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Generalized solutions of the dynamic problem of perfect elastoplasticity. (English. Russian original) Zbl 0604.73027

J. Appl. Math. Mech. 49, 503-509 (1985); translation from Prikl. Mat. Mekh. 49, 655-662 (1985).
The concept of a generalized solution of an initial boundary value problem for the system of Prandtl-Reuss equations is introduced. It is shown that a generalized solution exists and is unique, and represents within the domain of elasticity a solution of the initial-boundary value problem of the dynamic theory of elasticity. An effective method for the approximate determination of the generalized solution is given, and conditions at its strong discontinuities are obtained. The basic results of this paper were published earlier without proof e.g. in Usp. Mat. Nauk 37, No.5(227), 189-190 (1982; Zbl 0513.73039).

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
35A15 Variational methods applied to PDEs
74C99 Plastic materials, materials of stress-rate and internal-variable type
46N99 Miscellaneous applications of functional analysis
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References:

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