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On one contact problem of plane elasticity for a doubly connected domain: application to a hexagon

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Abstract

The paper addresses a problem of plane elasticity theory for a doubly connected body whose external boundary is a regular hexagon boundary, and the internal boundary is the required full-strength hole including the origin of coordinates. Hexagon’s two vertices are laid at the axis Oy, and the middle points of its two opposite sides are laid at the axis Ox. This full-strength hole is cycle symmetric. It is assumed that to every link of the broken line of the outer boundary of the given body are applied absolutely smooth rigid stamps with rectilinear bases, which are under action of the force P that applies to their middle points. There is no friction between the surface of given elastic body and stamps. The unknown full-strength contour is free from outer actions. Using the methods of complex analysis, the analytical image of Kolosov–Muskhelishvili’s complex potentials (characterizing an elastic equilibrium of the body) and unknown parts of its boundary are determined under the condition that the tangential normal moment arising at it takes a constant value. Such holes are called full-strength holes. Numerical analysis are also performed and the corresponding graphs are constructed.

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Authors and Affiliations

  1. Department of Computer Sciences, Faculty of Exact and Natural Sciences, Tbilisi State University, Iv. Javakhishvili 2, University st., 0143, Tbilisi, Georgia

    N. Odishelidze

  2. Department of Applied Physics II, Polytechnic School, Malaga University, Campus El Ejido s/n, 29013, Malaga, Spain

    F. Criado-Aldeanueva

  3. Department of Statistics and Operational Research, Faculty of Sciences, Malaga University, Campus Teatinos s/n, 29071, Malaga, Spain

    F. Criado & J. M. Sanchez

Authors
  1. N. Odishelidze
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  2. F. Criado-Aldeanueva
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  3. F. Criado
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  4. J. M. Sanchez
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Correspondence to F. Criado-Aldeanueva.

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Odishelidze, N., Criado-Aldeanueva, F., Criado, F. et al. On one contact problem of plane elasticity for a doubly connected domain: application to a hexagon. Z. Angew. Math. Phys. 64, 193–200 (2013). https://doi.org/10.1007/s00033-012-0222-z

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  • DOI: https://doi.org/10.1007/s00033-012-0222-z

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