×
Kuksin, S. B.

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).

Cited in 1 Document

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

Keywords:

method of monotone semigroups; initial boundary value problem; system of Prandtl-Reuss equations; dynamic theory of elasticity; approximate determination of the generalized solution; strong discontinuities

Citations:

Zbl 0534.73029; Zbl 0513.73039
PDF BibTeX XML Cite
\textit{S. B. Kuksin}, J. Appl. Math. Mech. 49, 503--509 (1985; Zbl 0604.73027); translation from Prikl. Mat. Mekh. 49, 655--662 (1985)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Kuksin, S.B., Use of monotonic semigroups in the theory of perfect elastoplasticity, Uspekhi matem. nauk, 37, 5, (1982) · Zbl 0513.73039
[2] Kuksin, S.B., Mathematical correctness of the boundary value problems of ideal elastoplasticity, Uspekhi matem. nauk, 38, 2, (1983) · Zbl 0596.73016
[3] Freudenthal, A.; Geiringer, H., Mathematical theories of inelastic continua, (1962), Fizmatgiz Moscow · Zbl 0106.17101
[4] Klyushnikov, V.D., Mathematical theory of plasticity, (1979), Izd-vo MGU Moscow · Zbl 0482.73026
[5] Mosolov, P.P.; Myasnikov, V.P., Mechanics of rigid-plastic media, (1981), Nauka Moscow · Zbl 0551.73002
[6] Duvaut, G.; Lions, J.L., Inequalities in mechanics and physics, (1976), Springer-Verlag Berlin · Zbl 0331.35002
[7] Alekseyev, V.M.; Tikhomirov, V.M.; Fomin, S.V., Optimal control, (1979), Nauka Moscow · Zbl 0516.49002
[8] Brezis, H., Operateurs maximaux monotones et semigroupes de contractions dans LES espaces de Hilbert, (1973), L. North-Holland Amsterdam · Zbl 0252.47055
[9] Rochafellar, R.T., Convex analysis, (1970), Princeton Univ. Press Princeton, N.Y
[10] Ovsyannikov, L.V., Lectures on the fundamentals of gas dynamics, (1981), Nauka Moscow · Zbl 0539.76079
[11] Teman, R., Navier-Stokes equations, (1977), North-Holland Amsterdam-Oxford · Zbl 0406.35053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.