Equilibrium problem for a Timoshenko plate with a cohesion of the edges of a defect on the front surface

The issues of mathematical correctness for a new model of a plate containing a defect with certain properties are investigated. To describe the properties of the defect, the well-known mathematical model of the Timoshenko plate with inequality-type conditions on crack faces is taken as a basis. It is assumed that the defect depends on the damage parameter, which characterizes the interaction of the crack faces. Unique solvability of the corresponding variational problem is proved. Limit passages with respect to the damage parameter are studied. In particular, it is established that for a family of problems for the plates with the defect, as the damage parameter tends to infinity, a problem for a Timoshenko plate with a vertical through crack is obtained as a limit problem.