Equilibrium problem for a Timoshenko plate contacting by its lateral surface along a strip of a given width

A new model of a transversally isotropic Timoshenko plate is justified, which may come into contact by its side surface with a non-deformable obstacle along a strip of a given width. The non-deformable obstacle restricts displacements and rotation angles of the plate along the outer side edge. The obstacle is defined by a cylindrical surface, the generatrices of which are perpendicular to the middle plane of the plate. A problem is formulated in variational form. A set of admissible displacements is specified in a suitable Sobolev space in the framework of a clamping condition and a non-penetration condition. 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 is 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 side surface.