Abstract
We study the mixed boundary value problem for equations of two-diemensional theory of elasticity in a domain with a cut with unilateral constraints for the solutions on the cut. It is assumed that the solution belongs to the space of rigid displacements in a part of the domain, i.e., has a given structure. Under rather general sufficiently smooth perturbations of the domain, we obtain an expression for the derivative of the energy functional with respect to the perturbation parameter.
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