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Optimal control of crack growth in elastic body with inclusions. (English) Zbl 1480.74272

Summary: In the paper, an optimal control problem of crack growth is considered, allowing to choose the most safe inclusions in elastic bodies from the standpoint of their influence on a crack propagation.

MSC:

74R10 Brittle fracture
74G65 Energy minimization in equilibrium problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
Full Text: DOI

References:

[1] Ciarlet, P. G., Mathematical Elasticity, v.1: Three-dimensional Elasticity (1988), North-Holland: North-Holland Amsterdam/New York/Oxford/Tokyo · Zbl 0648.73014
[2] Fichera, G., Boundary value problems of elasticity with unilateral constraints, (Handbuch der Physik, Band 6a/2 (1972), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York)
[3] Hoffmann, K.-H.; Khludnev, A. M., Fictitious domain method for the Signorini problem in a linear elasticity, Adv. Math. Sci. Appl., 14, 2, 465-481 (2004) · Zbl 1134.74368
[4] Khludnev, A. M., Theory of cracks with possible contact between crack faces, Russ. Survey Mech., 3, 4, 41-82 (2005)
[5] Khludnev, A.M., 2009. On a crack located at the boubdary of rigid inclusion. Preprint of IGiL SO RAN, N 1-09, 1-18.; Khludnev, A.M., 2009. On a crack located at the boubdary of rigid inclusion. Preprint of IGiL SO RAN, N 1-09, 1-18.
[6] Khludnev, A. M.; Kovtunenko, V. A., Analysis of Cracks in Solids (2000), WIT Press: WIT Press Southampton/Boston
[7] Khludnev, A. M.; Ohtsuka, K.; Sokolowski, J., On derivative of energy functional for elastic bodies with cracks and unilateral conditions, Quart. Appl. Math., 60, 1, 99-109 (2002) · Zbl 1075.74040
[8] Khludnev, A. M.; Sokolowski, J., The derivative of the energy functional along the crack length in problems of the theory of elasticity, J. Appl. Math. Mech., 64, 449-456 (2000) · Zbl 1017.74059
[9] Khludnev, A. M.; Tani, A., Unilateral contact problems for two inclined elastic bodies, Eur. J. Mech. A/Solids, 27, 3, 365-377 (2008) · Zbl 1154.74372
[10] Kovtunenko, V. A., Invariant energy integrals for the non-linear crack problem with possible contact of the crack surfaces, J. Appl. Math. Mech., 67, 99-110 (2003) · Zbl 1067.74562
[11] Leblond, J. B., Basic results for elastic fracture mechanics with frictionless contact between crack lips, Eur. J. Mech. A/Solids, 19, 633-647 (2000) · Zbl 0966.74006
[12] Rudoy, E. M., Differentiation of energy functionals in two-dimensional elasticity theory for solids with curvilinear cracks, J. Appl. Mech. Tech. Phys., 45, 843-852 (2004) · Zbl 1087.74008
[13] Rudoy, E. M., Differentiation of energy functional in the problem for curvilinear crack with possible contact between crack faces, Izvesiya RAN, 6, 113-127 (2007)
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