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Optimal Control of Inclusion and Crack Shapes in Elastic Bodies

Author

Listed:
  • A. Khludnev

    (Russian Academy of Sciences)

  • G. Leugering

    (Lehrstuhl II Universität Erlangen)

  • M. Specovius-Neugebauer

    (University of Kassel)

Abstract

The paper is concerned with the control of the shape of rigid and elastic inclusions and crack paths in elastic bodies. We provide the corresponding problem formulations and analyze the shape sensitivity of such inclusions and cracks with respect to different perturbations. Inequality type boundary conditions are imposed at the crack faces to provide a mutual nonpenetration between crack faces. Inclusion and crack shapes are considered as control functions and control objectives, respectively. The cost functional, which is based on the Griffith rupture criterion, characterizes the energy release rate and provides the shape sensitivity with respect to a change of the geometry. We prove an existence of optimal solutions.

Suggested Citation

  • A. Khludnev & G. Leugering & M. Specovius-Neugebauer, 2012. "Optimal Control of Inclusion and Crack Shapes in Elastic Bodies," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 54-78, October.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:1:d:10.1007_s10957-012-0053-2
    DOI: 10.1007/s10957-012-0053-2
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    Cited by:

    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.

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