| Abstract: | The mathematical content of variational problems of the mechanics of rigid-plastic media reduces to minimizing convex functionals in non-reflexive spaces of solenoidal vector fields. Different formulations are presented in /1/. Problems are examined there in which discontinuous velocity fields occur. The initial functional is undetermined in such fields. In this connection, the problem is posed of constructing that extension of the original set of kinematically allowable velocity fields as would contain all their possible discontinuities allowed by the mechanics of rigidly plastic media, and of continuing the original functional into the extension obtained. This problem is solved in this paper for the case when the velocity field is given on the whole surface of the rigid-plastic body. |
