Abstract
We present some formulations of the static and dynamic contact problem with friction by means of boundary integral equations, which include domain integrals. After stating the equations of motion and the boundary conditions to the dynamic contact problem, we use a time stepping algorithm to transform this problem into a sequence of static problems, each of them formulated as a variational inequality. The penalty method and a smoothing procedure for the friction functional yield an approximation by a nonlinear variational equation. Recent results concerning the existence of solutions to the stated problems are given. Transforming the bilinear form of elastic energy into a boundary integral by means of the Steklov-Poincaré operator, one obtains a boundary integral equation, which is discretized with the Galerkin-method. At the end, a fully dynamic formulation using a Faedo-Galerkin scheme is proposed, which combines a boundary integral equation with a domain integral equation.
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References
G. Duvaut and J. L. Lions. Inequalities in Mechanics and Physics. Springer-Verlag, Berlin Heidelberg New-York, 1976.
J. Gwinner. A penalty approximation for unilateral contact problems in nonlinear elasticity. Math. Methods Appl Sci., 11(4):447–458, 1989.
H. Han. A Boundary Element approximation of a Signorini problem with friction obeying Coulomb law. Journal of Computational Mathematics, 12(2):147–162, 1994.
G. C. Hsiao and H. Han. The Boundary Element Method for a contact problem. In Q. Du and M. Tanaka, editors, Theory and Applications of Boundary Elements, pages 33–38, Beijing, 1988, Tsinghua University.
J. Jarušek. Contact problems with bounded friction. Coercive case. Czechoslovak Mathematical Journal, 33(108):237–261, 1983.
A. Klarbring, A. Mikelic and M. Shillor. On friction problems with normal compliance. Nonlinear Analysis, 13(8):935–955, 1989.
J. A. C. Martins and J. T. Oden. Models and computational methods for dynamic friction phenomena. Computer Methods in Applied Mechanics and Engineering, 52:527–634, 1985.
J. A. C. Martins and J. T. Oden. Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. Nonlinear Analysis, 11(3):407–428, 1987.
H. Schmitz and G. Schneider. Boundary Element solution of the Dirichlet-Signorini problem by a penalty method. Bericht Nr. 27, Seminar Analysis und Anwendungen, Universität Stuttgart, 1990.
H. Schmitz, G. Schneider and W. L. Wendland. Boundary Element Methods for problems involving unilateral boundary conditions. In P. Wriggers and W. Wagner, editors, Nonlinear Computational Mechanics: State of the Art, pages 212–225. Springer-Verlag, 1991.
W. Spann. On the Boundary Element Method for the Signorini problem of the Laplacian. Numerische Mathematik, 65:337–365, 1993.
K. Willner and L. Gaul. A penalty approach for contact description by FEM based on interface physics. In Proceedings of Contact Mechanics, 1995, to appear.
E. Zeidler. Vorlesungen über nichtlineare Funktionalanalysis II (Monotone Operatoren). B.G. Teubner, Leipzig, 1977.
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© 1997 Springer Science+Business Media Dordrecht
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Eck, C., Wendland, W.L. (1997). A Boundary Integral Formulation of Contact Problems with Friction. In: Morino, L., Wendland, W.L. (eds) IABEM Symposium on Boundary Integral Methods for Nonlinear Problems. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5706-3_8
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DOI: https://doi.org/10.1007/978-94-011-5706-3_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6406-4
Online ISBN: 978-94-011-5706-3
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