A symmetric boundary element method for contact problems with friction

Mathematics and Computers in Simulation

Volumn 50, Issue 1-4, 1999, Pages 43-61

  Eck, C ^a   Steinbach, O ^b   Wendland, W L ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Boundary element method; Coulomb law of friction; Penalty method; Static contact problem; Steklov Poincar operator

Indexed keywords

EID: 0002222739     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(99)00060-9     Document Type: Article

References (18)

1. M. Costabel, Boundary integral operators on Lipschitz domains: elementary results, SIAM J. Math. Anal. 19 (1988) 613-626.
2. M. Costabel, M. Dauge, Invertibility of the biharmonic layer operator, Prepubl. 95-13, IRMAR, Univ. Rennes 1, URA CNRS, 1995, p. 305.
3. G. Duvaut, J.L. Lions, Inequalities in Mechanics and Physics, Springer, Berlin, 1976.
4. C. Eck, J. Jarušek, Existence results for the semicoercive static contact problem with Coulomb friction, Nonl. Anal. TMA (1999), to appear.
5. C. Eck, J. Jarušek, Existence results for the static contact problem with Coulomb friction, Math. Mod. Meth. Appl. Sci. 8 (1998) 445-468.
6. H. Hertz, Über die Berührung fester elastischer Körper, JF Math. 92 (1881) 156-171.
7. G.C. Hsiao, E. Schnack, W.L. Wendland, Hybrid coupled finite-boundary element methods for elliptic systems of second order, in preparation.
8. G.C. Hsiao, W.L. Wendland, A finite element method for some integral equation of the first kind, J. Math. Anal. Appl. 58 (1977) 449-481.
9. J. Jarušek, Contact problems with bounded friction, coercive case, Czechosl. Math. J. 33 (1983) 237-261.
10. N. Kikuchi, J.T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, PA, 1988.
11. D. Kinderlehrer, Remarks about Signorini's problem in linear elasticity, Ann. Scuola Norm. Sup. Pisa cl. Sci. 4 (1981) 605-645.
12. A. Klarbring, A. Mikelic, M. Shillor, On friction problems with normal compliance, Nonl. Anal. TMA 13 (1989) 935-955.
13. J.A.C. Martins, J.T. Oden, Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws, Nonl. Anal. TMA 11 (1987) 407-428.
14. J. Nečas, J. Jarušek, J. Haslinger, On the solution of the variational inequality to the Signorini problem with small friction, Bollettino UMI 17 (1980) 796-811.
15. P.D. Panagiotopoulos, A nonlinear programming approach to the unilateral contact- and friction boundary value problem, Ingenieur-Archiv 44 (1975) 421-432.
16. O. Steinbach, Gebietszerlegungsmethoden mit Randintegralgleichungen und effiziente numerische Lösungsverfahren für gemischte Randwertprobleme, Doctoral Thesis, University of Stuttgart, 1996.
17. O. Steinbach, W.L. Wendland, The construction of some efficient preconditioners in the boundary element methods, Adv. Comput. Math. 9 (1998) 191-216.
18. E. Zeidler, Nonlinear Functional Analysis and its Applications, II/B Nonlinear Monotone Operators, Springer, Berlin, 1990.