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Title: Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method (English)
Author: Nečas, Jindřich
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 28
Issue: 3
Year: 1983
Pages: 199-214
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level. (English)
Keyword: Kachanov’s iterative method
Keyword: elastostatics
Keyword: deformation
Keyword: unilateral contact
Keyword: elastoplastic body
Keyword: rigid foundation
Keyword: neglecting friction
Keyword: governed by Hencky-von Mises stress strain relations
Keyword: weak solution
Keyword: minimum of potential energy
Keyword: corresponding variational inequality
Keyword: secant modules
Keyword: classical Signorini’s problem
Keyword: convergence
Keyword: no numerical applications
MSC: 49A29
MSC: 49J40
MSC: 58E35
MSC: 73E99
MSC: 73T05
MSC: 74A55
MSC: 74C99
MSC: 74G30
MSC: 74H25
MSC: 74M15
idZBL: Zbl 0512.73097
idMR: MR0701739
DOI: 10.21136/AM.1983.104027
Date available: 2008-05-20T18:22:13Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies.Elsevier, Amsterdam 1981.
Reference: [2] J. Haslinger I. Hlaváček: Contact between elastic bodies.Apl. mat. 25 (1980), 324-348, 26 (1981), 263-290, 321-344.
Reference: [3] I. Hlaváček J. Nečas: On inequalities of Korn's type.Arch. Ratl. Mech. Anal., 36 (1970), 305-334. MR 0252844, 10.1007/BF00249518
Reference: [4] J. Nečas: On regularity of solutions to nonlinear variational inequalities for second-order elliptic systems.Rend. di Matematica 2 (1975), vol. 8, Ser. VL, 481-498. MR 0382827
Reference: [5] L. M. Kačanov: Mechanika plastičeskich sred.Moskva 1948.
Reference: [6] G. Fichera: Boundary value problems of elasticity with unilateral constraints.In: S. Flüge (ed): Encycl. of Physics, vol. VIa/2, Springer-Verlag, Berlin, 1972.
Reference: [7] I. Hlaváček J. Lovíšek: A finite element analysis for the Signorini problem in plane elastostatics.Apl. mat. 22, (1977) 215-228, 25 (1980), 273-285. MR 0446014


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