Some coplanar punch and crack problems in three-dimensional elastostatics

Abstract
Certain three-dimensional punch and crack problems for an elastic half-space and an infinite elastic solid respectively reduce to Dirichlet or Neumann problems in potential theory in which the potential is to be determined at all points of an infinite three-dimensional space, given its values or the values of its normal derivative on two or more coplanar circular regions. These problems are shown to be governed by infinite sets of Fredholm integral equations of the second kind, which can be solved approximately by iteration when the spacing between the circular regions is sufficiently large compared with their radii. The stress distributions in a half-space indented by two flat-ended circular punches and in an infinite solid containing two or more coplanar penny-shaped cracks opened under pressure are thus investigated.

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