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Optimal control of rigidity parameters of thin inclusions in composite materials

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Abstract

In the paper, an equilibrium problem for an elastic body with a thin elastic and a volume rigid inclusion is analyzed. It is assumed that the thin inclusion conjugates with the rigid inclusion at a given point. Moreover, a delamination of the thin inclusion is assumed. Inequality type boundary conditions are considered at the crack faces to prevent a mutual penetration between the faces. A passage to the limit is justified as the rigidity parameter of the thin inclusion goes to infinity. The main goal of the paper is to analyze an optimal control problem with a cost functional characterizing a deviation of the displacement field from a given function. A rigidity parameter of the thin inclusion serves as a control function. An existence theorem to this problem is proved.

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics of SB RAS, Novosibirsk State University, Novosibirsk, Russia, 630090

    A. M. Khludnev

  2. DIEI Dipartimento di Ingegneria Elettrica e dell’Informazione “M. Scarano”, Universita di Cassino e del Lazio Meridionale, 03043, Cassino, Italy

    L. Faella

  3. Dipartimento di Scienze e Tecnologie, Universita del Sannio, 82100, Benevento, Italy

    C. Perugia

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  1. A. M. Khludnev
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  2. L. Faella
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  3. C. Perugia
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Correspondence to A. M. Khludnev.

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Khludnev, A.M., Faella, L. & Perugia, C. Optimal control of rigidity parameters of thin inclusions in composite materials. Z. Angew. Math. Phys. 68, 47 (2017). https://doi.org/10.1007/s00033-017-0792-x

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  • DOI: https://doi.org/10.1007/s00033-017-0792-x

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