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An Optimal Size of a Rigid Thin Stiffener Reinforcing an Elastic Two-Dimensional Body on the Outer Edge

Author

Listed:
  • Nyurgun Lazarev

    (North-Eastern Federal University)

  • Galina Semenova

    (North-Eastern Federal University)

Abstract

The equilibrium problem for a two-dimensional body with a crack is studied. We suppose that the body consists of two parts: an elastic part and a rigid thin stiffener on the outer edge of the body. Inequality-type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. For a family of variational problems, dependence of their solutions on the length of the thin rigid stiffener is investigated. It is shown that there exists a solution of an optimal control problem. For this problem, the cost functional is defined by a continuous functional on a solution space, while the length parameter serves as a control parameter.

Suggested Citation

  • Nyurgun Lazarev & Galina Semenova, 2018. "An Optimal Size of a Rigid Thin Stiffener Reinforcing an Elastic Two-Dimensional Body on the Outer Edge," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 614-626, August.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:2:d:10.1007_s10957-018-1291-8
    DOI: 10.1007/s10957-018-1291-8
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    Cited by:

    1. Alexander Khludnev & Antonio Corbo Esposito & Luisa Faella, 2020. "Optimal Control of Parameters for Elastic Body with Thin Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 184(1), pages 293-314, January.
    2. Alexander Khludnev & Alexander Rodionov, 2023. "Elasticity Tensor Identification in Elastic Body with Thin Inclusions: Non-coercive Case," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 993-1010, June.

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