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A mixed problem of plane elasticity theory for a multiply connected domain with partially unknown boundary: the case of a rhombus

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Abstract

This paper addresses a problem of plane elasticity theory for a multiply connected domain, whose external boundary is a rhombus and the internal boundary is the required two holes that are symmetric with respect to its diagonals. Absolutely rigid punches with rectilinear bases are applied to each segment of the outer boundary of the given body, and they are under the action of the forces P that apply to their middle points. There is no friction between the surface of the given elastic body and the punches. The boundaries of the unknown holes are free from external loads. Tangential stresses are equal to zero along the entire boundary of the domain, and the normal displacements on the linear parts of the boundary are constant. The shapes of the holes’ contours and the stress state of the given body are determined, provided that the tangential normal stress arising at the holes’ contours takes a constant value. Such holes are called full-strength holes. Full-strength contours and stress state are found by means of complex analysis. The solution is written in quadratures. Numerical analyses are presented, and the corresponding plots are constructed.

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Authors and Affiliations

  1. Interdisciplinary Department (Mathematics, Computer Sciences), Faculty of Exact and Natural Sciences, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    Nana Odishelidze

  2. Department of Applied Physics II, Polytechnic School, Malaga University, Campus El Ejido, Málaga, Spain

    Francisco Criado-Aldeanueva

  3. Department of Statistics and Operational Research, Faculty of Sciences, Malaga University, Campus Teatinos, Málaga, Spain

    J. M. Sanchez

Authors
  1. Nana Odishelidze
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  2. Francisco Criado-Aldeanueva
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  3. J. M. Sanchez
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Correspondence to Francisco Criado-Aldeanueva.

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Odishelidze, N., Criado-Aldeanueva, F. & Sanchez, J.M. A mixed problem of plane elasticity theory for a multiply connected domain with partially unknown boundary: the case of a rhombus. Z. Angew. Math. Phys. 66, 2899–2907 (2015). https://doi.org/10.1007/s00033-015-0546-6

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  • DOI: https://doi.org/10.1007/s00033-015-0546-6

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