Axisymmetric indentation of an elastic layer supported by a Winkler foundation

Abstract Axisymmetric indentation problems of an elastic layer supported by a Winkler foundation are studied in this paper. The indentation on the upper surface is made by a rigid axisymmetric conical, paraboloidal or ellipsoidal indenter. Fundamental solutions for an arbitrary surface load are derived first. The above problems are formulated into an integral equation which is solved numerically. Extensive results are provided for contact radii, displacements and contact pressures. A layer on a rigid smooth base is treated as a special case of the Winkler foundation. The associated analytical solutions for the rigid indenters on a half space arc retrieved as the layer depth approaches infinity. Conversely, useful relations are also derived from thin plate theory for relatively shallow layers.