메뉴 건너뛰기




Volumn 42, Issue 1, 1998, Pages 145-173

Formulation and comparison of algorithms for frictional contact problems

Author keywords

Complementarity; Contact; Finite elements; Friction; Interior point method; Newton's method

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; ELASTICITY; FINITE ELEMENT METHOD; INTERFACES (MATERIALS); MATHEMATICAL MODELS;

EID: 0032075417     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19980515)42:1<145::AID-NME358>3.0.CO;2-L     Document Type: Article
Times cited : (218)

References (37)
  • 1
    • 85081194232 scopus 로고    scopus 로고
    • Existence of solutions to discrete semicoercive fractional contact problems
    • forthcoming
    • A. Klarbring and J. S. Pang, 'Existence of solutions to discrete semicoercive fractional contact problems', SIAM J. Optim., forthcoming.
    • SIAM J. Optim.
    • Klarbring, A.1    Pang, J.S.2
  • 2
    • 0026820003 scopus 로고
    • Static contact problems - A review
    • Z.-H. Zhong and J. Mackerle, 'Static contact problems - a review', Engng. Comput., 9, 3-37 (1992).
    • (1992) Engng. Comput. , vol.9 , pp. 3-37
    • Zhong, Z.-H.1    Mackerle, J.2
  • 3
    • 0000371577 scopus 로고
    • Mathematical programming in contact problems
    • M. H. Aliabdali and C. A. Brebbia (eds), Computational Mechanics Publications, Southampton
    • A. Klarbring, 'Mathematical programming in contact problems', in M. H. Aliabdali and C. A. Brebbia (eds), Computational Methods in Contact Mechanics, Computational Mechanics Publications, Southampton, 1993, pp. 233-263.
    • (1993) Computational Methods in Contact Mechanics , pp. 233-263
    • Klarbring, A.1
  • 4
    • 51249168203 scopus 로고
    • Finite element algorithms for contact problems
    • P. Wriggers, 'Finite element algorithms for contact problems', Arch. Comput. Meth. Engng., 2, 1-49 (1995).
    • (1995) Arch. Comput. Meth. Engng. , vol.2 , pp. 1-49
    • Wriggers, P.1
  • 7
    • 0025546089 scopus 로고
    • Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction
    • A. Klarbring, 'Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction', Ing. Arch., 60, 529-541 (1990).
    • (1990) Ing. Arch. , vol.60 , pp. 529-541
    • Klarbring, A.1
  • 8
    • 0001979399 scopus 로고    scopus 로고
    • Frictional contact algorithms based on semismooth Newton methods
    • M. Fukushima and L. Qi (eds.), Kluwer Academic Publishers, Dordrecht, Forthcoming
    • P. W. Christensen and J. S. Pang, 'Frictional contact algorithms based on semismooth Newton methods', in M. Fukushima and L. Qi (eds.), Reformulation-Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer Academic Publishers, Dordrecht, Forthcoming.
    • Reformulation-Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods
    • Christensen, P.W.1    Pang, J.S.2
  • 9
    • 0030653151 scopus 로고    scopus 로고
    • An augmented Lagrangian method for fretting problems
    • N. Strömberg, 'An augmented Lagrangian method for fretting problems', European J. Mech. A/Solids, 16, 573-593 (1997).
    • (1997) European J. Mech. A/Solids , vol.16 , pp. 573-593
    • Strömberg, N.1
  • 10
    • 85081191769 scopus 로고    scopus 로고
    • A Newton method for three-dimensional fretting problems
    • Linköping submitted for publication
    • N. Strömberg, 'A Newton method for three-dimensional fretting problems', Internal Report, LiTH-IKP-R-950, Linköping (1997), submitted for publication.
    • (1997) Internal Report, LiTH-IKP-R-950
    • Strömberg, N.1
  • 11
    • 0026255347 scopus 로고
    • A mixed formulation for factional contact problems prone to Newton like solution methods
    • P. Alart and A. Curnier, 'A mixed formulation for factional contact problems prone to Newton like solution methods', Comput. Meth. Appl. Mech. Engng., 92, 353-375 (1991).
    • (1991) Comput. Meth. Appl. Mech. Engng. , vol.92 , pp. 353-375
    • Alart, P.1    Curnier, A.2
  • 12
    • 0026626125 scopus 로고
    • An augmented Lagrangian treatment of contact problems involving friction
    • J. C. Simo and T. A. Laursen, 'An augmented Lagrangian treatment of contact problems involving friction', Comput. Struct., 42, 97-116 (1992).
    • (1992) Comput. Struct. , vol.42 , pp. 97-116
    • Simo, J.C.1    Laursen, T.A.2
  • 13
    • 0001226430 scopus 로고
    • New inequality and functional for contact with friction: The implicit standard material approach
    • G. De Saxce and Z. Q. Feng, 'New inequality and functional for contact with friction: the implicit standard material approach', Mech. Struct. Mach., 19, 301-325 (1991).
    • (1991) Mech. Struct. Mach. , vol.19 , pp. 301-325
    • De Saxce, G.1    Feng, Z.Q.2
  • 14
    • 0001903634 scopus 로고
    • Mathematical programming and augmented Lagrangian methods for frictional contact problem
    • A. Curnier (ed.), PPUR
    • A. Klarbring, 'Mathematical programming and augmented Lagrangian methods for frictional contact problem', in A. Curnier (ed.), Proceedings Contact Mechanics International Symposium, PPUR, 1992, pp. 409-422.
    • (1992) Proceedings Contact Mechanics International Symposium , pp. 409-422
    • Klarbring, A.1
  • 15
    • 0029379465 scopus 로고
    • On augmented Lagrangian algorithms for thermomechanical contact problems with friction
    • G. Zavarise, P. Wriggers and B. A. Schrefler, 'On augmented Lagrangian algorithms for thermomechanical contact problems with friction', Int. J. Numer. Meth. Engng., 38, 2929-2949 (1995).
    • (1995) Int. J. Numer. Meth. Engng. , vol.38 , pp. 2929-2949
    • Zavarise, G.1    Wriggers, P.2    Schrefler, B.A.3
  • 16
    • 0029776098 scopus 로고    scopus 로고
    • A frictional contact element for strongly curved contact problems
    • A. Heege and P. Alart, 'A frictional contact element for strongly curved contact problems', Int. J. Numer. Meth. Engng., 39, 165-184 (1996).
    • (1996) Int. J. Numer. Meth. Engng. , vol.39 , pp. 165-184
    • Heege, A.1    Alart, P.2
  • 17
    • 0001601094 scopus 로고
    • Newton's method for B-differentiable equations
    • J. S. Pang, 'Newton's method for B-differentiable equations', Math. Oper. Res., 15, 311-341 (1990).
    • (1990) Math. Oper. Res. , vol.15 , pp. 311-341
    • Pang, J.S.1
  • 18
    • 0000304337 scopus 로고    scopus 로고
    • An interior point potential reduction method for constrained equations
    • T. Wang, R. D. C. Monteiro and J. S. Pang, 'An interior point potential reduction method for constrained equations', Math. Program., 74, 159-196 (1996).
    • (1996) Math. Program. , vol.74 , pp. 159-196
    • Wang, T.1    Monteiro, R.D.C.2    Pang, J.S.3
  • 19
    • 0000003120 scopus 로고    scopus 로고
    • On dynamic multi-rigid-body contact problems with Coulomb friction
    • J. C. Trinkle, J. S. Pang, S. Sudarsky and G. Lo, 'On dynamic multi-rigid-body contact problems with Coulomb friction', Z. Angew. Math. Mech., 77, 267-279 (1997).
    • (1997) Z. Angew. Math. Mech. , vol.77 , pp. 267-279
    • Trinkle, J.C.1    Pang, J.S.2    Sudarsky, S.3    Lo, G.4
  • 20
    • 45549113871 scopus 로고
    • A mathematical programming approach to contact problems with friction and varying contact surface
    • A. Klarbring and G. Björkman, 'A mathematical programming approach to contact problems with friction and varying contact surface', Comput. Struct., 30, 1185-1198 (1988).
    • (1988) Comput. Struct. , vol.30 , pp. 1185-1198
    • Klarbring, A.1    Björkman, G.2
  • 21
    • 0025684251 scopus 로고
    • A solution scheme for three-dimensional multi-body contact problems using mathematical programming
    • G. Holmberg, 'A solution scheme for three-dimensional multi-body contact problems using mathematical programming', Comput. Struct., 37, 503-514 (1990).
    • (1990) Comput. Struct. , vol.37 , pp. 503-514
    • Holmberg, G.1
  • 25
    • 0027543961 scopus 로고
    • A non-smooth version of Newton's method
    • L. Qi and J. Sun, 'A non-smooth version of Newton's method', Math. Program., 58, 353-368 (1993).
    • (1993) Math. Program. , vol.58 , pp. 353-368
    • Qi, L.1    Sun, J.2
  • 26
    • 0001393203 scopus 로고
    • Global convergence of damped Newton's method for non-smooth equations via the path search
    • D. Ralph, 'Global convergence of damped Newton's method for non-smooth equations via the path search', Math. Oper. Res., 19, 352-389 (1994).
    • (1994) Math. Oper. Res. , vol.19 , pp. 352-389
    • Ralph, D.1
  • 29
    • 0030104686 scopus 로고    scopus 로고
    • A class of smoothing functions for non-linear and mixed complementarity problems
    • C. Chen and O. L. Mangasarian, 'A class of smoothing functions for non-linear and mixed complementarity problems', Comput. Optim. Appl., 5, 97-138 (1996).
    • (1996) Comput. Optim. Appl. , vol.5 , pp. 97-138
    • Chen, C.1    Mangasarian, O.L.2
  • 30
    • 0043189808 scopus 로고    scopus 로고
    • A semismooth equation approach to the solution of nonlinear complementarity problems
    • T. De Luca, F. Facchinei and C. Kanzow, 'A semismooth equation approach to the solution of nonlinear complementarity problems', Math. Program., 75, 407-439 (1996).
    • (1996) Math. Program. , vol.75 , pp. 407-439
    • De Luca, T.1    Facchinei, F.2    Kanzow, C.3
  • 31
    • 0002579086 scopus 로고    scopus 로고
    • Smoothing of mixed complementarity problems
    • M. C. Ferris and J. S. Pang (eds.), SIAM Publications, Philadelphia
    • S. A. Gabriel and J. J. More, 'Smoothing of mixed complementarity problems', in M. C. Ferris and J. S. Pang (eds.), Complementarity and Variational Problems: State of the Art, SIAM Publications, Philadelphia, 1997, pp. 105-116.
    • (1997) Complementarity and Variational Problems: State of the Art , pp. 105-116
    • Gabriel, S.A.1    More, J.J.2
  • 33
    • 0014604308 scopus 로고
    • Multiplier and gradient methods
    • M. R. Hestenes, 'Multiplier and gradient methods', J. Opt. Theory Appl., 4, 303-320 (1969).
    • (1969) J. Opt. Theory Appl. , vol.4 , pp. 303-320
    • Hestenes, M.R.1
  • 34
    • 0002380692 scopus 로고
    • A method for non-linear constraints in minimization problems
    • R. Fletcher (ed.), Academic Press, New York
    • M. J. D. Powell, 'A method for non-linear constraints in minimization problems', in R. Fletcher (ed.), Optimization, Academic Press, New York, 1969, pp. 283-298.
    • (1969) Optimization , pp. 283-298
    • Powell, M.J.D.1
  • 35
    • 0016059769 scopus 로고
    • Augmented Lagrangian multiplier functions and duality in nonconvex programming
    • R. T. Rockafellar, 'Augmented Lagrangian multiplier functions and duality in nonconvex programming', SIAM J. Control, 12, 268-285 (1974).
    • (1974) SIAM J. Control , vol.12 , pp. 268-285
    • Rockafellar, R.T.1
  • 36
    • 0001546137 scopus 로고
    • A damped-Newton method for the linear complementarity problem
    • E. L. Allgower and K. Georg (eds.), Lectures in Applied Mathematics, American Mathematical Society, Providence, RI
    • P. T. Harker and J. S. Pang, 'A damped-Newton method for the linear complementarity problem', in E. L. Allgower and K. Georg (eds.), Computational Solution of Nonlinear Systems of Equations, Lectures in Applied Mathematics, Vol. 26, American Mathematical Society, Providence, RI, 1990, pp. 265-284.
    • (1990) Computational Solution of Nonlinear Systems of Equations , vol.26 , pp. 265-284
    • Harker, P.T.1    Pang, J.S.2
  • 37
    • 0026837319 scopus 로고
    • Solution of large displacement contact problems with friction using Newton's method for generalized equations
    • A. Klarbring and G. Björkman, 'Solution of large displacement contact problems with friction using Newton's method for generalized equations', Int. J. Numer. Meth. Engng., 34, 249-269 (1992).
    • (1992) Int. J. Numer. Meth. Engng. , vol.34 , pp. 249-269
    • Klarbring, A.1    Björkman, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.