Geodesic
Optimal control of a rigidity parameter of thin inclusions in elastic bodies with curvilinear cracks
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 135-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper concerns an optimal control problem for a 2D elastic body with a thin rigid inclusion and a crack. Inequality type boundary conditions are imposed at the crack faces to provide a mutual non-penetration between the crack faces. The cost functional characterizes a derivative of the energy functional with respect to the crack length. A rigidity of the inclusion is considered as a control function. The main result consists in a proof of the solution existence to the optimal control problem.
Keywords: crack, thin inclusion, nonlinear boundary conditions, optimal control, derivative of energy functional. 
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     title = {Optimal control of a~rigidity parameter of thin inclusions in elastic bodies with curvilinear cracks},
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V. V. Shcherbakov. Optimal control of a rigidity parameter of thin inclusions in elastic bodies with curvilinear cracks. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 135-149. http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a11/

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