Abstract
Faced with the growing importance taken by contact phenomena with friction in many problems issued from structural mechanics (metal forming, structure assembling, cracking,...) a great number of big finite element codes have developed modules treating these very special limit conditions. Modelisation of friction together with an appropriate numerical treatment is a difficult problem which remains largely open. Future developments in this domain will have to rest on a strong concertation between structural mechanicians, tribologists, mathematicians, numerical analysts and physicists from industry.
However during this past decade a mathematical formulation together with numerical methods appropriate to Coulomb friction models with unilateral contact has been developed. Corresponding numerical procedures are or may be introduced into Finite Element codes and are to be compared to methods more directly inspired by the physics of the problem such as contact finite elements (evanescent third body) or iterative procedures on the boundary conditions.
A formulation in terms of a variational inequality may in turn be solved in different ways. We present here one of these, underlining its advantages and disadvantages with regard to other approaches. It consists of a diagonal fixed point algorithm based on a “Gauss-Seidel projected overrelaxed method” together with several adjustments which enable to gain in performance. This method is developed in the code PROTIS at the L.M.A. and also introduced in different large scale codes (MODULEF, EVPCYCL).
The performances of a numerical method associated to a given formulation have to be appreciated under different angles. There is not only the precision (in the phenomenon’s description) or the cost of the computation (a factor wich tends to be not essential) but also the facility with which the procedure can be implemented into an existing code. We examine here the proposed method under all these aspects.
An erratum to this chapter is available at http://dx.doi.org/10.1007/978-3-7091-2967-8_18
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Duvaut, G., Lions, J.L.: Les inéquations en Mécanique et en Physique, Dunod, Paris, 1972.
Duvaut, G.: Equilibre d’un solide élastique avec contact unilatéral et frottement de Coulomb, C.R. Acad. Sci., Paris, Série A, t. 290, 263, 1980.
Cocu, M.: Existence- of solutions of Signorini problem with friction, Int. J. Engn. Sci., 22, n°5, 567, 1984.
Campos, L.T., Oden, J.T., Kikuchi, N.: A numerical Analysis of a class of contact problems with friction in elastostatics, Computer Meth. in Applied Mech. and Eng., 34, 821, 1982.
Panagiotopoulos, P.D.: Inequality Problems in Mechanics and Applications, Birkhäuser, Boston-Basel, Stuttgart, 1985.
Raous, M.: Contacts unilatéraux avec frottement en viscoélasticité, in “Unilateral Problems in Structural Analysis”, Ed. G. Del Piero, F. Maceri, CISM Publisher, Springer-Verlag, Vienne, 1985.
Kalker, J.J.: On the Contact Problem in Elastostatics, in “Unilateral Problems in Structural Analysis”, Ed. G. Del Piero, F. Maceri, CISM Publishers, Springer-Verlag, Vienne, 1985.
Curnier, A.: A theory of friction, Int. J. of Solids & Structures, 20, 7, 637, 1984.
Raous, M.: Comportement d’un solide fissuré sous charges alternatives en viscoplasticité, Journal de Mécanique Théorique et Appliquée, n° Spécial “4e Colloque Franco-Polonais”, 1982.
Bazaraa, M.S., Shetty, CM., Nonlinear Programming, John Wiley & Sons, New York, 1975.
Klarbring, A.: Contact problems in linear elasticity, Thesis, Dpt of Mech. Engn., Linkoping University, Sweden, 1985.
Glowinski, R., Lions, J.L., Tremolieres, R., Analyse Numérique des Inéquations Variationnelles, Dunod, Paris, 1976.
Latil, J.C., Méthode d’Eléments Finis et Inéquations. Notice du Code PROTIS, Note Interne L.M.A. n° 2188, 1986.
Taallah, F.: Méthode de condensation pour un algorithme de Gauss-Seidel relaxé avec projection, Mémoire de DEA-Math. Appliquées, Université de Provence, 1985.
Lebon F.: Résolution d’inéquations variationnelles par méthodes multigrilles, Mémoire de DEA-Math. Appliquées, Université de Provence, 1985.
Raous, M.: On Two Variational Inequalities arising from a Periodic Viscoelastic Unilateral Problem, in “Variational Inequalities and Complementarity Problems”, Ed. Gianessi-Cottle-Lions, J. Wiley, 1979.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Wien
About this paper
Cite this paper
Raous, M., Latil, J.C. (1987). Codes D’elements Finis Pour des Problemes de Contacts Unilateraux Avec Frottement Formules in Termes D’inequations Variationnelles. In: Del Piero, G., Maceri, F. (eds) Unilateral Problems in Structural Analysis — 2. International Centre for Mechanical Sciences, vol 304. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2967-8_14
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2967-8_14
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82036-0
Online ISBN: 978-3-7091-2967-8
eBook Packages: Springer Book Archive