Updated lagrangian formulation of contact problems using variational inequalities

International Journal for Numerical Methods in Engineering

Volumn 40, Issue 16, 1997, Pages 2975-2993

  Refaat, M H ^a   Meguid, S A ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Elasto plastic contact; Incremental variational inequality; Successive approximation; Updated lagrangian

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; ELASTOPLASTICITY; FRICTION; MATHEMATICAL PROGRAMMING; PLASTIC DEFORMATION; VARIATIONAL TECHNIQUES;

COULOMB'S LAW; ELASTOPLASTIC CONTACTS; JAUMANN OBJECTIVE STRESS; LAGRANGIAN FORMULATION; VARIATIONAL INEQUALITIES;

CONTACTS (FLUID MECHANICS);

EID: 0031207164     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19970830)40:16<2975::AID-NME203>3.0.CO;2-E     Document Type: Article

References (15)

1. H. Hertz, 'Über die Berührung Fester Elastischer Körper (On the contact of elastic solids)', J. reine angewandte Math., 92, 156 (1882).
2. K. L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985.
3. K. J. Bathe and A. Chaudhary, 'A solution method for planar and axisymmetric contact problems', Int. J. Numer. Meth. Engng., 21, 65 (1985).
4. H. Parisch, 'A consistent tangent stiffness matrix for three dimensional non-linear contact analysis', Int. J. Numer. Meth. Engng., 28, 1803 (1989).
5. S. K. Pascoe and J. E. Mottershed, 'Linear elastic contact problems using curved elements and including dynamic friction', Int. J. Numer. Meth. Engng., 26, 1631 (1988).
6. S. J. Kim and J. H. Kim, 'Finite element analysis of laminated composites with contact constraints by extended interior penalty methods', Int. J. Numer. Meth. Engng., 36, 3421 (1993).
7. G. Donida, G. Bernetti and R. Bruschi, 'The penalty function method for problems of contact', Comput. Struct., 36, 777 (1990).
8. A. L. Eterovic and K. J. Bathe, 'On the treatment of inequality constraints arising from contact conditions in finite element analysis', Comput. Struct., 35, 203 (1990).
9. J. B. Böhm, 'A comparison of different contact algorithms with applications', Comput. Struct., 26, 207 (1987).
10. N. Kikuchi, 'Contact problems by using penalty regularization methods', in Contact Mechanics and Wear of RaillWheel Systems, University of Waterloo Press, Canada, 1982.
11. M. H. Refaat, 'Nonlinear finite element analysis of frictional contact problems using variational inequalities', Ph.D. thesis, University of Toronto, 1995.
12. N. Kikuchi and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SLAM, Elsevier, Amsterdam, 1988.
13. M. H. Refaat and S. A. Meguid, 'On the elastic solution of frictional contact problems using variational inequalities', Int. J. Mech. Sei., 36, 329 (1994).
14. P. E. Gill, W. Murray and M. H. Wright, 'Practical Optimization', Academic Press, London, 1981.
15. R. Glowinski, T. C. Lions and R. Tremolieres, 'Numerical Analysis of Variational Inequalities', North-Holland, Amsterdam, 1981.