Torsion of a Conical-form Rigid Cylinder Embedded in an Infinite Elastic Thick Plate

Abstract

The problem of torsion of a conical-form rigid cylinder embedded in an elastic half space has been investigated in a previous paper. The problem may be regarded as an analytical model of stress analysis in drilling. The principal object of this paper is an application of the problem of a half space to one of an infinite thick plate. The method of solution used here is to distribute torsional body forces in a thick plate so as to satisfy the boundary conditions of a conical hole of an infinite elastic thick plate. For this purpose, we apply Green's functions for torsional body force problems of an infinite elastic thick plate. Stresses and displacements of the thick plate with a conical hole and torques necessary to twist the conical-form rigid cylinder are shown graphically and compared with the results about an elastic half space.