Geodesic
Optimal location of a rigid inclusion for an equilibrium problem describing Kirchhoff–Love plate with nonpenetration conditions for known configurations of plate edges
Matematičeskie zametki SVFU, Tome 28 (2021) no. 2, pp. 16-33 Cet article a éte moissonné depuis la source Math-Net.Ru

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A nonlinear model describing equilibrium of a cracked plate with a volume rigid inclusion is studied. It is assumed that under the action of certain given loads, plates have deformations with a certain predetermined configuration of edges near the crack. On the crack curve we impose a nonlinear boundary condition as a system of inequalities and an equality describing the nonpenetration of the opposite crack faces. For a family of variational problems, we study the dependence of their solutions on the location of the inclusion. We formulate an optimal control problem with a cost functional defined by an arbitrary continuous functional on a suitable Sobolev space. For this problem, the location parameter of the inclusion serves as a control parameter. We prove continuous dependence of the solutions on the location parameter and the existence of a solution to the optimal control problem.
Keywords: variational inequality, crack, nonpenetration conditions, optimal control problem, rigid inclusion. 
@article{SVFU_2021_28_2_a1,
     author = {N. P. Lazarev and E. F. Sharin and G. M. Semenova},
     title = {Optimal location of a rigid inclusion for an equilibrium problem describing {Kirchhoff{\textendash}Love} plate with nonpenetration conditions for known configurations of plate edges},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {16--33},
     year = {2021},
     volume = {28},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2021_28_2_a1/}
}
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N. P. Lazarev; E. F. Sharin; G. M. Semenova. Optimal location of a rigid inclusion for an equilibrium problem describing Kirchhoff–Love plate with nonpenetration conditions for known configurations of plate edges. Matematičeskie zametki SVFU, Tome 28 (2021) no. 2, pp. 16-33. http://geodesic.mathdoc.fr/item/SVFU_2021_28_2_a1/