Abstract
We consider the equilibrium problem for elastic bodies with thin rigid inclusions under the action of external forces. It is assumed that there is a delamination crack in the domain and linear boundary conditions are imposed on the crack faces. We study the dependence of the solution on perturbations of the domain shape. We calculate the material derivative of the solution with respect to the shape perturbation parameter. To illustrate the obtained result, we compute the derivative of the energy functional with respect to the domain shape and write a necessary condition for the problem of optimization of the length of a rigid inclusion. We derive a differential equation and bounded conditions for the derivative of the solution with respect to the length of the rigid inclusion. Bibliography: 14 titles.
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