Optimal Control of Inclusion and Crack Shapes in Elastic Bodies

Khludnev A, Leugering G, Specovius-Neugebauer M (2012)

Publication Type: Journal article

Publication year: 2012

Journal

Journal of Optimization Theory and Applications Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

DOI: 10.1007/s10957-012-0053-2

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.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik

Additional Organisation(s)

Exzellenz-Cluster Engineering of Advanced Materials

Involved external institutions

Universität Kassel DE Germany (DE) Russian Academy of Sciences / Росси́йская акаде́мия нау́к (RAS) RU Russian Federation (RU)

How to cite

APA:

Khludnev, A., Leugering, G., & Specovius-Neugebauer, M. (2012). Optimal Control of Inclusion and Crack Shapes in Elastic Bodies. Journal of Optimization Theory and Applications. https://doi.org/10.1007/s10957-012-0053-2

MLA:

Khludnev, A., Günter Leugering, and M. Specovius-Neugebauer. "Optimal Control of Inclusion and Crack Shapes in Elastic Bodies." Journal of Optimization Theory and Applications (2012).

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