Fictitious domain method for an equilibrium problem of the Timoshenko-type plate with a crack crossing the external boundary at zero angle

The equilibrium problems for homogeneous and inhomogeneous plates with a crack is considered. We impose the nonpenetration condition, which has the form of inequality (such as Signorini type condition), on the crack faces. In this paper, we deal with the cases that the crack intersects the external boundary at zero angle (on the mid-plane). Using the fictitious domain method, we establish the unique solvability of four equilibrium problems for different cases of non-Lipschitz domains. In these cases a precise connection between equilibrium problems for a plate contacting with a rigid obstacle and for a plate with a crack is identified.