On an optimal control problem for the shape of thin inclusions in elastic bodies
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An optimal control problem is considered for a two-dimensional elastic body with a straight thin rigid inclusion and a crack adjacent to it. It is assumed that the thin rigid inclusion delaminates and has a kink. On the crack faces the boundary conditions are specified in the form of equalities and inequalities which describe the mutual nonpenetration of the crack faces. The derivative of the energy functional along the crack length is used as the objective functional, and the position of the kink point, as the control function. The existence is proved of the solution to the optimal control problem.
Keywordscrack thin rigid inclusion nonlinear boundary conditions optimal control derivative of energy functional
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