Critères d’injectivité et de surjectivité pour certaines applications de ℝ n dans lui-même ; application à la mécanique du contact
Alart, Pierre
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 27 (1993), p. 203-222 / Harvested from Numdam
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Publié le : 1993-01-01
@article{M2AN_1993__27_2_203_0,
     author = {Alart, Pierre},
     title = {Crit\`eres d'injectivit\'e et de surjectivit\'e pour certaines applications de $\mathbb {R}^n$ dans lui-m\^eme ; application \`a la m\'ecanique du contact},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {27},
     year = {1993},
     pages = {203-222},
     mrnumber = {1211616},
     zbl = {0767.73064},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/M2AN_1993__27_2_203_0}
}

Alart, Pierre. Critères d’injectivité et de surjectivité pour certaines applications de $\mathbb {R}^n$ dans lui-même ; application à la mécanique du contact. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 27 (1993) pp. 203-222. http://gdmltest.u-ga.fr/item/M2AN_1993__27_2_203_0/

[1] G. Duvaut, 1982, Loi de frottement non locale, J. Méc. Th. et Appl., numéro spécial, 73-78. | MR 670346 | Zbl 0497.73115

[2] J. Necas, J. Jarusek, J. Haslinger, 1980, On the Solution of the Variational Inequatlity to the Signorini Problem with Small Friction, Bolletino U.M.I, (5) 17. B, 796-811. | MR 580559 | Zbl 0445.49011

[3] A. Klarbring, 1985, Contact Problems in Linear Elasticity, Ph. D. Thesis n° 133, University of Linkoping.

[4] P. Alart, A. Curnier, 1991, A Mixed Formulation for Frictional Contact Problems Prone to Newton like Solution Methods, Computer Methods in Applied Mechanics and Engineering, 92, (3), 353-375. | MR 1141048 | Zbl 0825.76353

[5] I. Capuzzo Dolcetta, U. Mosco, 1979, Implicit Complementarity Problems and Quasi-Vanational Inequalities, in Gianessi, Cottle, Lions eds, Variiational Inequalities and Complementarity Problems, J. Wiley. | Zbl 0486.49004

[6] V. Janovsky, 1981, Catastrophic Features of Coulomb Friction Model, Proc. Mathematics of Elements and Applications, Brunel University. | Zbl 0504.73077

[7] A. Curnier, P. Alart, 1988, A Generalized Newton Method for Contact Problem with Friction, J. Méc. Th. Et Appl., numéro spécial : Numerical Methods in Mechanics of Contact Involving Friction, 67-82. | MR 988336 | Zbl 0679.73046

[8] F. H. Clarke, 1983, Optimization and Nonsmooth Analysis, Wiley. | MR 709590 | Zbl 0582.49001

[9] T. Parthasarathy, 1983, On Global Univalence Theorems, Lecture Notes, 977, Springer Verlag. | MR 694845 | Zbl 0506.90001

[10] S. Banach, S. Mazur, 1934, Uber mehrdeutige stetige abbildungen, Studia Math. 5, 174-178. | JFM 60.1227.03

[11] M. Kojima, R. Saigal, 1979, A Study of PC1 Homeomorphisms on Subdivided Polyhedrons, SIAM J. Math. Anal., 10, (6), 1299-1312. | MR 547815

[12] J. Ortega, W. Rheinbolt, 1970, Iterative Solutions of Non Linear Equations on Several Variables, Academic Press, New York. | Zbl 0241.65046

[13] M. Kojima, R. Saigal, 1980, On the Relationship between Conditions that Insure a PL Mapping is a Homeomorphism, Mathematics of Operations Research, 5, (1). | MR 561158 | Zbl 0441.57018

[14] R. S. Palais, 1959, Natural Operations on Differential Forms, Trans. Amer. Math. Soc., 92, 125-141. | MR 116352 | Zbl 0092.30802

[15] C. Licht, E. Pratt, M. Raous, 1990, Remarks on a Numerical Method for Unilateral Contact Including Friction, in «Unilateral Problems in Structural Analysis», Capri, Juin 89, ed. CISM. | MR 1169548 | Zbl 0762.73076

[16] C. Mellouki-Filali, 1988, Problème des milieux continus en contact avec frottement ; stabilité et convergence des algorithmes numériques, thèse de 3e cycle, Université Montpellier II.