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Approximation of the Signorini problem with friction by a mixed finite element method. (English) Zbl 0486.73099


MSC:

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

[1] Aubin, J. P., Approximation of Elliptic Boundary Value Problems (1972), Wiley-Interscience: Wiley-Interscience New York
[2] Duvaut, G.; Lions, J. L., Les inéquations en mécanique et en physique (1972), Dunod: Dunod Paris · Zbl 0298.73001
[3] Ekeland, I.; Temam, R., Analyse convex et problèmes variationnelles (1974), Dunod: Dunod Paris
[4] Haslinger, J., Mixed formulation of elliptic variational inequalities and its approximation, Apl. Mat., 26, 462-475 (1981) · Zbl 0483.49003
[5] Haslinger, J.; Hlaváček, I., Contact between elastic bodies. Part III. Dual finite element analysis, Apl. Mat., 26, 321-344 (1981) · Zbl 0513.73088
[6] Hlaváček, I.; Lovíšek, J., A finite element analysis of the Signorini problem in plane elastostatics, Apl. Mat., 22, 215-228 (1977) · Zbl 0369.65031
[7] Nečas, J.; Hlaváček, I., On inequalities of Korn’s type, Arch. Rat. Mech. Anal., 36, 304-334 (1970) · Zbl 0193.39002
[8] Nečas, J.; Jarušek, J.; Haslinger, J., On the solution of the variational inequality to the Signorini problem, Boll. Un. Mat. Ital. B (5), 17, 796-811 (1980) · Zbl 0445.49011
[9] Oden, J. F.; Kikuchi, N., Contact Problems in Elasiticity, (TICOM Report 79-8 (July 1979), University of Texas at Austin)
[10] Panagiotopoulos, P. D., A non-linear programming approach to the unilateral contact-and friction-boundary value problem in the theory of elasticity, Ingr.-Arch., 44, 421-432 (1975) · Zbl 0332.73018
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