A formulation based on localized Lagrange multipliers for BEM-FEM coupling in contact problems

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 6-8, 2008, Pages 623-640

  González, José A ^a   Park, K C ^b   Felippa, Carlos A ^b   Abascal, Ramón ^a  

^a UNIVERSIDAD DE SEVILLA   (Spain)

^b University of Colorado at Boulder   (United States)

Author keywords

Boundary element method; Contact; Finite element method; Localized Lagrange multipliers

Indexed keywords

BOUNDARY ELEMENT METHOD; FINITE ELEMENT METHOD; FRICTION; INTERFACES (MATERIALS); LAGRANGE MULTIPLIERS; NUMERICAL METHODS;

FRICTIONAL CONTACT PROBLEMS; LOCALIZED LAGRANGE MULTIPLIERS;

CONTACTS (FLUID MECHANICS);

BOUNDARY ELEMENT METHOD; CONTACTS (FLUID MECHANICS); FINITE ELEMENT METHOD; FRICTION; INTERFACES (MATERIALS); LAGRANGE MULTIPLIERS; NUMERICAL METHODS;

EID: 36049048368     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.08.020     Document Type: Article

References (37)

1. Alart P. Méthode de newton généralisée en mécanique du contact. J. Math. Pures Appl. 76 (1997) 83-108
2. Alart P., and Curnier A. A mixed formulation for frictional contact problems prone to newton like solution methods. Comp. Appl. Mech. Engrg. 32 (1991) 353-475
3. Belgacem F.B., Hild P., and Laborde P. The mortar finite element method for contact problems. Mathl. Comput. Model. 28 4-8 (1998) 263-271
4. Brebbia C.A., and Georgiou P. Combination of boundary and finite elements for elastostatics. Appl. Math. Model. 3 (1979) 212-220
5. Christensen P.W., Klarbring A., Pang J.S., and Strömberg N. Formulation and comparison of algorithms for frictional contact problems. Int. J. Numer. Methods Engrg. 42 (1998) 145-173
6. Crisfield M.A. Re-visiting the contact patch test. Int. J. Numer. Methods Engrg. 48 (2000) 435-449
7. DeSaxe G., and Feng Z.W. New inequality and functional for contact with friction: the implicit standard approach. Mech. Struct. Mach. 19 (1991) 301-325
8. Ezawa Y., and Okamoto N. Development of contact stress analysis programs using the hybrid method of FEM and BEM. Comput. Struct. 58 1 (1996) 13-20
9. Fisher K.A., and Wriggers P. Frictionless 2d contact formulations for finite deformations based on the mortar method. Comput. Mech. 36 (2005) 226-244
10. Flemisch B., Puso M.A., and Wohlmuth B.I. A new dual mortar method for curved interfaces: 2d elasticity. Int. J. Numer. Methods Engrg. 63 (2005) 813-832
11. González J.A., and Abascal R. An algorithm to solve coupled 2d rolling contact problems. Int. J. Numer. Methods Engrg 49 (2000) 1143-1167
12. González J.A., and Abascal R. Solving 2d transient rolling contact problems using the bem and mathematical programming. Int. J. Numer. Methods Engrg 53 (2002) 843-874
13. González J.A., Park K.C., and Felippa C.A. Partitioned formulation of frictional contact problems using localized Lagrange multipliers. Commun. Numer. Methods Engrg. 22 (2005) 319-333
14. González J.A., Park K.C., and Felippa C.A. FEM and BEM coupling in elastostatics using localized Lagrange multipliers. Int. J. Numer. Methods Engrg. (2006)
15. Gumaste U.A., Park K.C., and Felippa C.A. A family of partitioned time integration algorithms for parallel analysis of heterogeneous structural systems. Comput. Mech. 24 (2000) 463-475
16. Hild P. Numerical implementation of two nonconforming finite element method for unilateral contact. Comput. Methods Appl. Mech. Engrg. 184 (2000) 99-123
17. Hu G.D., and Wriggers P. On the adaptive finite element method of steady-state rolling contact for hyperelasticity in finite deformations. Comput. Methods Appl. Mech. Engrg. 191 (2002) 1333-1348
18. Hughes T.J.R., Taylor R.L., Sackman J.L., Curnier A., and Kanoknukulchai W. A finite element method for a class of contact-impact problems. Comput. Methods Appl. Mech. Engrg. 8 (1976) 249-276
19. Laursen T.A. Computational Contact and Impact Mechanics. Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis (2002), Springer, Berlin, Heidelberg, New York
20. McDevitt T.W., and Laursen T.A. A mortar finite element formulation for frictional contact problems. Int. J. Numer. Methods Engrg. 48 (2000) 1525-1547
21. Oysu C., and Fenner R.T. Coupled FEM-BEM for elastoplastic contact problems using Lagrange multipliers. Appl. Math. Model. 30 3 (2006) 231-247
22. Pang J.S. Newton's method for B-differentiable equations. Math. Oper. Res. 15 2 (1990) 311-341
23. Papadopoulos P., and Taylor R.L. A mixed formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Engrg. 94 (1992) 373-384
24. Park K.C., and Felippa C.A. A variational framework for solution method developments in structural mechanics. J. Appl. Mech. 65 (1998) 242-249
25. Park K.C., and Felippa C.A. A variational principle for the formulation of partitioned structural systems. Int. J. Numer. Methods Engrg. 47 (2000) 395-418
26. Park K.C., Felippa C.A., and Gumaste U.A. A localized version of the method of Lagrange multipliers and its applications. Comput. Mech. 24 (2000) 476-490
27. Park K.C., Felippa C.A., and Rebel G. A simple algorithm for localized construction of non-matching structural interfaces. Int. J. Numer. Methods Engrg. 53 (2002) 2117-2142
28. Puso M.A., and Laursen T.A. A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. Engrg. 193 (2004) 601-629
29. Rebel G., Park K.C., and Felippa C.A. A contact formulation based on localized Lagrange multipliers: formulation and application to two-dimensional problems. Int. J. Numer. Methods Engrg. 54 2 (2002) 263-297
30. Simó J.C., and Laursen T.A. An augmented lagragian treatment of contact problems involving friction. Comput. Struct. 42 (1992) 97-116
31. Simó J.C., Wriggers P., and Taylor R.L. A perturbed Lagrangian formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Engrg. 50 (1985) 163-180
32. Taylor R.L., and Papadopoulos P. On a patch test for contact problems in two dimensions. In: Wriggers W.W. (Ed). Nonlinear Computational Mechanics (1991), Springer, Berlin 690-702
33. Wohlmuth B.I. A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal. 38 (2000) 989-1012
34. Wriggers P. Computational Contact Mechanics (2002), Wiley
35. Zienkiewicz O.C., Kelly D.W., and Bettes P. The coupling of the finite element method and boundary solution procedures. Int. J. Numer. Methods Engrg. 11 (1977) 355-375
36. O.C. Zienkiewicz, D.W. Kelly, P. Bettes, Energy methods in finite element analysis, Chapter Marriage a la mode, the best of both worlds (finite elements and boundary integrals), John Wiley and Son, 1979, pp. 81-106.
37. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method for Solid and Structural Mechanics. sixth ed. (2005), Elsevier