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. 
@article{SJIM_2013_16_1_a13,
     author = {V. V. Shcherbakov},
     title = {On an optimal control problem of thin inclusions shapes in elastic bodies},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {138--147},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a13/}
}
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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/