Differentiation of energy functional with respect to delamination's length in problem of contact between plate and beam

The paper considers a model which describes a contact between an elastic plate and an elastic beam. In this model, there may be a delamination, i. e. the displacements of the plate and the beam may not coincide on a part of beam's midline. The purposes of the research are to prove the differentiability of the energy functional with respect to the delamination's length and to find the explicit formula for the corresponding derivative.