We propose a solution for an elastic, axisymmetric, indentation problem. The indenter is a rigid cylinder on an elastic layer in contact with an elastic substrate. The goal is to provide a contact law between the applied force and the displacement of the coating in two cases: frictionless interaction and perfect binding between the coating and the substrate. As examples we have considered situations in which the substrate is either softer, similarly stiff, or stiffer than the coating, both for compressible or incompressible materials.

SUMMARYA method for minimum weight design of non-linear elastic structures with prescribed buckling strength is presented. The problem is treated for simple critical states both in the case of the bifurcation point and in the case of the turning point. Problems are shown to illustrate the applicability of the method.

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