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On the existence of optimal shapes in contact problems — Perfectly plastic bodies

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Abstract

The optimal shape design of a two-dimensional elastic perfectly plastic body (a punch) on a rigid frictionless foundation is analysed. The problem is to find the boundary part of the body where the unilateral boundary conditions are assumed in such a way that certain energy integral of the system in the equilibrium will be minimized. It is assumed that the material of the body is elastic perfectly plastic, obeying the Henckys law. The variational formulation in terms of stresses is utilized. The existence of optimal shapes is proved.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, KAM MFF UK, Malostranské 2/25, CS-11800, Prague, Czechoslovakia

    J. Haslinger

  2. Department of Mathematics, University of Jyväskylä, Seminaarinkatu 15, SF-40100, Jyväskylä, Finland

    P. Neittaanmäki

Authors
  1. J. Haslinger
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  2. P. Neittaanmäki
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Communicated by W. Wendland and S.N. Aduri, March 31, 1986

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Haslinger, J., Neittaanmäki, P. On the existence of optimal shapes in contact problems — Perfectly plastic bodies. Computational Mechanics 1, 293–299 (1986). https://doi.org/10.1007/BF00273705

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  • DOI: https://doi.org/10.1007/BF00273705

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