Mechanics of Solids

The uniqueness of solution in the small sense of tasks of equally-stressed reinforcement of composite metal plates in conditions of steady-state creep

A. P. Yankovskii

Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation

Abstract: The uniqueness of a solution in the small sense (in the sense of lack of infinitely close solution) is proved for the boundary-value problem of equally-stressed reinforcing metal composite plates in conditions of steady creep of materials of all phases of the composition, when in addition to static and kinematic boundary conditions and boundary conditions for the densities of the reinforcement, which is natural in such problems, on the contour of the plates an additional boundary conditions are specified for angles of reinforcement. In a large sense (in the sense of significant differences solution) this problem can have multiple, but not infinitely close, alternative solutions because of the nonlinearity of the static boundary conditions and equally-stressed of reinforcement. The study of the problem of uniqueness of the solution of this problem is necessary when examining the issue of correctness setting of problems of equally-stressed of reinforcement.

Keywords: equal-stressed reinforcement, metal-composite plate, steady-state creep, uniqueness of solution, correctness of boundary value problem.

UDC: 539.376

MSC: 74K20, 74R20

Original article submitted 17/X/2014
revision submitted – 27/XI/2014

DOI: 10.14498/vsgtu1346

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