Punch Problem for Planar Anisotropic Elastic Half-Plane

Abstract

The two dimensional punch problem for planar anisotropic elastic half-plane is revisited using the Lekhnitskii's formulation with aid of the Fourier transform and boundary integral equation. Four different conditions of contact problem for the rigid punch are analyzed in this study. From the combination of surface Green's function of half-plane and Hooke's law of anisotropic material, a set of Fredholm integral equations are obtained for mixed boundary value problems. After solving the integral equation according to specified contact condition, the explicit distributions of surface traction under the punch are obtained in closed-form. From the surface traction and Green's function of anisotropic half-plane, the full-field solutions of stresses are constructed. Numerical calculations of surface traction under the rigid punch are presented base on the analysis and are discussed in detail.

Mechanics of frictional contact for an arbitrary oriented orthotropic material

“…The three‐dimensional contact problem of transversely isotropic multilayers bonded to the transversely isotropic half plane is studied by Kuo and Keer using the Hankel transform technique. Lin considered the frictional contact problem of an anisotropic half plane indented by a rigid flat punch.…”