Torsion of an elastic half-space with a cylindrical cavity by a punch

Abstract

Torsion of an elastic half-space with a vertical cylindrical cavity by a coaxial punch bonded to a flat boundary and rotated under action of the torque about the axis is considered in this article by employing Weber–Orr integral transforms. We suggest two novel methods reducing the problem to the regular integral equations of the second kind, which are effective for different intervals of geometric parameters and permit to derive a nearly exact approximate solution of the problem for all values of the parameters. The effect of the cavity on the mechanical characteristics in comparison with the well-known Reissner–Sagoci problem is studied in detail. In particular, it is shown that the discrepancies are very small if the punch radius is more than twice as large as the cavity radius and are large if the radii of the punch and cavity are close, that is, the strong edge effect is observed. Simple asymptotic formulas describing the edge effect and the case of a large radius punch are given. Results of this study can be helpful for theoretical modeling of borehole stress fields in structural and mechanical designs applications, for heapstead buildings foundations design as well as for a variety of other engineering problems of a medium with a similar geometry such as mineshafts, wells and boreholes.