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Volumn 256, Issue , 2013, Pages 38-55

Generalized Newton's methods for the approximation and resolution of frictional contact problems in elasticity

Author keywords

Augmented Lagrangian; Contact; Friction; Generalized Newton's method; Nitsche's method

Indexed keywords

AUGMENTED LAGRANGIANS; DISCRETIZED PROBLEMS; EXISTENCE AND UNIQUENESS RESULTS; FINITE ELEMENT; FRICTION CONDITIONS; FRICTIONAL CONTACT PROBLEMS; GENERALIZED NEWTON; NITSCHE'S METHOD; NUMERICAL EXPERIMENTATIONS;

EID: 84872717280     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.12.008     Document Type: Article
Times cited : (55)

References (43)
  • 1
    • 0030706340 scopus 로고    scopus 로고
    • Méthode de Newton Généralisée en Mécanique du contact
    • Alart P. Méthode de Newton Généralisée en Mécanique du contact. J. Math. Pure Appl. 1997, 76:83-108.
    • (1997) J. Math. Pure Appl. , vol.76 , pp. 83-108
    • Alart, P.1
  • 2
    • 0024128351 scopus 로고
    • A generalized Newton method for contact problems with friction
    • Alart P., Curnier A. A generalized Newton method for contact problems with friction. J. Mech. Theor. Appl. 1988, 7(1):67-82.
    • (1988) J. Mech. Theor. Appl. , vol.7 , Issue.1 , pp. 67-82
    • Alart, P.1    Curnier, A.2
  • 3
    • 0026255347 scopus 로고
    • A mixed formulation for frictional contact problems prone to Newton like solution methods
    • Alart P., Curnier A. A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput. Methods Appl. Mech. Engrg. 1991, 92:353-375.
    • (1991) Comput. Methods Appl. Mech. Engrg. , vol.92 , pp. 353-375
    • Alart, P.1    Curnier, A.2
  • 4
    • 0037972493 scopus 로고    scopus 로고
    • Hybrid finite element methods for Signorini's problem
    • Ben Belgacem F., Renard Y. Hybrid finite element methods for Signorini's problem. Math. Comput. 2003, 72:1117-1145.
    • (2003) Math. Comput. , vol.72 , pp. 1117-1145
    • Ben Belgacem, F.1    Renard, Y.2
  • 5
    • 33947656993 scopus 로고    scopus 로고
    • Field Level-sets placement and velocity based formulations of contact-impact problems
    • Ben Dhia H., Zammali M., Field Level-sets placement and velocity based formulations of contact-impact problems. Int. J. Numer. Methods Engrg. 2007, 69:2711-2735.
    • (2007) Int. J. Numer. Methods Engrg. , vol.69 , pp. 2711-2735
    • Ben Dhia, H.1    Zammali, M.2
  • 6
    • 33846920933 scopus 로고    scopus 로고
    • Hybrid frictional contact particles-in elements
    • Ben Dhia H., Zarroug M. Hybrid frictional contact particles-in elements. Eur. J. Comput. Mech. 2002, 11:417-430.
    • (2002) Eur. J. Comput. Mech. , vol.11 , pp. 417-430
    • Ben Dhia, H.1    Zarroug, M.2
  • 8
    • 0032143137 scopus 로고    scopus 로고
    • Various numerical methods for solving unilateral contract problems with friction
    • Chabrand P., Dubois F., Raous M. Various numerical methods for solving unilateral contract problems with friction. Math. Comput. Model 1998, 28(4-8):97-108.
    • (1998) Math. Comput. Model , vol.28 , Issue.4-8 , pp. 97-108
    • Chabrand, P.1    Dubois, F.2    Raous, M.3
  • 9
    • 84872715263 scopus 로고    scopus 로고
    • A Nitsche-base method for unilateral contact problems: numerical analysis, SIAM J. Numer. Anal., submitted for publication.
    • F. Chouly, P. Hild. A Nitsche-base method for unilateral contact problems: numerical analysis, SIAM J. Numer. Anal., submitted for publication.
    • Chouly, F.1    Hild, P.2
  • 10
    • 84872743695 scopus 로고    scopus 로고
    • Symmetric and non-symmetric variants of Nitsche's method for contact problems in elasticity: theory and numerical experiments, submitted for publication.
    • F. Chouly, P. Hild, Y. Renard. Symmetric and non-symmetric variants of Nitsche's method for contact problems in elasticity: theory and numerical experiments, submitted for publication.
    • Chouly, F.1    Hild, P.2    Renard, Y.3
  • 12
    • 0037066652 scopus 로고    scopus 로고
    • A semi-smooth Newton method for elasto-plastic contact problem
    • Christensen P.W. A semi-smooth Newton method for elasto-plastic contact problem. Int. J. Solids Struct. 2002, 39:2323-2341.
    • (2002) Int. J. Solids Struct. , vol.39 , pp. 2323-2341
    • Christensen, P.W.1
  • 13
    • 0032143148 scopus 로고    scopus 로고
    • The bipotential method: a constructive approach to design the complete contact law with friction and improved numerical algorithms
    • DeSaxcé G. The bipotential method: a constructive approach to design the complete contact law with friction and improved numerical algorithms. Math. Comput. Model. 1998, 28(4-8):225-245.
    • (1998) Math. Comput. Model. , vol.28 , Issue.4-8 , pp. 225-245
    • DeSaxcé, G.1
  • 15
    • 3242828407 scopus 로고    scopus 로고
    • Existence results for the static contact problem with Coulomb friction
    • Eck C., Jarušek J. Existence results for the static contact problem with Coulomb friction. Math. Models Methods Appl. Sci. 1998, LV-8:445-468.
    • (1998) Math. Models Methods Appl. Sci. , vol.LV8 , pp. 445-468
    • Eck, C.1    Jarušek, J.2
  • 17
    • 33646192762 scopus 로고    scopus 로고
    • Stabilized Lagrange multiplier methods for bilateral elastic contact with friction
    • Heintz P., Hansbo P. Stabilized Lagrange multiplier methods for bilateral elastic contact with friction. Comput. Methods Appl. Mech. Engrg. 2006, 195:4323-4333.
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 4323-4333
    • Heintz, P.1    Hansbo, P.2
  • 18
    • 84872727416 scopus 로고    scopus 로고
    • Non-unique slipping in the Coulomb friction model in two-dimensional linear elasticity.
    • P. Hild, Non-unique slipping in the Coulomb friction model in two-dimensional linear elasticity.
    • Hild, P.1
  • 19
    • 24944540239 scopus 로고    scopus 로고
    • Multiple solutions of stick and separation type in the Signorini model with Coulomb friction
    • Hild P. Multiple solutions of stick and separation type in the Signorini model with Coulomb friction. Z. Angew. Math. Mech. 2005, 85:673-680.
    • (2005) Z. Angew. Math. Mech. , vol.85 , pp. 673-680
    • Hild, P.1
  • 20
    • 84868380592 scopus 로고    scopus 로고
    • An improved a priori error analysis for finite element approximations of Signorini's problem
    • Hild P., Renard Y. An improved a priori error analysis for finite element approximations of Signorini's problem. SIAM J. Numer. Anal. 2012, 50(5):2400-2419.
    • (2012) SIAM J. Numer. Anal. , vol.50 , Issue.5 , pp. 2400-2419
    • Hild, P.1    Renard, Y.2
  • 21
    • 18144376701 scopus 로고    scopus 로고
    • A primal-dual active set strategy for non-linear multibody contact problems
    • Hüber S., Wohlmuth B. A primal-dual active set strategy for non-linear multibody contact problems. Comput. Methods Appl. Mech. Engrg. 2005, 194(27):3147-3166.
    • (2005) Comput. Methods Appl. Mech. Engrg. , vol.194 , Issue.27 , pp. 3147-3166
    • Hüber, S.1    Wohlmuth, B.2
  • 22
    • 0001724126 scopus 로고
    • Contact problems with bounded friction. Coercive case
    • Jarušek J. Contact problems with bounded friction. Coercive case. Czechoslovak Math. J. 1983, 33:237-261.
    • (1983) Czechoslovak Math. J. , vol.33 , pp. 237-261
    • Jarušek, J.1
  • 23
    • 29244443983 scopus 로고    scopus 로고
    • Three-dimensional quasi-static frictional contact by using second-order cone linear complementarity problem
    • Kanno Y., Martins J.A.C., Pinto da Costa A. Three-dimensional quasi-static frictional contact by using second-order cone linear complementarity problem. Int. J. Numer. Methods Engrg. 2006, 65:62-83.
    • (2006) Int. J. Numer. Methods Engrg. , vol.65 , pp. 62-83
    • Kanno, Y.1    Martins, J.A.C.2    Pinto da Costa, A.3
  • 24
    • 30744472462 scopus 로고    scopus 로고
    • Hybrid discretization of the Signorini problem with Coulomb friction, theoretical aspects and comparison of some numerical solvers
    • Khenous H., Pommier J., Renard Y. Hybrid discretization of the Signorini problem with Coulomb friction, theoretical aspects and comparison of some numerical solvers. Appl. Numer. Math. 2006, 56/2:63-192.
    • (2006) Appl. Numer. Math. , pp. 63-192
    • Khenous, H.1    Pommier, J.2    Renard, Y.3
  • 26
    • 0022605197 scopus 로고
    • Quadratic programs in frictionless contact problems
    • Klarbring K.C. Quadratic programs in frictionless contact problems. Int. J. Engrg. Sci. 1986, 24(7):1207-1217.
    • (1986) Int. J. Engrg. Sci. , vol.24 , Issue.7 , pp. 1207-1217
    • Klarbring, K.C.1
  • 27
    • 0032222082 scopus 로고    scopus 로고
    • Existence of solutions to discrete semicoercive frictional contact problems
    • Klarbring K.C., Pang J.-S. Existence of solutions to discrete semicoercive frictional contact problems. SIAM J. Optim. 1998, 8:414-442.
    • (1998) SIAM J. Optim. , vol.8 , pp. 414-442
    • Klarbring, K.C.1    Pang, J.-S.2
  • 28
    • 25444494721 scopus 로고    scopus 로고
    • Generalized Newton methods for the 2D-Signorini contact problem with friction in function space
    • Kunish K., Stadler G. Generalized Newton methods for the 2D-Signorini contact problem with friction in function space. Math. Model. Numer. Anal. 2005, 39(4):827-854.
    • (2005) Math. Model. Numer. Anal. , vol.39 , Issue.4 , pp. 827-854
    • Kunish, K.1    Stadler, G.2
  • 29
    • 39449138069 scopus 로고    scopus 로고
    • Fixed point strategies for elastostatic frictional contact problems
    • Laborde P., Renard Y. Fixed point strategies for elastostatic frictional contact problems. Math. Methods Appl. Sci. 2008, 31:415-441.
    • (2008) Math. Methods Appl. Sci. , vol.31 , pp. 415-441
    • Laborde, P.1    Renard, Y.2
  • 30
    • 38249006501 scopus 로고
    • Algorithm symmetrization of Coulomb frictional problems using augmented Lagrangians
    • Laursen T.A., Simo J.C. Algorithm symmetrization of Coulomb frictional problems using augmented Lagrangians. Comput. Methods Appl. Mech. Engrg 1993, 108:133-146.
    • (1993) Comput. Methods Appl. Mech. Engrg , vol.108 , pp. 133-146
    • Laursen, T.A.1    Simo, J.C.2
  • 31
    • 0036670681 scopus 로고    scopus 로고
    • An optimization technique for the solution of the Signorini problem using the boundary element method
    • Leontiev A., Huacasi W., Herskovits J. An optimization technique for the solution of the Signorini problem using the boundary element method. Struct. Multidisc. Optim. 2002, 24:72-77.
    • (2002) Struct. Multidisc. Optim. , vol.24 , pp. 72-77
    • Leontiev, A.1    Huacasi, W.2    Herskovits, J.3
  • 32
    • 84951671794 scopus 로고
    • über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randdbedingungen unterworfen sind
    • Nitsche J. über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randdbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 1971, 36:9-15.
    • (1971) Abh. Math. Sem. Univ. Hamburg , vol.36 , pp. 9-15
    • Nitsche, J.1
  • 33
    • 0027543961 scopus 로고
    • A nonsmooth version of Newton's method
    • Qi L., Sun J. A nonsmooth version of Newton's method. Math. Program. 1993, 58:353-367.
    • (1993) Math. Program. , vol.58 , pp. 353-367
    • Qi, L.1    Sun, J.2
  • 34
    • 0002441233 scopus 로고
    • Preconditionned conjugate gradient method for a unilateral problem with friction, in: A. Curnier (Ed.), Contact Mechanics, PPUR, Lausane
    • M. Raous, S. Barbarin, Preconditionned conjugate gradient method for a unilateral problem with friction, in: A. Curnier (Ed.), Contact Mechanics, PPUR, Lausane 1992, pp. 423-432.
    • (1992) , pp. 423-432
    • Raous, M.1    Barbarin, S.2
  • 35
    • 33947241227 scopus 로고    scopus 로고
    • A uniqueness criterion for the Signorini problem with Coulomb friction
    • Renard Y. A uniqueness criterion for the Signorini problem with Coulomb friction. SIAM J. Math. Anal. 2006, 38:452-467.
    • (2006) SIAM J. Math. Anal. , vol.38 , pp. 452-467
    • Renard, Y.1
  • 37
    • 84872705200 scopus 로고    scopus 로고
    • Computational Experience with an Interior Point Algorithm for Large Scale Contact Problems, Technical Report 04.22, MIP, Université Paul Sabatier, Toulouse
    • G. Tanoh, Y. Renard, D. Noll. Computational Experience with an Interior Point Algorithm for Large Scale Contact Problems, Technical Report 04.22, MIP, Université Paul Sabatier, Toulouse, 2004. http://www.optimization-online.org/DB_HTML/2004/12/1012.html.
    • (2004)
    • Tanoh, G.1    Renard, Y.2    Noll, D.3
  • 38
    • 78651359675 scopus 로고    scopus 로고
    • Robust implementation of contact under friction and large sliding with the extended finite element method
    • Siavelis M., Massin P., Guiton M.L.E., Mazet S., Moës N. Robust implementation of contact under friction and large sliding with the extended finite element method. Eur. J. Comput. Mech. 2010, 19(1-2-3):189-203.
    • (2010) Eur. J. Comput. Mech. , vol.19 , Issue.1-23 , pp. 189-203
    • Siavelis, M.1    Massin, P.2    Guiton, M.L.E.3    Mazet, S.4    Moës, N.5
  • 39
    • 0026626125 scopus 로고
    • An augmented Lagrangian treatment of contact problems involving friction
    • Simo J.C., Laursen T.A. An augmented Lagrangian treatment of contact problems involving friction. Comput. Struct. 1992, 42:97-116.
    • (1992) Comput. Struct. , vol.42 , pp. 97-116
    • Simo, J.C.1    Laursen, T.A.2
  • 40
    • 84872713439 scopus 로고    scopus 로고
    • Infinite-dimensional Semi-smooth Newton and Augmented Lagrangian Methods for Friction and Contact Problems in Elasticity, Ph.D. Thesis
    • G. Stadler, Infinite-dimensional Semi-smooth Newton and Augmented Lagrangian Methods for Friction and Contact Problems in Elasticity, Ph.D. Thesis, 2004.
    • (2004)
    • Stadler, G.1
  • 41
    • 84872704300 scopus 로고    scopus 로고
    • Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces, MOS-SIAM Series on Optimization, SIAM, Philadelphia
    • M. Ulbrich, Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces, MOS-SIAM Series on Optimization, SIAM, Philadelphia, 2011.
    • (2011)
    • Ulbrich, M.1
  • 42
    • 36749094499 scopus 로고    scopus 로고
    • A formulation for frictionless contact problems using a weak form introduced by Nitsche
    • Wriggers P., Zavarise G. A formulation for frictionless contact problems using a weak form introduced by Nitsche. Comput. Mech. 2008, 41:407-420.
    • (2008) Comput. Mech. , vol.41 , pp. 407-420
    • Wriggers, P.1    Zavarise, G.2


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