We propose a mathematical model of motion of an elastic body along a hard surface in the absence of friction forces. The formulations of the problem in the form of a variational inequality and in the form of the extremum variational problem are obtained. For the discretization of the extremum variational problem, we use the finite-element method. As an example, we consider the motion of a body with rectangular cross section under the conditions of plane deformation. We investigate strains and stresses formed in the case of motion along the surfaces in the horizontal and vertical directions.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 1, pp. 84–93, January–March, 2013.
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Kuz’menko, V.І., Mykhal’chuk, H.I. Contact Problems of Motion of Elastic Bodies Along Hard Surfaces. J Math Sci 201, 99–110 (2014). https://doi.org/10.1007/s10958-014-1976-y
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DOI: https://doi.org/10.1007/s10958-014-1976-y