Critères d’injectivité et de surjectivité pour certaines applications de ℝ n dans lui-même ; application à la mécanique du contact

Pierre Alart

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1993)

  • Volume: 27, Issue: 2, page 203-222
  • ISSN: 0764-583X

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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 27.2 (1993): 203-222. <http://eudml.org/doc/193701>.

@article{Alart1993,
author = {Alart, Pierre},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nondifferentiable continuous mappings; Clarke's generalized Jacobian; homotopy approach; uniqueness conditions; contact problems with friction},
language = {fre},
number = {2},
pages = {203-222},
publisher = {Dunod},
title = {Critères d’injectivité et de surjectivité pour certaines applications de $\mathbb \{R\}^n$ dans lui-même ; application à la mécanique du contact},
url = {http://eudml.org/doc/193701},
volume = {27},
year = {1993},
}

TY - JOUR
AU - Alart, Pierre
TI - Critères d’injectivité et de surjectivité pour certaines applications de $\mathbb {R}^n$ dans lui-même ; application à la mécanique du contact
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1993
PB - Dunod
VL - 27
IS - 2
SP - 203
EP - 222
LA - fre
KW - nondifferentiable continuous mappings; Clarke's generalized Jacobian; homotopy approach; uniqueness conditions; contact problems with friction
UR - http://eudml.org/doc/193701
ER -

References

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  1. [1] G. DUVAUT, 1982, Loi de frottement non locale, J. Méc. Th. et Appl., numéro spécial, 73-78. Zbl0497.73115MR670346
  2. [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. Zbl0445.49011MR580559
  3. [3] A. KLARBRING, 1985, Contact Problems in Linear Elasticity, Ph. D. Thesis n° 133, University of Linkoping. 
  4. [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. Zbl0825.76353MR1141048
  5. [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. Zbl0486.49004
  6. [6] V. JANOVSKY, 1981, Catastrophic Features of Coulomb Friction Model, Proc. Mathematics of Elements and Applications, Brunel University. Zbl0504.73077
  7. [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. Zbl0679.73046MR988336
  8. [8] F. H. CLARKE, 1983, Optimization and Nonsmooth Analysis, Wiley. Zbl0582.49001MR709590
  9. [9] T. PARTHASARATHY, 1983, On Global Univalence Theorems, Lecture Notes, 977, Springer Verlag. Zbl0506.90001MR694845
  10. [10] S. BANACH, S. MAZUR, 1934, Uber mehrdeutige stetige abbildungen, Studia Math. 5, 174-178. Zbl60.1227.03JFM60.1227.03
  11. [11] M. KOJIMA, R. SAIGAL, 1979, A Study of PC1 Homeomorphisms on Subdivided Polyhedrons, SIAM J. Math. Anal., 10, (6), 1299-1312. MR547815
  12. [12] J. ORTEGA, W. RHEINBOLT, 1970, Iterative Solutions of Non Linear Equations on Several Variables, Academic Press, New York. Zbl0241.65046
  13. [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). Zbl0441.57018MR561158
  14. [14] R. S. PALAIS, 1959, Natural Operations on Differential Forms, Trans. Amer. Math. Soc., 92, 125-141. Zbl0092.30802MR116352
  15. [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. Zbl0762.73076MR1169548
  16. [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. 

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