isotropic medium, slot of variable width, end zones of slot, contact of slot faces, stick of slot faces, slipping of slot faces, body forces.

A plane problem on compression of homogeneous plane with a slot of variable width is considered. The compression of the plane is carried out by body forces. The variable width of the slot is comparable with elastic deformations. Slot faces are under internal pressure. It is assumed that the slot has end zones in a state of plastic flow of the material. Case of occurrence of several sections of the slot faces contact is investigated. It is assumed that in some part of the contact section a stick of the slot faces occurs and in the remaining part a slippage of the slot faces is possible. Equilibrium problem for the slot with partially contacting bonds under the influence of body and surface loads is reduced to a problem of linear conjugation of analytic functions. Contact stresses, sizes of the contact, stick and end zones are found.

Mirsalimov Vagif e-mail: mir-vagif@mail.ru, Doctor of Physical and Mathematical Sciences, Professor, Azerbaijan Technical University, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.