Fankina, Irina Vladimirovna On the equilibrium problem for a two-layer structure with the upper layer covering a defect tip. (Russian. English summary) Zbl 1435.35373 Sib. Èlektron. Mat. Izv. 17, 141-160 (2020). Summary: The equilibrium problem of a two-layer elastic structure is investigated. In the lower layer there is a rectilinear defect. The upper layer covers one of the defect tips and is glued to the lower layer along its edge. Nonlinear boundary conditions are used to model the defect. Using the variational approach, the existence of a solution of the problem is established. Passages to the limit in the problem with respect to a parameter characterizing the elasticity of the upper layer, as well as to the defect damage parameter are carried out. The optimal control problem is considered, in which the cost functional is the derivative of the energy functional with respect to the defect length, and two parameters mentioned above act as control functions. The solvability of the optimal control problem is proved. Cited in 1 Document MSC: 35Q74 PDEs in connection with mechanics of deformable solids 74R10 Brittle fracture 74M05 Control, switches and devices (“smart materials”) in solid mechanics 35Q93 PDEs in connection with control and optimization 93C20 Control/observation systems governed by partial differential equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35A15 Variational methods applied to PDEs 74B20 Nonlinear elasticity 49J40 Variational inequalities Keywords:two-layer structure; nonpenetration condition; defect; damage parameter; variational inequality; optimal control problem × Cite Format Result Cite Review PDF Full Text: DOI References: [1] A.M. Khludnev,On modeling elastic bodies with defects, Sib. Electron. Math. Izv.,15(2018), 153-166. Zbl 1390.35354 · Zbl 1390.35354 [2] A.M. Khludnev,On thin inclusions in elastic bodies with defects, Z. Angew. Math. Phys., 70:45 (2019). 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