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The Quarterly Journal of Mechanics and Applied Mathematics 1997 50(2):303-319; doi:10.1093/qjmam/50.2.303
© 1997 by Oxford University Press
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INTERACTION OF AN ARBITRARY FORCE WITH A FLEXIBLE PUNCH OR WITH A PENNY-SHAPED CRACK

V. I. FABRIKANT

( Prisoner 167932 D, Donnacona Jail, Donnacona, Quebec, Canada G0A 1TO )

Two mathematically equivalent problems are solved exactly and in terms of elementary functions. A penny-shaped crack in a transversely isotropic elastic space is interacting with arbitrarily located point forces, applied in such a way that the tangential displacements outside the crack vanish. The problem of finding the tangential stress produced by such loading is solved exactly and in closed form. The second problem is that of interaction of an arbitrary point force inside the transversely isotropic elastic half-space and a flexible punch. The method of solution is based on the previously published results of the author. The results are of fundamental value, since they effectively give the Green's functions for solving any relevant problem of interaction.


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