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Solution of one mixed problem of plate bending for a domain with partially unknown boundary

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Abstract

The paper addresses the problem of finding a full-strength contour in the problem of plate bending for a cycle-symmetric doubly connected domain. An isotropic elastic plate, bounded by a regular polygon, is weakened by a required full-strength hole whose symmetry axes are the regular polygon diagonals. Rigid bars are attached to each component of the broken line of the outer boundary of the plate. The plate bends under the action of concentrated moments applied to the middle points of the bars. An unknown part of the boundary is free from external forces. Using the methods of complex analysis, the analytical image of Kolosov–Muskhelishvili’s complex potentials (characterising an elastic equilibrium of the body) and of an unknown full-strength contour are determined. A numerical analysis is performed and the corresponding plots are obtained by means of the Mathcad system.

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Authors and Affiliations

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

    N. Odishelidze

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

    F. Criado-Aldeanueva

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

    F. Criado & J. M. Sanchez

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  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. Solution of one mixed problem of plate bending for a domain with partially unknown boundary. Acta Mech 219, 169–179 (2011). https://doi.org/10.1007/s00707-010-0441-3

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  • DOI: https://doi.org/10.1007/s00707-010-0441-3

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