Khludnev, Aleksandr Mikhaĭlovich On modeling elastic bodies with defects. (English) Zbl 1390.35354 Sib. Èlektron. Mat. Izv. 15, 153-166 (2018). In this paper, the author considers some mathematical analysis problems on the equilibrium for 2D elastic bodies with thin defects, which are characterized with a damage parameter. Solution existence of the problems considered is proved, and different equivalent problem formulations are proposed. Dependence of solutions on the damage parameter and the defect length is investigated. The author derives a formula for the derivative of the energy functional with respect to the defect length and prove that the formula can be written in the form of an invariant integral. An optimal control problem is investigated with a cost functional equal to the derivative of the energy functional with respect to the defect length, and the damage parameter being a control function. Reviewer: Dongbing Zha (Shanghai) Cited in 11 Documents MSC: 35Q74 PDEs in connection with mechanics of deformable solids 35Q93 PDEs in connection with control and optimization 35B40 Asymptotic behavior of solutions to PDEs 74B20 Nonlinear elasticity 35A15 Variational methods applied to PDEs 74R05 Brittle damage 93C23 Control/observation systems governed by functional-differential equations Keywords:defect; damage parameter; non-penetration boundary conditions; variational inequality; optimal control; derivative of energy functional × Cite Format Result Cite Review PDF Full Text: DOI References: [1] S. Almi, {\it Energy release rate and quasi-static evolution via vanishing viscosity in a fracture}{\it model depending on the crack opening }, ESAIM: COCV, 23:3 (2017), 791-826. MR3660449 · Zbl 1373.49011 [2] M. Bach, A.M. Khludnev, V.A. Kovtunenko, {\it Derivatives of the energy functional for 2D-}{\it problems with a crack under Signorini and friction conditions}, Math. Meth. Appl. 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