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

Abstract

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.