Equilibrium problem for a Kirchhoff–Love plate contacting with the lateral surface along a strip of a given width

A new model of a Kirchhoff–Love plate is justified, which may come into contact by its lateral surface with a non-deformable obstacle along a strip of a given width. The non-deformable obstacle restricts displacements of the plate along the outer lateral surface. The obstacle is specified by a cylindrical surface, the generatrices of which are perpendicular to the midplane of the plate. A problem is formulated in variational form. A set of admissible displacements is determined in a suitable Sobolev space in the framework of a clamping condition and a non-penetration condition of the Signorini type. The non-penetration condition is given as a system of two inequalities. The existence and uniqueness of a solution to the problem is proven. An equivalent differential formulation and optimality conditions are found under the assumption of additional regularity of the solution to the variational problem. A qualitative connection has been established between the proposed model and a previously studied problem in which the plate is in contact over the entire lateral surface.