The Axisymmetric Indentation of Semi-Infinite Transversely Isotropic Space by Heated Annular Punch

Abstract

The problem of determining the distribution of stress in a semi – infinite elastic solid when a rigid body of prescribed shape is pressed against its free surface is associated with the name of Boussinesq, since it was first discussed in classical Treatise [1]. A detailed account of punch problem may be formed in Sneddon [2] and Green and Zerna [3]. Recently, Shibuya et.al. [4] devised a novel technique for determining stress distribution in elastic half space indented by flat annular punch. Shibuya et.al. [5] also extended this technique  to determine stress distribution in an elastic slab indented by  a pair of flat rigid annular punches.

George and Sneddon [6] were first to study the axially symmetric problem of elastic half space indented by heated punch. Keer and Fu [7] also studied the thermo – elastic stress distribution problem due to combined loading of rigid, non– symmetrical, circular punches indenting thick elastic plate.  The axisymmetric Boussinesq problem for heated annular punch was discussed by Kumar and Hiremath [8]. The problem of determining axisymmetric distribution in a thick elastic plate indented by a pair of heated annular punches was also studied by Kumar and Hiremath [9].

The present paper extends the method of Kumar and Hiremath [8, 9] to study the problem of determining stress distribution in a transversely isotropic  half space indented by a heated annular rigid punch. The mixed boundary value problem is reduced to the solution of triple integral equations, which in turn are reduced to the solution of linear simultaneous algebraic equations. These are solved numerically.