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Shape derivative of the energy functional in a problem for a thin rigid inclusion in an elastic body

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Abstract

The equilibrium problem of the elastic body with a delaminated thin rigid inclusion is considered. In this case, there is a crack between the rigid inclusion and the elastic body. We suppose that the nonpenetration conditions are prescribed on the crack faces. We study the dependence of the energy of the body on domain variations. The formula for the shape derivative of the energy functional is obtained. Moreover, it is shown that for the special cases of the domain perturbations such derivative can be represented as invariant integrals.

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics of the Russian Academy of Sciences, 630090, Novosibirsk, Russia

    E. M. Rudoy

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    E. M. Rudoy

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  1. E. M. Rudoy
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Rudoy, E.M. Shape derivative of the energy functional in a problem for a thin rigid inclusion in an elastic body. Z. Angew. Math. Phys. 66, 1923–1937 (2015). https://doi.org/10.1007/s00033-014-0471-0

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  • DOI: https://doi.org/10.1007/s00033-014-0471-0

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