the crack by forces applied over the crack can be found by perturbing on their values in an infinite solid containing a crack of the same radius and under the same applied forces, provided the radius of the crack is small compared with a typical length of the solid of revolution. The problem of determining the stresses in the solid of revolution is shown to be governed by a Fredholm integral equation of the second kind, which holds whatever the ratio of the crack radius to the typical length, but which, when this ratio is small, is readily solved by iteration to give stresses perturbing on those in an infinite solid. A similar method can be applied to an infinite solid containing two or more cracks when the crack radii are small compared with a typical length of the crack array.

Type
Research Article
Information
Mathematika , Volume 9 , Issue 1 , June 1962 , pp. 25 - 37
Copyright
Copyright © University College London 1962

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.Collins, W. D., Proc. Royal Soc., A, 266 (1962), 359–386.Google Scholar
2.Collins, W. D., Quart. J. Mech. App. Math., 14 (1961), 101–117.CrossRefGoogle Scholar
3.Collins, W. D., To be published.Google Scholar
4.Love, A. E. H., Mathematical theory of elasticity (Fourth Edition, Cambridge, 1952).Google Scholar
5.Weinstein, A., Trans. American Math. Soc., 63 (1948), 342–354.CrossRefGoogle Scholar
6.Bateman, H., Partial differential equations of mathematical physics (Cambridge, 1932), 408.Google Scholar
7.Mackie, A. G., J. Rational Mech. Analysis, 4 (1955), 733–750.Google Scholar
8.Copson, E. T., Proc. Edinburgh Math. Soc. (2), 8 (1947–50), 14–19.CrossRefGoogle Scholar
9.Weinstein, A., Quart. App. Math., 10 (1952–53), 77–81.CrossRefGoogle Scholar
10.Willis, H. F., Phil. Mag. (7), 39 (1948), 455–459.CrossRefGoogle Scholar
11.Watson, G. N., Theory of Bessel functions (Second Edition, Cambridge, 1958).Google Scholar
12.Erdélyi, A. et al. , Higher transcendental functions I (McGraw-Hill, 1953).Google Scholar
13.Collins, W. D., Proc. Cambridge Phil. Soc, 57 (1961), 623–627.CrossRefGoogle Scholar
14.Ling, C. B., Quart. App. Math., 10 (1952–53), 149–156.CrossRefGoogle Scholar