Elastoplastic problem for a plate with partially unknown boundary

In this paper there is considered the Elastoplastic problem for infinite plate, that is weakened by two identical square holes. The boundaries of the holes are partially unknown contours. The plate is in a stressed state, a region of plasticity contains only unknown parts of holes contours and does not spread inside of the plate. Applying the theory of functions of a complex variable and the conformal mapping theory the problem is reduced to a boundary value problem of the analytic function theory and the solution of this problem is obtained, the unknown parts of the holes contours are defined.