Constraints in structural and rigid body mechanics: a frictional contact problem

Simon R. Eugster1, Christian Glocker1
1Department of Mechanical and Process Engineering, Center of Mechanics, Institute for Mechanical Systems, ETH Zurich, Zurich, Switzerland

Tóm tắt

Từ khóa


Tài liệu tham khảo

Acary V, Brogliato B (2008) Numerical methods for nonsmooth dynamical systems: applications in mechanics and electronics. Lecture notes in applied and computational mechanics, vol 35. Springer, Berlin

Alart P, Curnier A (1991) A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput Methods Appl Mech Eng 92:353–375

Antman SS (1981) Material constraints in continuum mechanics. Atti Della Accademia Nazionale dei Lincei, Rendiconti, Classe di Scienze Fisiche, Matematiche e Naturali 70(8):256–264

Antman SS (2005) Nonlinear problems of elasticity, applied mathematical sciences, vol 107, 2nd edn. Springer, New York

Antman SS, Marlow RS (1991) Material constraints, Lagrange multipliers, and compatibility. Applications to rod and shell theories. Arch Ration Mech Anal 116:257–299

Ballard P, Millard A (2009) Poutres et arcs élastiques. Les Éditions de l’École Polytechnique

Bertails F, Audoly B, Cani MP, Querleux B, Leroy F, Lévêque JL (2006) Super-helices for predicting the dynamics of natural hair. In: ACM transactions on graphics (proceedings of the ACM SIGGRAPH ’06 conference), ACM, pp 1180–1187

Bertails-Descoubes F, Cadoux F, Daviet G, Acary V (2011) A nonsmooth newton solver for capturing exact coulomb friction in fiber assemblies. ACM Trans Graph 30(1):6–1614

Biot M (1974) Non-linear thermoelasticity, irreversible thermodynamics and elastic instability. Indiana Univ Math J 23:309–335

Brogliato B, Ten Dam A, Paoli L, Génot F, Abadie M (2002) Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Appl Mech Rev 55:107

Chamekh M, Mani-Aouadi S, Moakher M (2009) Modeling and numerical treatment of elastic rods with frictionless self-contact. Comput Methods Appl Mech Eng 198(47–48):3751–3764

Cho YH (2008) Numerical simulation of the dynamic responses of railway overhead contact lines to a moving pantograph, considering a nonlinear dropper. J Sound Vib 315(3):433–454

Collina A, Bruni S (2002) Numerical simulation of pantograph-overhead equipment interaction. Veh Syst Dyn 38(4):261–291

Dufva K, Kerkkänen K, Maqueda L, Shabana A (2007) Nonlinear dynamics of three-dimensional belt drives using the finite-element method. Nonlinear Dyn 48:449–466

Eugster SR (2009) Dynamics of an elevator: 2-dimensional modeling and simulation. Master’s thesis, ETH Zurich

Frémond M (1989) Internal constraints and constitutive laws. In: Rodrigues JF (ed) Mathematical models for phase change problems. pp 3–18

Frémond M (2001) Internal constraints in mechanics. Philos Trans R Soc Lond A: Math Phys Eng Sci 359(1789):2309–2326

Frémond M, Gormaz R, San Martín JA (2003) Collision of a solid with an incompressible fluid. Theoret Comput Fluid Dyn 16:405–420

Glocker Ch (2001) Set-valued force laws, dynamics of non-smooth systems. Lecture notes in applied mechanics, vol 1. Springer, Berlin

Glocker Ch (2004) Concepts for modeling impacts without friction. Acta Mech 168:1–19

Glocker Ch (2006a) An introduction to impacts. In: Haslinger J, Stavroulakis G (eds) Nonsmooth mechanics of solids. CISM courses and lectures, vol 485. Springer, Wien, pp 45–101

Glocker Ch (2006b) Simulation von harten Kontakten mit Reibung: Eine iterative Projektionsmethode. In: VDI-Berichte No. 1968: Schwingungen in Antrieben 2006 Tagung, Fulda, VDI Verlag, Düsseldorf, vol 1968

Goyal S, Perkins N, Lee CL (2008) Non-linear dynamic intertwining of rods with self-contact. Int J Non-Linear Mech 43(1):65–73

Jean M (1999) The non-smooth contact dynamics method. Comput Methods Appl Mech Eng 177(3-4):235–257

Kerkkänen K, García-Vallejo D, Mikkola A (2006) Modeling of belt-drives using a large deformation finite element formulation. Nonlinear Dyn 43:239–256

Leine RI, Nijmeijer H (2004) Dynamics and bifurcations of non-smooth mechanical systems. Lecture notes in applied and computational mechanics, vol 18. Springer, Berlin

Möller M (2012) Consistent integrators for non-smooth dynamical systems. PhD thesis, ETH Zurich

Moreau JJ (1985) Standard inelastic shocks and the dynamics of unilateral constraints. In: Del Piero G, Maceri F (eds) Unilateral problems in structural analysis. Proceedings of the second meeting on unilateral problems in structural analysis ravello, September 22–24, 1983, pp 173–221

Moreau JJ (1988a) Bounded variation in time. In: Moreau JJ, Panagiotopoulos PD, Strang G (eds) Topics in nonsmooth mechanics. Birkhäuser Verlag, Basel, pp 1–74

Moreau JJ (1988b) Unilateral contact and dry friction in finite freedom dynamics. In: Moreau JJ, Panagiotopoulos PD (eds) Non-smooth mechanics and applications CISM courses and lectures. Springer, Wien, pp 1–82

Moreau JJ (2003) Fonctionnelles convexes, Séminaire sur les équations aux dérivées partielles, Collège de France, 1966, et Edizioni del Dipartimento di Ingeneria Civile dell’Università di Roma Tor Vergata, Roma

Naghdi PM, Rubin MB (1984) Constrained theories of rods. J Elast 14:343–361

Papastavridis JG (2002) Analytical mechanics: a comprehensive treatise on the dynamics of constrained systems: for engineers, physicists, and mathematicians. Oxford University Press, Oxford

Rajagopal KR, Srinivasa AR (2005) On the nature of constraints for continua undergoing dissipative processes. Proc R Soc A: Math Phys Eng Sci 461(2061):2785–2795

Rauter FG, Pombo J, Ambrósio J, Pereira M (2007) Multibody modeling of pantographs for pantograph-catenary interaction. In: Eberhard P (ed) IUTAM symposium on multiscale problems in multibody system contacts, IUTAM bookseries, vol 1. Springer, Dordrecht, pp 205–226

Rockafellar R (1970) Convex analysis. Princeton mathematical series. Princeton University Press, Princeton, NJ

Romano G, Sacco E (1987) Convex problems in structural mechanics. In: Del Piero G, Maceri F (eds) Unilateral problems in structural analysis-2: proceedings of the second meeting on unilateral problems in structural analysis prescudin, June 17–20, 1985, pp 279–297

Rubin MB (2000) Cosserat theories: shells, rods, and points. Solid mechanics and its applications. Kluwer Academic Publishers, Dordrecht

Salençon J (2001) Handbook of continuum mechanics: general concepts, thermoelasticity. Physics and astronomy online library. Springer, Berlin

Studer C (2009) Numerics of unilateral contacts and friction: modeling and numerical time integration in non-smooth dynamics. Lecture notes in applied and computational mechanics, vol 47. Springer, Berlin

Truesdell C (1968) Essays in the history of mechanics. Springer, New York

Truesdell C, Noll W (2003) The non-linear field theories of mechanics, 3rd edn. Springer, Berlin

Yi L, Ji-Shun L, Guo-Ding C, Yu-Jun X, Ming-De D (2010) Multibody dynamics modeling of friction winder systems using absolute nodal coordination formulation. In: Huang G, Mak K, Maropoulos P (eds) Proceedings of the 6th CIRP-sponsored international conference on digital enterprise technology, advances in intelligent and soft computing, vol 66. Springer, Berlin, Heidelberg, pp 533–546