Stress distribution near a penny-shaped crack on an off-diametral plane in a sphere

Abstract

The singular stress problem of a penny-shaped crack situated symmetrically on an off-diametral plane of a sphere is presented in this paper when the surface of the crack is subjected to a known pressure. The problem is solved by using integral transforms and is reduced to the solution of a Fredholm integral equation of the second kind. It is shown that the present solution agrees with already known solution when the off-diametral plane becomes the diametral plane.

COMMUNICATED BY:

• R. P. Gilbert

Keywords:

• Off-diametral plane
• sphere
• penny-shaped crack

2010 Mathematics Subject Classifications:

• 74B10
• 74B15

Disclosure statement

No potential conflict of interest was reported by the authors.