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Optimal Control of Parameters for Elastic Body with Thin Inclusions

Author

Listed:
  • Alexander Khludnev

    (Novosibirsk State University)

  • Antonio Corbo Esposito

    (Universita di Cassino e del Lazio Meridionale)

  • Luisa Faella

    (Universita di Cassino e del Lazio Meridionale)

Abstract

In this paper, an equilibrium problem for 2D non-homogeneous anisotropic elastic body is considered. It is assumed that the body has a thin elastic inclusion and a thin rigid inclusion. A connection between the inclusions at a given point is characterized by a junction stiffness parameter. The elastic inclusion is delaminated, thus forming an interfacial crack with the matrix. Inequality-type boundary conditions are imposed at the crack faces to prevent interpenetration. Existence of solutions is proved; different equivalent formulations of the problem are discussed; junction conditions at the connection point are found. A convergence of solutions as the junction stiffness parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is investigated. An analysis of limit models is provided. An optimal control problem is analyzed with the cost functional equal to the derivative of the energy functional with respect to the crack length. A solution existence of an inverse problem for finding the junction stiffness and rigidity parameters is proved.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:1:d:10.1007_s10957-019-01620-w
    DOI: 10.1007/s10957-019-01620-w
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    References listed on IDEAS

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    1. Alexander Khludnev, 2017. "Rigidity Parameter Identification for Thin Inclusions Located Inside Elastic Bodies," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 281-297, January.
    2. 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.
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    Cited by:

    1. 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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    1. 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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