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Nečas, Jindřich; Hlaváček, Ivan

Solution of Signorini’s contact problem in the deformation theory of plasticity by secant modules method. (English) Zbl 0512.73097

Apl. Mat. 28, No. 3, 199-214 (1983).
Reviewer: H. Bufler
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0512.73097

Cited in 10 Documents

MSC:

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
49J40 Variational inequalities

Keywords:

Kachanov’s iterative method; elastostatics; deformation; unilateral contact; elastoplastic body; rigid foundation; neglecting friction; governed by Hencky-von Mises stress strain relations; weak solution; minimum of potential energy; corresponding variational inequality; secant modules; classical Signorini’s problem; convergence; no numerical applications
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\textit{J. Nečas} and \textit{I. Hlaváček}, Apl. Mat. 28, 199--214 (1983; Zbl 0512.73097)
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References:

[1] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies. Elsevier, Amsterdam 1981.
[2] J. Haslinger I. Hlaváček: Contact between elastic bodies. Apl. mat. 25 (1980), 324-348, 26 (1981), 263-290, 321-344.
[3] I. Hlaváček J. Nečas: On inequalities of Korn’s type. Arch. Ratl. Mech. Anal., 36 (1970), 305-334. · Zbl 0193.39001
[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.
[5] L. M. Kačanov: Mechanika plastičeskich sred. Moskva 1948.
[6] G. Fichera: Boundary value problems of elasticity with unilateral constraints. S. Flüge (ed): Encycl. of Physics, vol. VIa/2, Springer-Verlag, Berlin, 1972.
[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. · Zbl 0369.65031
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