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Volumn 91, Issue 2, 2011, Pages 155-175

A formulation of the linear discrete Coulomb friction problem via convex optimization

Author keywords

Contact mechanics; Convex analysis; Convex optimization; Coulomb friction; Fixed point theorem; Nonsmooth mechanics; Painlev 's problem; Second order cone programming.

Indexed keywords


EID: 78751668343     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.201000073     Document Type: Article
Times cited : (45)

References (70)
  • 1
    • 38949194973 scopus 로고    scopus 로고
    • Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics, Lecture Notes in Applied and Computational Mechanics, (Springer, Berlin, Heidelberg, New York, 2008).
    • V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics, Lecture Notes in Applied and Computational Mechanics, Vol. 35 (Springer, Berlin, Heidelberg, New York, 2008).
    • , vol.35
    • Acary, V.1    Brogliato, B.2
  • 2
    • 78751653544 scopus 로고    scopus 로고
    • Dynamic simulation of rigid bodies: Modelling of frictional contact, in: Impacts in Mechanical Systems: Analysis and Modelling, edited by B. Brogliato, Lecture Notes in Physics (LNP) (Springer, Berlin, Heidelberg, New York, 2000) 61-144.
    • M. Abadie, Dynamic simulation of rigid bodies: Modelling of frictional contact, in: Impacts in Mechanical Systems: Analysis and Modelling, edited by B. Brogliato, Lecture Notes in Physics (LNP) Vol. 551 (Springer, Berlin, Heidelberg, New York, 2000), pp. 61-144.
    • , vol.551
    • Abadie, M.1
  • 3
    • 0026255347 scopus 로고
    • A mixed formulation for frictional contact problems prone to Newton like solution method
    • P. Alart and A. Curnier, A mixed formulation for frictional contact problems prone to Newton like solution method, Comput. Methods Appl. Mech. Eng. 92(3), 353-375 (1991).
    • (1991) Comput. Methods Appl. Mech. Eng. , vol.92 , Issue.3 , pp. 353-375
    • Alart, P.1    Curnier, A.2
  • 4
    • 78751678917 scopus 로고    scopus 로고
    • Applications of an Existence Result for the Coulomb Friction Problem, to appear in the edited volume of CMIS 2009 Conference (Springer, Berlin, Heidelberg, New York, 2010).
    • V. Acary and F. Cadoux, Applications of an Existence Result for the Coulomb Friction Problem, to appear in the edited volume of CMIS 2009 Conference (Springer, Berlin, Heidelberg, New York, 2010).
    • Acary, V.1    Cadoux, F.2
  • 5
    • 84983947646 scopus 로고
    • Hard and soft fingered robot grippers. The linear complementarity approach
    • A. Al-Fahed, G. Stavroulakis, and P. Panagiotopoulos, Hard and soft fingered robot grippers. The linear complementarity approach, Z. Angew. Math. Mech. 71, 257-265 (1991).
    • (1991) Z. Angew. Math. Mech. , vol.71 , pp. 257-265
    • Al-Fahed, A.1    Stavroulakis, G.2    Panagiotopoulos, P.3
  • 6
    • 2342458706 scopus 로고    scopus 로고
    • Second-order cone programming
    • F. Alizadeh and D. Goldfarb, Second-order cone programming, Math. Program. 95, 3-51 (2003).
    • (2003) Math. Program. , vol.95 , pp. 3-51
    • Alizadeh, F.1    Goldfarb, D.2
  • 7
    • 0000413099 scopus 로고
    • n dans lui-même; application à la mécanique du contact.)
    • n dans lui-même; application à la mécanique du contact.), RAIRO, Model. Math. Anal. Numer. (France) 27(2), 203-222 (1993).
    • (1993) RAIRO, Model. Math. Anal. Numer. (France) , vol.27 , Issue.2 , pp. 203-222
    • Alart, P.1
  • 8
    • 0030706340 scopus 로고    scopus 로고
    • Méthode de Newton généralisée en mécanique du contact, .
    • P. Alart, Méthode de Newton généralisée en mécanique du contact, J. Math. Pure Appl. (France) 76(1), 83 (1997).
    • (1997) J. Math. Pure Appl. (France) , vol.76 , Issue.1 , pp. 83
    • Alart, P.1
  • 9
    • 0034262382 scopus 로고    scopus 로고
    • Existence results for quasi-static contact problems with Coulomb friction
    • L.E. Andersson, Existence results for quasi-static contact problems with Coulomb friction, Appl. Math. Optim. 42, 169-202 (2000).
    • (2000) Appl. Math. Optim. , vol.42 , pp. 169-202
    • Andersson, L.E.1
  • 11
    • 0032760580 scopus 로고    scopus 로고
    • A counter-example to uniqueness in quasi-static elastic contact problems with small friction
    • P. Ballard, A counter-example to uniqueness in quasi-static elastic contact problems with small friction, Int. J. Eng. Sci. 37, 163-178 (1999).
    • (1999) Int. J. Eng. Sci. , vol.37 , pp. 163-178
    • Ballard, P.1
  • 12
    • 0039014134 scopus 로고    scopus 로고
    • The dynamics of discrete mechanical systems with perfect unilateral constraints
    • P. Ballard, The dynamics of discrete mechanical systems with perfect unilateral constraints, Arch. Ration. Mech. Anal. 154, 199-274 (2000).
    • (2000) Arch. Ration. Mech. Anal. , vol.154 , pp. 199-274
    • Ballard, P.1
  • 13
    • 0001057945 scopus 로고
    • Issues in computing contact forces for non penetrating rigid bodies
    • D. Baraff, Issues in computing contact forces for non penetrating rigid bodies, Algorithmica 10, 292-352 (1993).
    • (1993) Algorithmica , vol.10 , pp. 292-352
    • Baraff, D.1
  • 14
    • 15744376785 scopus 로고    scopus 로고
    • Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem.
    • P. Ballard and S. Basseville, Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem., ESAIM, Math. Model. Numer. Anal. 39(1), 59-77 (2005).
    • (2005) ESAIM, Math. Model. Numer. Anal. , vol.39 , Issue.1 , pp. 59-77
    • Ballard, P.1    Basseville, S.2
  • 15
    • 77953959963 scopus 로고    scopus 로고
    • Weak formulations and solution multiplicity of equilibrium configurations with Coulomb friction
    • M. Bostan and P. Hild, Weak formulations and solution multiplicity of equilibrium configurations with Coulomb friction, Math. Model. Nat. Phenom. 4(1), 147-162 (2009).
    • (2009) Math. Model. Nat. Phenom. , vol.4 , Issue.1 , pp. 147-162
    • Bostan, M.1    Hild, P.2
  • 16
    • 78751653696 scopus 로고    scopus 로고
    • Convex Optimization (Cambridge University Press, Cambridge, 2004).
    • S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004).
    • Boyd, S.1    Vandenberghe, L.2
  • 17
    • 0024128351 scopus 로고
    • A generalized Newton method for contact problems with friction
    • A. Curnier and P. Alart, A generalized Newton method for contact problems with friction, J. Mec. Theor. Appl. Suppl. (France) 1-7, 67-82 (1988).
    • (1988) J. Mec. Theor. Appl. Suppl. (France) , vol.1-7 , pp. 67-82
    • Curnier, A.1    Alart, P.2
  • 18
    • 78751669857 scopus 로고    scopus 로고
    • Optimisation et analyse convexe pour la dynamique non régulière, PhD thesis (Univ. J. Fourier, Grenoble, 2009).
    • F. Cadoux, Optimisation et analyse convexe pour la dynamique non régulière, PhD thesis (Univ. J. Fourier, Grenoble, 2009).
    • Cadoux, F.1
  • 19
    • 78751658072 scopus 로고    scopus 로고
    • An optimization-based algorithm for Coulomb's frictional contact
    • F. Cadoux, An optimization-based algorithm for Coulomb's frictional contact, ESAIM Proc. 27, 54-69 (2009).
    • (2009) ESAIM Proc. , vol.27 , pp. 54-69
    • Cadoux, F.1
  • 21
    • 78751660130 scopus 로고    scopus 로고
    • Existence of a fixed point for a nonsmooth function arising in numerical mechanics, to appear in Set-Valued and Variational Analysis.
    • F. Cadoux and J. Malick, Existence of a fixed point for a nonsmooth function arising in numerical mechanics, to appear in Set-Valued and Variational Analysis.
    • Cadoux, F.1    Malick, J.2
  • 22
    • 78751671129 scopus 로고    scopus 로고
    • Les Inéquations en Mécanique et en Physique (Dunod, Paris, 1972).
    • G. Duvaut and J. Lions, Les Inéquations en Mécanique et en Physique (Dunod, Paris, 1972).
    • Duvaut, G.1    Lions, J.2
  • 23
    • 78751654160 scopus 로고    scopus 로고
    • Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, 1983).
    • J. Dennis and R. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, 1983).
    • Dennis, J.1    Schnabel, R.2
  • 24
    • 0001226430 scopus 로고
    • New inequality and functional for contact with friction: The implicit standard material approach
    • G. De Saxcé and Z.Q. Feng, New inequality and functional for contact with friction: The implicit standard material approach, Mech. Struct. Mach. 19(3), 301-325 (1991).
    • (1991) Mech. Struct. Mach. , vol.19 , Issue.3 , pp. 301-325
    • De Saxcé, G.1    Feng, O.2
  • 25
    • 0032143148 scopus 로고    scopus 로고
    • The bipotential method: a constructive approach to design the complete contact law with friction and improved numerical algorithms
    • G. De Saxcé and Z.Q. Feng, The bipotential method: a constructive approach to design the complete contact law with friction and improved numerical algorithms, Math. Comput. Model. 28(4-8), 225-245 (1998).
    • (1998) Math. Comput. Model. , vol.28 , Issue.4-8 , pp. 225-245
    • De Saxcé, G.1    Feng, O.2
  • 26
    • 0037391292 scopus 로고    scopus 로고
    • Existence of solutions for the dynamical frictional contact problem of isotropic viscoelastic bodies
    • C. Eck and J. Jarušek, Existence of solutions for the dynamical frictional contact problem of isotropic viscoelastic bodies, Nonlinear Anal. 53, 157-181 (2003).
    • (2003) Nonlinear Anal. , vol.53 , pp. 157-181
    • Eck, C.1    Jarušek, J.2
  • 27
    • 78751675018 scopus 로고    scopus 로고
    • Unilateral Contact Problems: Variational Methods and Existence Theorems, Pure and Applied Mathematics, (CRC Press, Boca Raton 2005).
    • C. Eck, J. Jarušek, and M. Krbec, Unilateral Contact Problems: Variational Methods and Existence Theorems, Pure and Applied Mathematics, Vol. 270 (CRC Press, Boca Raton 2005).
    • , vol.270
    • Eck, C.1    Jarušek, J.2    Krbec, M.3
  • 28
    • 84989444330 scopus 로고
    • 2D and 3D frictional contact algorithms and applications in a large deformation context
    • Z.Q. Feng, 2D and 3D frictional contact algorithms and applications in a large deformation context, Commun. Numer. Methods Eng. 11, 409-416 (1995).
    • (1995) Commun. Numer. Methods Eng. , vol.11 , pp. 409-416
    • Feng, O.1
  • 29
    • 78751676113 scopus 로고    scopus 로고
    • Practical Methods of Optimization, second edition (John Wiley & Sons, Chichester, 1987).
    • R. Fletcher, Practical Methods of Optimization, second edition (John Wiley & Sons, Chichester, 1987).
    • Fletcher, R.1
  • 30
    • 84887435608 scopus 로고    scopus 로고
    • and (eds.), Novel Approaches in Civil Engineering, Lecture Notes in Applied and Computational Mechanics, (Springer, Berlin, Heidelberg, New York, 2004).
    • M. Frémond and F. Maceri (eds.), Novel Approaches in Civil Engineering, Lecture Notes in Applied and Computational Mechanics, Vol. 14 (Springer, Berlin, Heidelberg, New York, 2004).
    • , vol.14
    • Frémond, M.1    Maceri, F.2
  • 31
  • 32
    • 67349188924 scopus 로고    scopus 로고
    • Curve squealing of trains: Measurement, modelling and simulation
    • C. Glocker, E. Cataldi-Spinola, and R. Leine, Curve squealing of trains: Measurement, modelling and simulation, J. Sound Vib. 324(1-2), 365-386 (2009).
    • (2009) J. Sound Vib. , vol.324 , Issue.1-2 , pp. 365-386
    • Glocker, C.1    Cataldi-Spinola, E.2    Leine, R.3
  • 33
    • 10844238213 scopus 로고    scopus 로고
    • Object-oriented software for quadratic programming
    • E. Gertz and S. Wright, Object-oriented software for quadratic programming, ACM Trans. Math. Softw. 29(1), 58-81 (2003).
    • (2003) ACM Trans. Math. Softw. , vol.29 , Issue.1 , pp. 58-81
    • Gertz, E.1    Wright, S.2
  • 34
    • 0020887530 scopus 로고
    • Approximation of the Signorini problem with friction, obeying the Coulomb law
    • J. Haslinger, Approximation of the Signorini problem with friction, obeying the Coulomb law, Math. Methods Appl. Sci. 5, 422-437 (1983).
    • (1983) Math. Methods Appl. Sci. , vol.5 , pp. 422-437
    • Haslinger, J.1
  • 35
    • 0039993075 scopus 로고
    • Least square method for solving contact problems with friction obeying Coulomb's law
    • J. Haslinger, Least square method for solving contact problems with friction obeying Coulomb's law, Appl. Math. 29(3), 212-224 (1984).
    • (1984) Appl. Math. , vol.29 , Issue.3 , pp. 212-224
    • Haslinger, J.1
  • 36
    • 78751659573 scopus 로고    scopus 로고
    • Quasistatic contact problems in viscoelasticty and viscoplasticity (American Mathematical Society, Providence, 2002).
    • W. Han and M. Sofonea, Quasistatic contact problems in viscoelasticty and viscoplasticity (American Mathematical Society, Providence, 2002).
    • Han, W.1    Sofonea, M.2
  • 37
    • 78751659709 scopus 로고    scopus 로고
    • Convex Analysis and Minimization Algorithms, (Springer, Heidelberg, 1993).
    • J.B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, Vol. I and II (Springer, Heidelberg, 1993).
    • , vol.1-2
    • Hiriart-Urruty, J.B.1    Lemaréchal, C.2
  • 38
    • 0032029719 scopus 로고    scopus 로고
    • A Gauss Seidel like algorithm to solve frictional contact problems
    • F. Jourdan, P. Alart, and M. Jean, A Gauss Seidel like algorithm to solve frictional contact problems, Comput. Methods Appl. Mech. Eng. 155(1), 31-47 (1998).
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.155 , Issue.1 , pp. 31-47
    • Jourdan, F.1    Alart, P.2    Jean, M.3
  • 39
    • 78751676664 scopus 로고    scopus 로고
    • Catastrophic features of Coulomb friction model, in: The Mathematics of Finite Elements and Applications, edited by J. R. Whiteman (Academic Press, London, 1981) 259-264.
    • V. Janovský, Catastrophic features of Coulomb friction model, in: The Mathematics of Finite Elements and Applications, edited by J. R. Whiteman (Academic Press, London, 1981), pp. 259-264.
    • Janovský, V.1
  • 40
    • 0001724126 scopus 로고
    • Contact problems with bounded friction. Coercive case
    • J. Jarušek, Contact problems with bounded friction. Coercive case, Czech. Math. J. 33, 237-261 (1983).
    • (1983) Czech. Math. J. , vol.33 , pp. 237-261
    • Jarušek, J.1
  • 41
    • 0001367137 scopus 로고
    • Contact problems with bounded friction. Semicoercive case
    • J. Jarušek, Contact problems with bounded friction. Semicoercive case, Czech. Math. J. 34, 619-629 (1984).
    • (1984) Czech. Math. J. , vol.34 , pp. 619-629
    • Jarušek, J.1
  • 42
    • 0347420091 scopus 로고    scopus 로고
    • Dynamic contact problems with small Coulomb friction for visco-electic bodies. Existence of solutions
    • J. Jarušek and C. Eck, Dynamic contact problems with small Coulomb friction for visco-electic bodies. Existence of solutions, Math. Models Methods Appl. Sci. 9(1), 11-34 (1999).
    • (1999) Math. Models Methods Appl. Sci. , vol.9 , Issue.1 , pp. 11-34
    • Jarušek, J.1    Eck, C.2
  • 43
    • 78751654432 scopus 로고    scopus 로고
    • Unilaterality and dry friction in the dynamics of rigid bodies collections, in: Proc. of Contact Mech. Int. Symp., edited by A. Curnier (Presses Polytechniques et Universitaires Romandes, Lausanne, 1992) 31-48.
    • M. Jean and J. Moreau, Unilaterality and dry friction in the dynamics of rigid bodies collections, in: Proc. of Contact Mech. Int. Symp., edited by A. Curnier (Presses Polytechniques et Universitaires Romandes, Lausanne, 1992), pp. 31-48.
    • Jean, M.1    Moreau, J.2
  • 44
    • 0024140512 scopus 로고
    • Implementation of unilateral contact and dry friction in computer codes dealing with large deformations problems
    • M. Jean and G. Touzot, Implementation of unilateral contact and dry friction in computer codes dealing with large deformations problems, J. Mec. Theor. Appl. 7(1), 145-160 (1988).
    • (1988) J. Mec. Theor. Appl. , vol.7 , Issue.1 , pp. 145-160
    • Jean, M.1    Touzot, G.2
  • 45
    • 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(5), 1185-1198 (1988).
    • (1988) Comput. Struct. , vol.30 , Issue.5 , pp. 1185-1198
    • Klarbring, A.1    Björkman, G.2
  • 46
    • 78751674708 scopus 로고    scopus 로고
    • Methods of Descent for Nondifferentiable Optimization, Lecture Notes in Mathematics (Springer, Berlin, Heidelberg, New York, 1985).
    • K. Kiwiel, Methods of Descent for Nondifferentiable Optimization, Lecture Notes in Mathematics Vol. 1133 (Springer, Berlin, Heidelberg, New York, 1985).
    • , vol.1133
    • Kiwiel, K.1
  • 47
    • 0022795271 scopus 로고
    • A mathematical programming approach to three-dimensional contact problems with friction
    • A. Klarbring, A mathematical programming approach to three-dimensional contact problems with friction, Comput. Methods Appl. Mech. Eng. 58, 175-200 (1986).
    • (1986) Comput. Methods Appl. Mech. Eng. , vol.58 , pp. 175-200
    • Klarbring, A.1
  • 48
    • 0032222082 scopus 로고    scopus 로고
    • Existence of solutions to discrete semicoercive frictional contact problems
    • A. Klarbring and J. Pang, Existence of solutions to discrete semicoercive frictional contact problems, SIAM J. Optim. 8(2), 414-442 (1998).
    • (1998) SIAM J. Optim. , vol.8 , Issue.2 , pp. 414-442
    • Klarbring, A.1    Pang, J.2
  • 49
    • 0007502705 scopus 로고    scopus 로고
    • The discrete steady sliding problem
    • A. Klarbring and J. Pang, The discrete steady sliding problem, Z. Angew. Math. Mech. 79(2), 75-90 (1999).
    • (1999) Z. Angew. Math. Mech. , vol.79 , Issue.2 , pp. 75-90
    • Klarbring, A.1    Pang, J.2
  • 50
    • 0032021609 scopus 로고    scopus 로고
    • Smoothing Newton method for solving two- and three-dimensional frictional contact problems
    • A. Leung, C. Guoqing, and C. Wanji, Smoothing Newton method for solving two- and three-dimensional frictional contact problems, Int. J. Numer. Methods Eng. 41, 1001-1027 (1998).
    • (1998) Int. J. Numer. Methods Eng. , vol.41 , pp. 1001-1027
    • Leung, A.1    Guoqing, C.2    Wanji, C.3
  • 51
    • 0023594165 scopus 로고
    • A contribution to the analysis of unilateral contact problems with friction
    • E. Mitsopoulou and I. Doudoumis, A contribution to the analysis of unilateral contact problems with friction, Solid Mech. Arch. 12(3), 165-186 (1987).
    • (1987) Solid Mech. Arch. , vol.12 , Issue.3 , pp. 165-186
    • Mitsopoulou, E.1    Doudoumis, I.2
  • 52
    • 38949160203 scopus 로고
    • On the solution of the unilateral contact frictional problem for general static loading conditions
    • E. Mitsopoulou and I. Doudoumis, On the solution of the unilateral contact frictional problem for general static loading conditions, Comput. Struct. 30(5), 1111-1126 (1988).
    • (1988) Comput. Struct. , vol.30 , Issue.5 , pp. 1111-1126
    • Mitsopoulou, E.1    Doudoumis, I.2
  • 53
    • 0039693879 scopus 로고
    • Quadratic programming in mechanics: dynamics of one sided constraints
    • J. Moreau, Quadratic programming in mechanics: dynamics of one sided constraints, SIAM J. Control 4(1), 153-158 (1966).
    • (1966) SIAM J. Control , vol.4 , Issue.1 , pp. 153-158
    • Moreau, J.1
  • 54
    • 78751677940 scopus 로고    scopus 로고
    • Unilateral Contact and Dry Friction in Finite Freedom Dynamics, in: Nonsmooth Mechanics and Applications, No. 302 in CISM, Courses and Lectures, edited by J. Moreau and P. D. Panagiotopoulos (Springer, Wien, New York, 1988) 1-82.
    • J. Moreau, Unilateral Contact and Dry Friction in Finite Freedom Dynamics, in: Nonsmooth Mechanics and Applications, No. 302 in CISM, Courses and Lectures, edited by J. Moreau and P. D. Panagiotopoulos (Springer, Wien, New York, 1988), pp. 1-82.
    • Moreau, J.1
  • 55
    • 0002226904 scopus 로고
    • Some numerical methods in multibody dynamics: Application to granular materials
    • J. Moreau, Some numerical methods in multibody dynamics: Application to granular materials, Eur. J. Mech. A, Solids Suppl. 4, 93-114 (1994).
    • (1994) Eur. J. Mech. A, Solids Suppl. , vol.4 , pp. 93-114
    • Moreau, J.1
  • 56
    • 0000328269 scopus 로고
    • On the solution of the variational inequality to the Signorini problem with small friction
    • J. Nečas, J. Jarušek, and J. Haslinger, On the solution of the variational inequality to the Signorini problem with small friction, Boll. U.M.I. 5(17-B), 796-811 (1980).
    • (1980) Boll. U.M.I. , vol.5 , Issue.17 B , pp. 796-811
    • Nečas, J.1    Jarušek, J.2    Haslinger, J.3
  • 57
    • 78751672645 scopus 로고    scopus 로고
    • Leçon sur le Frottement (Hermann, Paris, 1895).
    • P. Painlevé, Leçon sur le Frottement (Hermann, Paris, 1895).
    • Painlevé, P.1
  • 58
    • 78751666304 scopus 로고    scopus 로고
    • Multibody Dynamics with Unilateral Contacts, Non-linear Dynamics (John Wiley & Sons, New York, 1996).
    • F. Pfeiffer and C. Glocker, Multibody Dynamics with Unilateral Contacts, Non-linear Dynamics (John Wiley & Sons, New York, 1996).
    • Pfeiffer, F.1    Glocker, C.2
  • 59
    • 0028494492 scopus 로고
    • Three dimensional frictional contact analysis using the homotopy method
    • J. Park and B. Kwak, Three dimensional frictional contact analysis using the homotopy method, Trans ASME, J. Appl. Mech. 61, 703-709 (1994).
    • (1994) Trans ASME, J. Appl. Mech. , vol.61 , pp. 703-709
    • Park, J.1    Kwak, B.2
  • 60
    • 0000317447 scopus 로고    scopus 로고
    • A unified approach to frictional contact problem
    • J. Pang and D. Stewart, A unified approach to frictional contact problem, Int. J. Eng. Sci. 37, 1747-1768 (1999).
    • (1999) Int. J. Eng. Sci. , vol.37 , pp. 1747-1768
    • Pang, J.1    Stewart, D.2
  • 61
    • 0001233839 scopus 로고    scopus 로고
    • Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with Coulomb friction
    • J. Pang and J. Trinkle, Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with Coulomb friction, Math. Program. 73, 199-226 (1996).
    • (1996) Math. Program. , vol.73 , pp. 199-226
    • Pang, J.1    Trinkle, J.2
  • 62
    • 0035400656 scopus 로고    scopus 로고
    • Existence and approximation of a solution to quasistatic Signorini problem with local friction
    • R. Rocca and M. Cocu, Existence and approximation of a solution to quasistatic Signorini problem with local friction, Int. J. Eng. Sci. 39, 1233-1255 (2001).
    • (2001) Int. J. Eng. Sci. , vol.39 , pp. 1233-1255
    • Rocca, R.1    Cocu, M.2
  • 63
    • 0000319412 scopus 로고    scopus 로고
    • Force distributions in dense two-dimensional granular systems
    • F. Radjai, M. Jean, J. Moreau, and S. Roux, Force distributions in dense two-dimensional granular systems, Phys. Rev. Lett. 77, 274-277 (1996).
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 274-277
    • Radjai, F.1    Jean, M.2    Moreau, J.3    Roux, S.4
  • 64
    • 78751656319 scopus 로고    scopus 로고
    • Convex Analysis (Princeton University Press, Princeton, 1970).
    • R. Rockafellar, Convex Analysis (Princeton University Press, Princeton, 1970).
    • Rockafellar, R.1
  • 65
    • 0030213721 scopus 로고    scopus 로고
    • An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and Coulomb friction
    • D. Stewart and J. Trinkle, An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and Coulomb friction, Int J. Numer. Methods Eng. 39(15), 2673-2691 (1996).
    • (1996) Int J. Numer. Methods Eng. , vol.39 , Issue.15 , pp. 2673-2691
    • Stewart, D.1    Trinkle, J.2
  • 66
    • 0032282916 scopus 로고    scopus 로고
    • Convergence of a Time-Stepping Scheme for Rigid-Body Dynamics and Resolution of Painlevé's Problem
    • D. Stewart, Convergence of a Time-Stepping Scheme for Rigid-Body Dynamics and Resolution of Painlevé's Problem, Arch. Ration. Mech. Anal. 154, 215-260 (1998).
    • (1998) Arch. Ration. Mech. Anal. , vol.154 , pp. 215-260
    • Stewart, D.1
  • 67
    • 40949117258 scopus 로고    scopus 로고
    • Snake robot obstacle-aided locomotion: Modeling, simulations, and experiments
    • A. Transeth, R. Leine, C. Glocker, K. Pettersen, and P. Liljebäck, Snake robot obstacle-aided locomotion: Modeling, simulations, and experiments, IEEE Trans. Robot. 24(1), 88-104 (2008).
    • (2008) IEEE Trans. Robot. , vol.24 , Issue.1 , pp. 88-104
    • Transeth, A.1    Leine, R.2    Glocker, C.3    Pettersen, K.4    Liljebäck, P.5
  • 68
    • 78751652240 scopus 로고    scopus 로고
    • and (eds.), Computational Contact Mechanics, CISM Courses and Lectures (Springer, Berlin, Heidelberg, New York, 2008).
    • P. Wriggers and T. Laursen (eds.), Computational Contact Mechanics, CISM Courses and Lectures, Vol. 498 (Springer, Berlin, Heidelberg, New York, 2008).
    • , vol.498
    • Wriggers, P.1    Laursen, T.2
  • 69
    • 84891471348 scopus 로고    scopus 로고
    • Computational Contact Mechanics, 2nd edition (Springer, Berlin, Heidelberg, New York, 2006).
    • P. Wriggers, Computational Contact Mechanics, 2nd edition (Springer, Berlin, Heidelberg, New York, 2006).
    • Wriggers, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.