Equilibrium problem for a Kirchhoff–Love plate contacting by the side edge and the bottom boundary

A new model of a Kirchhoff–Love plate which is in contact with a rigid obstacle of a certain given configuration is proposed in the paper. The plate is in contact either on the side edge or on the bottom surface. A corresponding variational problem is formulated as a minimization problem for an energy functional over a non-convex set of admissible displacements subject to a non-penetration condition. The inequality type non-penetration condition is given as a system of inequalities that describe two cases of possible contacts of the plate and the rigid obstacle. Namely, these two cases correspond to different types of contacts by the plate side edge and by the plate bottom. The solvability of the problem is established. In particular case, when contact zone is known equivalent differential statement is obtained under the assumption of additional regularity for the solution of the variational problem.