Geodesic
On an optimal control problem of thin inclusions shapes in elastic bodies
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 138-147

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The paper concerns an optimal control problem for a 2D elastic body with a thin rigid inclusion and a crack. The thin rigid inclusion is supposed to delaminate and contain a kink. Inequality type boundary conditions are imposed at the crack faces to provide a mutual nonpenetration between the crack faces. The cost functional characterizes the derivative of the energy function with respect to the crack length. The position of the kink is considered as a control function. The main result is the existence of a solution to the optimal control problem.
Keywords: crack, thin rigid inclusion, nonlinear boundary conditions, optimal control, derivative of energy functional. 
V. V. Shcherbakov. On an optimal control problem of thin inclusions shapes in elastic bodies. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 138-147. http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a13/
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