contact; impact; implicit; multibody dynamics; nonlinear dynamics; time integration
Abstract :
[en] We present a new node-to-face frictional contact element for the simulation of the nonsmooth dynamics of systems composed of rigid and flexible bodies connected by kinematic joints. The equations of motion are integrated using a nonsmooth generalized-alpha time integration scheme and the frictional contact problem is formulated using a mixed approach, based on an augmented Lagrangian technique and a Coulomb friction law. The numerical results are independent of any user-defined penalty parameter for the normal or tangential component of the forces and, the bilateral and the unilateral constraints are exactly fulfilled both at position and velocity levels. Finally, the robustness and the performance of the proposed algorithm are demonstrated by solving several numerical examples of nonsmooth mechanical systems involving frictional contact.
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Duriez, C., Dubois, F., Kheddar, A., Andriot, C., Realistic haptic rendering of interacting deformable objects in virtual environments (2006) IEEE Trans Vis Comput Graph, 12, pp. 36-47
Pfeiffer, F., Glocker, C., (1996) Multibody Dynamics with Unilateral Contacts, , Wiley Series in Nonlinear Science, Hoboken, NJ, Wiley
Acary, V., Projected event-capturing time-stepping schemes for nonsmooth mechanical systems with unilateral contact and Coulomb friction (2013) Comput Methods Appl Mech Eng, 256, pp. 224-250
Pfeiffer, F., On non-smooth dynamics (2008) Meccanica, 43, pp. 533-554
Esche, S.K., Kinzel, G.L., Altan, T., Issues in convergence improvement for non-linear finite element programs (1997) Int J Numer Methods Eng, 40, pp. 4577-4594
Bostan, M., Hild, P., Weak formulations and solution multiplicity of equilibrium configurations with coulomb friction (2009) Math Modell Natur Phenomena, 4, pp. 147-162
Pennestrí, E., Rossi, V., Salvini, P., Valentini, P.P., Review and comparison of dry friction force models (2016) Nonlinear Dyn, 83, pp. 1785-1801
Marques, F., Flores, P., Claro, J.C.P., Lankarani, H.M., Modeling and analysis of friction including rolling effects in multibody dynamics: a review (2019) Multibody Syst Dyn, 45, pp. 223-244
Acary, V., Brémond, M., Huber, O., (2018) On Solving Contact Problems with Coulomb Friction: Formulations and Numerical Comparisons, pp. 375-457. , Cham, Springer International Publishing
Kikuchi, N., Oden, J.T., (1988) Contact Problems in Elasticity: A Study of Variational Inequalities Constrains and Finite Element Method, , Philadelphia, PA, SIAM
Belytschko, T., Neal, M.O., Contact-impact by the pinball algorithm with penalty and Lagrangian-methods (1991) Int J Numer Methods Eng, 31, pp. 547-572
Wriggers, P., (2002) Computational Contact Mechanics, , New York, NY, John Wiley and Sons
Cavalieri, F.J., Fachinotti, V., Cardona, A., A mortar contact algorithm for three-dimensional elasticity problems (2012) Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 28 (2), pp. 80-92
Lankarani, H., Nikravesh, P., Continuous contact force models for impact analysis in multibody analysis (1994) Nonlinear Dyn, 5, pp. 193-207
Brogliato, B., (1999) Nonsmooth Mechanics, , New York, NY, Springer
Acary, V., Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts (2012) Appl Numer Math, 62 (10), pp. 1259-1275
Simo, J.C., Laursen, T.A., An augmented Lagrangian treatment of contact problems involving friction (1992) Comput Struct, 42 (1), pp. 97-116
Love, G.R., Laursen, T.A., Improved implicit integrators for transient impact problems-dynamic frictional dissipation within an admissible conserving framework (2003) Comput Methods Appl Mech Eng, 192 (19), pp. 2223-2248
Areias, P.M.A., Sá, J., António, C.A., Algorithms for the analysis of 3D finite strain contact problems (2004) Int J Numer Methods Eng, 61, pp. 1107-1151
Alart, P., Curnier, A., A mixed formulation for frictional contact problems prone to Newton like solution methods (1991) Comput Methods Appl Mech Eng, 92 (3), pp. 353-375
Hestenes, M.R., Multiplier and gradient methods (1969) J Optim Theory and Applic, 4, pp. 303-320
Powell, M., A method for nonlinear constraints in optimization problems (1969) Optimization, pp. 283-298. , Fletcher R, ed., London, UK, Academic Press
Géradin, M., Cardona, A., (2001) Flexible Multibody Dynamics: A Finite Element Approach, , Hoboken. NJ, Wiley
Moreau, J.J., (1988) Unilateral Contact and Dry Friction in Finite Freedom Dynamics, pp. 1-82. , Vienna, Springer Vienna
Jean, M., The non-smooth contact dynamics method (1999) Comput Methods Appl Mech Eng, 177 (3), pp. 235-257
Dubois, F., Jean, M., Renuf, M., Mozul, R., Martin, A., Bagneris, M., (2011), LMGC90 CSMA
Acary, V., Pérignon, F., (2007), An introduction to SICONS INRIA. Tech. Rep. 0340
Cardona, A., Klapka, I., Géradin, M., Design of a new finite element programming environment (1994) Eng Comput, 11, pp. 365-381
Newmark, N.M., A method for computation for structural dynamics (1959) ASCE J Eng Mech Div, 85, pp. 67-94
Hilber, H., Hughes, T., Taylor, R., Improved numerical dissipation for time integration algorithms in structural dynamics (1977) Earthq Eng Struct Dyn, 5, pp. 283-292
Chung, J., Hulbert, G., Time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method (1993) ASME J Appl Mech, 60 (2), pp. 371-375
Bauchau, O.A., On the modeling of friction and rolling in flexible multi-body systems (1999) Multibody Syst Dyn, 3, pp. 209-239
Lens, E.V., Cardona, A., Géradin, M., Energy preserving time integration for constrained multibody systems (2004) Multibody Syst Dyn, 11 (1), pp. 41-61
Krause, R., Walloth, M., A time discretization scheme based on Rothe's method for dynamical contact problems with friction (2009) Comput Methods Appl Mech Eng, 199, pp. 1-19
Krause, R., Walloth, M., Presentation and comparison of selected algorithms for dynamic contact based on the newmark scheme (2012) Appl Numer Math, 62, pp. 1393-1410
Krause, R., Walloth, M., A family of space-time connecting discretization schemes for elastodynamic contact problems with local impact detection (2011) Int J Numer Methods Eng, 200, pp. 3425-3438
Brüls, O., Acary, V., Cardona, A., Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized-α scheme (2014) Comput Methods Appl Mech Eng, 281, pp. 131-161
Acary, V., Energy conservation and dissipation properties of time-integration methods for nonsmooth elastodynamics with contact (2016) J Appl Math Mech/Zeitschrift für Angewandte Mathematik und Mechanik, 96 (5), pp. 585-603
Cosimo, A., Galvez, J., Cavalieri, F.J., Cardona, A., Brüls, O., A robust nonsmooth generalized-α scheme for flexible systems with impacts (2020) Multibody Syst Dyn, 48 (5), pp. 127-149
Puso, M.A., Laursen, T.A., A mortar segment-to-segment frictional contact method for large deformations (2004) Comput Methods Appl Mech Eng, 193 (45), pp. 4891-4913
Cavalieri, F.J., Cardona, A., Numerical solution of frictional contact problems based on a mortar algorithm with an augmented Lagrangian technique (2015) Multibody System Dynamics, 35 (4), pp. 353-375
Gear, C.W., Leimkuhler, B., Gupta, G.K., Automatic integration of Euler-Lagrange equations with constraints (1985) J Comput Appl Math, 12, pp. 13:77-13:90
Chen, Q.-Z., Acary, V., Virlez, G., Brüls, O., A nonsmooth generalized-α scheme for flexible multibody systems with unilateral constraints (2013) Int J Numer Methods Eng, pp. 96:487-511
Brüls, O., Acary, V., Cardona, A., (2018) On the Constraints Formulation in the Nonsmooth Generalized-α Method, pp. 335-374. , New York, NY, Springer International Publishing
Martin, A., Brüls, O., Convergence of the generalized-α scheme for constrained mechanical systems (2007) Multibody Syst Dyn, 18 (2), pp. 185-202
Cardona, A., Géradin, M., (1994) Numerical Integration of Second Order Differential—Algebraic Systems in Flexible Mechanism Dynamics, pp. 501-529. , Netherlands, Springer
Bottasso, C., Bauchau, O., Cardona, A., Time-step-size-independent conditioning and sensitivity to perturbations in the numerical solution of index three differential algebraic equations (2007) SIAM J Sci Comput, 29, pp. 397-414
Brüls, O., Cardona, A., Arnold, M., Lie group generalized-α time integration of constrained flexible multibody systems (2012) Mech Mach Theory, 48, pp. 121-137
Rockafellar, R.T., Augmented Lagrangians and applications of the proximal point algorithm in convex programming (1976) Math Oper Res, 1, pp. 97-116
Leine, R.I., Wouw, N., (2008) Stability and Convergence of Mechanical Systems with Unilateral Constraints, , Berlin Heidelberg/Germany, Springer
Zander, R., Forg, M., Ulbrich, H., Impacts on beam structures: interactions of wave propagation and global dynamics (2007) IUTAM Symp Multiscale Prob Multibody Syst Contacts, 1, pp. 327-338
Glocker, C., Haslinger, J., Stavroulakis, G.E., An introduction to impacts (2006) Nonsmooth Mechanics of Solids, pp. 45-101. , eds., Vienna, Springer
Foerg, M., Geier, T., Neumann, L., Ulbrich, H., (2006), R-factor strategies for the augmented Lagrangian approach in multi-body contact mechanics. Paper presented at Proceedings of the IIIrd European Conference on Computational Mechanics
June, 316
García Orden, J.C., Goicolea, J., Conserving properties in constrained dynamics of flexible multibody systems (2000) Multibody Syst Dyn, 4 (4), pp. 225-244
Lens, E., Cardona, A., A nonlinear beam element formulation in the framework of an energy preserving time integration scheme for constrained multibody systems dynamics (2008) Comput Struct, 86 (1), pp. 47-63
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
