On Boussinesq’s problem for a cracked halfspace
- 220 Downloads
This paper examines the axisymmetric elastostatic problem that deals with the action of a concentrated normal force on the surface of an isotropic elastic halfspace containing a penny-shaped crack. The mathematical formulation of the elasticity problem should take into consideration the sense of action of the concentrated force. The paper presents the development of Fredholm integral equations of the second-kind that are associated with this category of problem and indicates the numerical technique that is adopted for their solution. The numerical results are presented for the stress intensity factors generated at the penny-shaped crack experiencing either opening or closure.
KeywordsBoussinesq’s problem Fredholm integral equations of the second-kind Mixed boundary value problems Penny-shaped crack Stress intensity factors
The work described in this paper was supported by a Discovery Grant awarded by the Natural Sciences and Engineering Research Council of Canada and the James McGill Research Chairs program. The constructive comments of the reviewers are duly acknowledged. The author is grateful to a former research associate Dr. M.C. Au for assistance with the numerical work.
- 2.Davis RO, Selvadurai APS (1996) Elasticity and geomechanics. Cambridge University Press, CambridgeGoogle Scholar
- 7.Lord Kelvin (1848) Note on the integrations of the equations of equilibrium of an elastic solid. Camb Dublin Math J 3:87–89Google Scholar
- 16.Sneddon IN (ed) (1977) Application of integral transforms in the theory of elasticity. International Centre for Mechanical Sciences, Courses and Lectures No. 220, Springer, ViennaGoogle Scholar
- 28.Cherepanov GP (1979) Mechanics of brittle fracture (Translation Editors R. de Witt and W.C. Cooley). McGraw-Hill, New YorkGoogle Scholar
- 29.Broberg KB (1999) Cracks and fracture. Academic Press, San DiegoGoogle Scholar