On the topological derivative due to kink of a crack with non-penetration. Anti-plane model |
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Authors: | AM Khludnev VA Kovtunenko A Tani |
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Institution: | 1. Lavrent''ev Institute of Hydrodynamics, 630090 Novosibirsk, Russia;2. Institute for Mathematics and Scientific Computing, Karl-Franzens-University of Graz, 8010 Graz, Austria;3. Department of Mathematics, Keio University, Yokohama 223-8522, Japan |
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Abstract: | A topological derivative is defined, which is caused by kinking of a crack, thus, representing the topological change. Using variational methods, the anti-plane model of a solid subject to a non-penetration condition imposed at the kinked crack is considered. The objective function of the potential energy is expanded with respect to the diminishing branch of the incipient crack. The respective sensitivity analysis is provided by a Saint-Venant principle and a local decomposition of the solution of the variational problem in the Fourier series. |
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