Thin inclusion in elastic body: identification of damage parameter

• Autorzy: Khludnev Alexander
• Języki publikacji: EN

Abstrakty

EN

In the paper, we consider an equilibrium problem for a 2D elastic body with a thin elastic inclusion crossing an external boundary. The elastic body has a defect which is characterized by a positive damage parameter. The presence of a defect means that the problem is formulated in a non-smooth domain. Non-linear boundary conditions at the defect faces are imposed to prevent the mutual penetration between the faces. Both variational and differential problem formulations are proposed, and existence of solutions is established. We study an asymptotics of solutions with respect to the damage parameter as well as with respect to a rigidity parameter of the inclusion. Identification problems for finding the damage parameter are investigated. To this end, existence of solutions of optimal control problems is proven.

Słowa kluczowe

EN

thin inclusion; defect; damage parameter; non-penetration boundary conditions; optimal control

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2019
• Tom: Vol. 48, No. 1
• Strony: 13--29
• Opis fizyczny: Bibliogr. 22 poz., rys.

Twórcy

autor

Khludnev Alexander

• Lavrentyev Institute of Hydrodynamics of RAS, and Novosibirsk State University, Novosibirsk 630090, Russia

Bibliografia

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• [3] KHLUDNEV, A. M. and KOVTUNENKO, V.A. (2000) Analysis of Cracks in Solids. WIT Press, Southampton-Boston.
• [4] KHLUDNEV, A.M. (2010) Elasticity problems in non-smooth domains. Fizmatlit, Moscow.
• [5] KHLUDNEV, A.M. (2015) Thin inclusions in elastic bodies crossing an external boundary. Z. Angew. Math. Mech., 95 (11), 1256-1267.
• [6] KHLUDNEV, A.M. (2017) Rigidity parameter identification for thin inclusions located inside elastic bodies. J. Opt. Theory Appl., 172 (1), 281-297.
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• [18] RUDOY, E.M. (2011) Asymptotics of energy functional for elastic body with a crack and rigid inclusion. 2D case. Appl. Math. Mechs, 75 (2), 719-729.
• [19] SACCOMANDI, G. and BEATTY, M.F. (2001) Universal relations for fiberreinforced elastic materials. Mathematics and Mechanics of Solids, 7, 99-110.
• [20] SHCHERBAKOV, V.V. (2014a) Optimal control of rigidity parameter of thin inclusions in elastic bodies with curvilinear cracks. J. Math. Sciences, 203(4), 591-604.
• [21] SHCHERBAKOV, V.V. (2014b) Existence of an optimal shape of the thin rigid inclusions in the Kirchhoff-Love plate. J. Appl. Industrial Mathematics, 8(1), 97-105.
• [22] YAO, J. (2015) Instability of a composite reinforced with coated inclusions due to interface debonding. Arch. Appl. Mech., 85(4), 415-432.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).