Contact problem for a stringer plate weakened by a periodic system of variable width slots

We consider an elastic isotropic plate reinforced by stringers and weakened by a periodic system of rectilinear slots of variable width. The variable width of the slots is comparable with elastic deformations. We study the case when the slots faces get in contact at some area. Determination of parameters characterizing the partial closure of variable width slots is reduced to the solution of a singular integral equation. The action of the stringers is replaced with unknown equivalent concentrated forces at the points of their connection with the plate. The contact stresses and contact zone sizes are found from the solution of the singular integral equation.