Review of formulations for elastostatic frictional contact problems

Structural and Multidisciplinary Optimization

Volumn 20, Issue 3, 2000, Pages 167-189

  Mijar, A R ^a   Arora, J S ^a  

^a IA United States   (United States)

Author keywords

Contact; Finite elements; Friction; Frictional contact; Optimization; Subdifferential

Indexed keywords

EID: 0000316323     PISSN: 1615147X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001580050147     Document Type: Review

References (48)

1. Agelet de Saracibar, C. 1998: Numerical analysis of coupled thermomechanical frictional contact problems. Computational model and applications. Arch. Comp. Meth. Engrg. 5, 243-301
2. Agelet de Saracibar, C.; Chiumenti, M. 1999: On the numerical modeling of frictional wear phenomenon. Comp. Meth. Appl. Mech. Engrg. 177, 401-426
3. Alart, P. 1992: A simple contact algorithm applied to large sliding and anisotropic friction. In: Curnier, A. (ed.) Proc. Int. Symp. on Contact Mechanics (held in Lausanne, Switzerland)
4. Alart, P.; Curnier, A. 1991: A mixed formulation for frictional contact problems prone to Newton like solution methods. Comp. Meth. Appl. Mech. Engrg. 92, 353-375
5. Arora, J.S. 1989: Introduction to optimum design. New York: McGraw-Hill
6. Arora, J.S.; Chahande, A.I.; Paeng, J.K. 1991: Multiplier methods for engineering optimization. Int. J. Numer. Meth. Engrg. 32, 1485-1525
7. Bathe, K.J. 1996: Finite element procedures. New Jersey: Prentice-Hall
8. Bathe, K.J.; Chaudhary, A. 1985: A solution method for planar and axisymmetric contact problems. Int. J. Numer. Meth. Engrg. 21, 65-88
9. Bendsøe, M.P.; Olhoff, N.; Taylor, J.E. 1993: A unified approach to the analysis and design of elasto-plastic structures with mechanical contact. In: Rozvany, G.I.N (ed.) Optimization of large structural systems (Proc. NATO/DFG ASI, held in Berchtesgaden, 1991), pp. 697-705. Dordrecht: Kluwer
10. Chahande, A.I.; Arora, J.S. 1994: Optimization of large structures subjected to dynamic loads with the multiplier method. Int. J. Numer. Meth. Engrg. 37, 413-430
11. Curnier, A. 1984: A theory of friction. Int. J. Solids Struct. 20, 637-647
12. Curnier, A.; Alart, P. 1988: A generalized Newton method for contact problems with friction. J. Theor. Appl. Mech. 7, 67-82
13. Giannakopoulos, A.E. 1989: The return mapping method for the integration of friction constitutive relations. Comp. & Struct. 32, 157-167
14. Goldsmith, W. 1960: Impact: The theory and physical behavior of colliding solids. London: Edward Arnold
15. Hallquist, J.O. 1991: LS-DYNASD Theoretical Manual. Lawrence Livermore National Laboratory
16. Hallquist, J.O.; Goudreau, G.L.; Benson, D.J. 1985: Sliding interfaces with contact impact in large-scale Lagrangian computations. Comp. Meth. Appl. Mech. Eng. 51, 107-137
17. Haug, E.; Chand, R.; Pan, K. 1977: Multibody elastic contact analysis by quadratic programming. J. Optimiz. Theory Appl. 21, 189-198
18. Heegaard, J.-H.; Curnier, A. 1993: An augmented Lagrangian method for discrete large-slip contact problems. Int. J. Numer. Meth. Engrg. 36, 569-593
19. Heege, A.; Alart, P. 1996: A frictional contact element for strongly curved contact problems. Int. J. Numer. Meth. Engrg. 39, 165-184
20. Hertz, H. 1881: Über die Berührung fester elastischer Körper. J. der Reine und Angewandte Mathematik 92, 156-171
21. Hertz, H. 1882: Über die Berührung fester elastischer Körper und Über die Härte. Verhandlungen des Vereins zur Beförderung des Gewerbfleises. Berlin
22. Hestenes, M.R. 1969: Multiplier and gradient methods. J. Optimiz. Theory Appl. 4, 303-320
23. Hughes, T.J.R.; Taylor, R.L.; Sackman, J.L.; Curnier, A.; Kanoknukulchai, W. 1976: A finite element method for a class of contact-impact problems. Comp. Meth. Appl. Mech. Engrg. 8, 249-276
24. Johnson, A.R.; Quigley, C.J. 1989: Frictionless geometrically nonlinear contact with quadratic programming. Int. J. Numer. Meth. Engrg. 28, 127-144
25. Ju, S.H.; Rowlands, R.E. 1999: A three-dimensional frictional contact element whose stiffness matrix is symmetric. J. Appl. Mech. 66, 460-467
26. Ju, J.-W.; Taylor, R.L. 1988: A perturbed Lagrangian formulation for the finite element solution of nonlinear frictional contact problems. J. de Mecanique Theorique et Appliquee 7, 1-14
27. Kikuchi, N.; Oden, J.T. 1988: Contact problems in elasticity: A study of variational inequalities and finite element methods. Philadelphia: SIAM
28. Klarbring, A. 1992: Mathematical programming and augmented Lagrangian methods for frictional contact problems. In: Curnier, A. (ed.) Proc. Int. Symp. on Contact Mechanics (held in Lausanne, Switzerland)
29. Laursen, T.A.; Simo, J.C. 1993: A continuum-based finite element formulation for the implicit solution of multi-body, large deformation frictional contact problems. Int. J. Numer. Meth. Engrg. 36, 3451-3485
30. Mäkelä, M.M.; Pekka, N. 1992: Nonsmooth optimization. Singapore: World Scientific Publishing Co.
31. McCormick, G.P. 1983: Nonlinear programming. John Wiley and Sons Inc.
32. Mijar, A.R.; Arora, J.S. 2000: Elastostatic frictional contact problem formulation using optimization techniques. In: Belegundu, A.D.; Mistree, F. (eds.) Optimization in industry. New York: ASME (in press)
33. Mottershead, J.E.; Pascoe, S.K.; English, R.G. 1992: A general finite element approach for contact stress analysis. Int. J. Numer. Meth. Engrg. 33, 765-779
34. Muvdi, B.B.; Al-Khafaji, A.W.; McNabb, J.W. 1997: Statics for engineers. Berlin, Heidelberg, New York: Springer
35. Oden, J.T.; Pires, E.B. 1983: Numerical analysis of certain contact problems in elasticity with nonclassical friction laws. Comp. Struct. 16, 481-485
36. Panagiotopoulos, P.D. 1985: Inequality problems in mechanics and applications. Boston Inc.
37. Powell, M.J.D. 1969: A method for nonlinear constraints in minimization problems. In: Fletcher, R. (ed.) Optimization. New York: Academic Press
38. Refaat, M.H.; Meguid, S.A. 1998: A new strategy for the solution of frictional contact problems. Int. J. Numer. Meth. Engrg. 43, 1053-1068
39. Rockafellar, R.T. 1973: A dual approach to solving nonlinear programming problems by unconstrained optimization. Math. Prog. 5, 354-373
40. Rockafellar, R.T. 1979: Lagrange multipliers and variational inequalities. In: Gianessi; Cottle; Lions (eds.) Variational inequalities and complementarity problems. New York: John Wiley
41. Signorini, A. 1933: Sopra akune questioni di elastostatica. Atti della Societa Italiana per il Progresso delle Scienze
42. Signorini, A. 1959: Questioni de elasticita nonlinearizzata e semi linearizzata. Rome: Rend. de Matematica
43. Simo, J.C.; Laursen, T.A. 1992: An augmented Lagrangian treatment of contact problems involving friction. Comp. Struct. 42, 97-116
44. Simo, J.C.; Wriggers, P.; Taylor, R.L. 1985: A perturbed Lagrangian formulation for the finite element solution of contact problems. Comp. Meth. Appl. Mech. Engrg. 50, 163-180
45. Stavroulakis, G.E.; Panagiotopoulos, P.D.; Al-Failed, A.M. 1991: On the rigid body displacements and rotations in unilateral contact problems and applications. Comp. Struct. 40, 599-614
46. Wriggers, P.; Zavarise, G. 1993: On the application of augmented Lagrangian techniques for nonlinear constitutive laws in contact interfaces. Comm. Numer. Meth. Engrg. 9, 815-824
47. Zavarise, G.; Wriggers, P.; Schrefler, B.A. 1995: On augmented Lagrangian algorithms for thermomechnical contact problems with friction. Int. J. Numer. Meth. Engrg. 38, 2929-2949
48. Zhong, Z.-H. 1993: Finite element procedures for contact-impact problems. New York: Oxford University Press