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Khludnev, A. M.; Kovtunenko, V. A.; Tani, A.

On the topological derivative due to kink of a crack with non-penetration. Anti-plane model. (English) Zbl 1203.49035

J. Math. Pures Appl. (9) 94, No. 6, 571-596 (2010).
Summary: 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.

Cited in 16 Documents

MSC:

49K40 Sensitivity, stability, well-posedness
35J20 Variational methods for second-order elliptic equations
49Q12 Sensitivity analysis for optimization problems on manifolds
74R10 Brittle fracture

Keywords:

kink of crack; non-penetration condition; variational inequality; shape sensitivity analysis; topological change; structure optimization
PDFBibTeX XMLCite
\textit{A. M. Khludnev} et al., J. Math. Pures Appl. (9) 94, No. 6, 571--596 (2010; Zbl 1203.49035)
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References:

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