heat conduction, circular plates, honeycomb structures, fiber composites, analytical solutions.

Use of piecewise-linear conditions of plasticity has allowed to receive whole number of deep and impressive analytical decisions flat and spatial tasks of the theory of plastic deformation [1], [2]. It is possible to hope that use kusochno of linear potentials will be useful as well at the decision and return tasks of the theory of plasticity. One of the most important in the theory plasticity the problem of optimum design of structures, the general is which statement has been formulated [3]–[5] over fifty years ago. The systems of the equations describing optimum projects under plasticity conditions Mises and the Treske, have been investigated in works [4]–[8]. It has been established that the systems of the resolving equations tasks of optimum design for smooth condition of plasticity (like Mises–Hill) are nonlinear systems of mixed-compound type.

Nemirovskii Yuri Vladimirovich, Dr. Sci. Phys. & Math., Professor, Leading Research Worker, S. Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the RAS, Novosibirsk, Russia.