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On the contact interaction between two rectangular plates

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Abstract

A mathematical model of contact interaction between two plates is presented, considering certain types of nonlinearity of each of the plates. Stress–strain state (SSS) of the interacting structural members is analyzed by the method of variational iterations, and the theorem of convergence of this method is provided. An iterative procedure for solving contact problems is developed and its convergence is also proved. Physical nonlinearity is considered by means of the method of variable parameters of elasticity. The SSS of a two-layer system of rectangular plates, depending on a type of boundary conditions as well as distances between plates, is investigated and supplemented with stress–strain curves \(\sigma _i^{(i)} (e_i^{(i)} )\)for each of the plates.

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Acknowledgments

This work has been supported by the Polish National Science Centre, MAESTRO 2, No. 2012/04/A/ST8/00738. The project has been also supported by the Grants RFBR 16-08-01108a and RFBR 16-01-00721a.

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Authors and Affiliations

  1. Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, Politehnicheskaya 77, Saratov, Russian Federation, 410054

    A. V. Krysko

  2. Cybernetic Institute, National Research Tomsk Polytechnic University, Lenin Avenue, 30, Tomsk, Russian Federation, 634050

    A. V. Krysko

  3. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924, Lodz, Poland

    J. Awrejcewicz

  4. Department of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524, Warsaw, Poland

    J. Awrejcewicz

  5. Department of Mathematics and Modelling, Saratov State Technical University, Politehnicheskaya 77, Saratov, Russian Federation, 410054

    M. V. Zhigalov & V. A. Krysko

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  1. A. V. Krysko
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  2. J. Awrejcewicz
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Correspondence to J. Awrejcewicz.

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Krysko, A.V., Awrejcewicz, J., Zhigalov, M.V. et al. On the contact interaction between two rectangular plates. Nonlinear Dyn 85, 2729–2748 (2016). https://doi.org/10.1007/s11071-016-2858-2

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  • DOI: https://doi.org/10.1007/s11071-016-2858-2

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