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A finite element analysis for the Signorini problem in plane elastostatics. (English) Zbl 0369.65031


MSC:

74S05 Finite element methods applied to problems in solid mechanics
49R50 Variational methods for eigenvalues of operators (MSC2000)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
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References:

[1] Signorini A.: Questioni di elasticità non linearizzata o semi-linearizzata. Rend. di Matem. e delle sue appl. 18 (1959). · Zbl 0091.38006
[2] Fichera G.: Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno. Mem. Ace. Naz. Lincei, s. VIII., 7, f. 5 (1964). · Zbl 0146.21204
[3] Fichera G.: Boundary Value Problems of Elasticity with Unilateral Constraints. Encycl. of Physics (ed. by S. Flügge), vol. VIa/2. Springer, Berlin 1972.
[4] Hlaváček I.: Dual Finite Element Analysis for Unilateral Boundary Value Problems. Apl. Mat. 22 (1977), 14-51.
[5] Nečas J.: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. · Zbl 1225.35003
[6] Scarpini F., Vivaldi M.: Error Estimates for the Approximation of Some Unilateral Problems. R.A.I.R.O. (1977). · Zbl 0358.65087
[7] Céa J.: Optimisation, théorie et algorithmes. Dunod, Paris 1971. · Zbl 0211.17402
[8] Frémond M.: Dual Formulations for Potential and Complementary Energies. Mathematics of Finite Elements and Appl. (ed. by J. R. Whiteman), Academic Press, 1973. · Zbl 0297.73062
[9] Panagiotopoulos P. D.: Unilateral Problems in the Theory of Elasticity. Ing. Archiv. 44, (1975), 421-432. · Zbl 0332.73018
[10] Mosco U., Strang G.: One-sided Approximations and Variational Inequalities. Bull. Amer. Math. Soc. 80 (1974), 308-312. · Zbl 0278.35026
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