A multiple contact problem for a system of interacting flat-ended cylindrical punches perfectly bonded to the surface of an elastic half-space is considered under the assumption that each of the punches is loaded by external forces which produce the punch’s translational displacements in three coordinate directions and small-angle rotations about the coordinate axes. An approximate solution is obtained by the Kachanov method that is based on the ideas of Kachanov originally introduced for the multiple crack problems. The obtained results are applied to the problem of the equilibrium stability of two neighboring rigid columns with their circular footings bonded to an elastic half-space.
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