This article is cited in 28 papers

The variational contact problem for elastic objects of different dimensions

A. M. Khludnev^a, K.-H. Hoffmann^b, N. D. Botkin<sup>b

a</sup> M. A. Lavrent'ev Institute of Hydrodynamics
^b Center of advanced european studies and research

Abstract: We consider the variational free boundary problem describing the contact of an elastic plate with a thin elastic obstacle. The contact domain is unknown a priori and should be determined. The problem is described by a variational inequality for a fourth-order operator. The constraint on the displacement is given on a set of dimension less than that of the solution domain. We find the boundary conditions on the set of the possible contact and their exact statement. We justify the mixed statement of the problem and analyze the limit cases corresponding to the unbounded increase of the elasticity coefficients of the contacting bodies.

Keywords: variational inequality, thin obstacle, contact problem.

UDC: 517.95

Received: 31.03.2005

 English version: Siberian Mathematical Journal, 2006, 47:3, 584–593

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