A general purpose formulation for nonsmooth dynamics with finite rotations: Application to the woodpecker toy

Equations of motion; Toys; Finite element codes; Finite rotations; Frictional contact; Horizontal displacements; Multi-body dynamic; Non-smooth dynamics; Simulation code; Unilateral constraints; Rotation

Abstract :

[en] The aim of this work is to extend the finite element multibody dynamics approach to problems involving frictional contacts and impacts. The nonsmooth generalized-α (NSGA) scheme is adopted, which imposes bilateral and unilateral constraints both at position and velocity levels avoiding drift phenomena. This scheme can be implemented in a general purpose simulation code with limited modifications of pre-existing elements. The study of the woodpecker toy dynamics sets up a good example to show the capabilities of the NSGA scheme within the context of a general finite element framework. This example has already been studied by many authors who generally adopted a model with a minimal set of coordinates and small rotations. It is shown that good results are obtained using a general purpose finite element code for multibody dynamics, in which the equations of motion are assembled automatically and large rotations are easily taken into account. In addition, comparing results between different models of the woodpecker toy, the importance of modeling large rotations and the horizontal displacement of the woodpecker's sleeve is emphasized. Copyright © 2021 by ASME.

Disciplines :

Mechanical engineering

Author, co-author :

Cosimo, Alejandro; Department of Aerospace and Mechanical Engineering, University of Liège, Allée de la Découverte 9 (B52), Liège, 4000, Belgium, Cimec, Universidad Nacional Del Litoral, Conicet, Colectora Ruta Nac.168, Paraje El Pozo, Santa Fe, 3000, Argentina

Cavalieri, Federico J.; Cimec, Universidad Nacional Del Litoral, Conicet, Colectora Ruta Nac.168, Paraje El Pozo, Santa Fe, 3000, Argentina

Galvez, Javier; Department of Aerospace and Mechanical Engineering, University of Liège, Allée de la Découverte 9 (B52), Liège, 4000, Belgium

Cardona, Alberto; Cimec, Universidad Nacional Del Litoral, Conicet, Colectora Ruta Nac.168, Paraje El Pozo, Santa Fe, 3000, Argentina

Bruls, Olivier ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire des Systèmes Multicorps et Mécatroniques

Title :

A general purpose formulation for nonsmooth dynamics with finite rotations: Application to the woodpecker toy

Publication date :

2021

Journal title :

Journal of Computational and Nonlinear Dynamics

ISSN :

1555-1415

eISSN :

1555-1423

Publisher :

American Society of Mechanical Engineers (ASME), United States

Volume :

Issue :

Pages :

031001-1

Peer reviewed :

Peer reviewed

Available on ORBi :

since 17 January 2022

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Bibliography

Geradin, M., and Cardona, A., 2001, Flexible Multibody Dynamics: A Finite Element Approach, John Wiley & Sons Inc, New York.
Laursen, T., 2003, Computational Contact and Impact Mechanics, Springer-Verlag, Berlin.
Negrut, D., Serban, R., and Tasora, A., 2018, "Posing Multibody Dynamics With Friction and Contact as a Differential Complementarity Problem," ASME J. Comput. Nonlinear Dyn., 13(1), p. 10.
Tasora, A., and Anitescu, M., 2010, "A Convex Complementarity Approach for Simulating Large Granular Flows," ASME J. Comput. Nonlinear Dyn., 5(3), p. 5.
Mylapilli, H., and Jain, A., 2017, "Complementarity Techniques for Minimal Coordinate Contact Dynamics," ASME J. Comput. Nonlinear Dyn., 12(2), p. 12.
Trinkle, J. C., 2003, "Formulation of Multibody Dynamics as Complementarity Problems," ASME Paper No: DETC2003/VIB-48342.
Acary, V., 2013, "Projected Event-Capturing Time-Stepping Schemes for Nonsmooth Mechanical Systems With Unilateral Contact and Coulomb's Friction," Comput. Methods Appl. Mech. Eng., 256, pp. 224-250.
Glocker, C., 2006, "An Introduction to Impacts," Nonsmooth Mechanics of Solids, J. Haslinger and G. E. Stavroulakis, eds., Springer, Vienna, pp. 45-101.
Pfeiffer, F., 1984, "Mechanische Systeme Mit Unstetigen Ubergangen," Ing. Arch., 54(3), pp. 232-240.
Glocker, C., and Pfeiffer, F., 1995, "Multiple Impacts With Friction in Rigid Multibody Systems," Nonlinear Dyn., 7(4), pp. 471-497.
Pfeiffer, F., and Glocker, C., 2000, "Contacts in Multibody Systems," J. Appl. Math. Mech., 64(5), pp. 773-782.
Leine, R. I., Van Campen, D., and Glocker, C., 2003, "Nonlinear Dynamics and Modeling of Various Wooden Toys With Impacts and Friction," J. Vib. Control, 1261, pp. 58-59.
Leine, R. I., and Van Campen, D. H., 2006, "Bifurcation Phenomena in Non-Smooth Dynamical Systems," Eur. J. Mech., A/Solids, 25(4), pp. 595-616.
Glocker, C., and Studer, C., 2005, "Formulation and Preparation for Numerical Evaluation of Linear Complementarity Systems in Dynamics," Multibody Syst. Dyn., 13(4), pp. 447-463.
Slavic, J., and Boltezar, M., 2006, "Non-Linearity and Non-Smoothness in Multi-Body Dynamics: Application to Woodpecker Toy," Proc. Inst. Mech. Eng., Part C, 220(3), pp. 285-296.
Charles, A., Casenave, F., and Glocker, C., 2018, "A Catching-Up Algorithm for Multibody Dynamics With Impacts and Dry Friction," Comput. Methods Appl. Mech. Eng., 334, pp. 208-237.
Peng, H., Song, N., and Kan, Z., 2020, "A Nonsmooth Contact Dynamic Algorithm Based on the Symplectic Method for Multibody System Analysis With Unilateral Constraints," Multibody Syst. Dyn., 49(2), pp. 119-153.
Peng, H., Song, N., and Kan, Z., 2020, "A Novel Nonsmooth Dynamics Method for Multibody Systems With Friction and Impact Based on the Symplectic Discrete Format," Int. J. Numer. Methods Eng., 121(7), pp. 1530-1557.
Dubois, F., Jean, M., Renouf, M., Mozul, R., Martin, A., and Bagneris, M., 2011, "LMGC90," Proceedings of the 10eme Colloque National en Calcul Des Structures (CSMA), Giens, France. May 9-13, pp. 1-8.
Acary, V., and Brogliato, B., 2008, Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics, Springer-Verlag, Berlin.
Heyn, T., Mazhar, H., Pazouki, A., Melanz, D., Seidl, A., Madsen, J., Bartholomew, A., Negrut, D., Lamb, D., and Tasora, A., 2013, "Chrono: A Parallel Physics Library for Rigid-Body, Flexible-Body, and Fluid Dynamics," Mech. Sci., 4, pp. 49-64.
Lacoursière, C., 2007, "Ghosts and Machines: Regularized Variational Methods for Interactive Simulations of Multibodies With Dry Frictional Contacts," Ph.D. thesis, Umea° University, Computing Science, Umea°, Sweden.
Cardona, A., Klapka, I., and Geradin, M., 1994, "Design of a New Finite Element Programming Environment," Eng. Comput., 11(4), pp. 365-381.
Cosimo, A., Galvez, J., Cavalieri, F. J., Cardona, A., and Bruls, O., 2020, "A Robust Nonsmooth Generalized-a Scheme for Flexible Systems With Impacts," Multibody Syst. Dyn., 48(2), pp. 127-149.
Bruls, O., Acary, V., and Cardona, A., 2014, "Simultaneous Enforcement of Constraints at Position and Velocity Levels in the Nonsmooth Generalized-a Scheme," Comput. Methods Appl. Mech. Eng., 281, pp. 131-161.
Bruls, O., Cardona, A., and Arnold, M., 2012, "Lie Group Generalized-a Time Integration of Constrained Flexible Multibody Systems," Mech. Mach. Theory, 48, pp. 121-137.
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, Berling.
Gear, C. W., Leimkuhler, B., and Gupta, G. K., 1985, "Automatic Integration of Euler-Lagrange Equations With Constraints," J. Comput. Appl. Math., 12-13, pp. 77-90.
Galvez, J., Cavalieri, F. J., Cosimo, A., Bruls, O., and Cardona, A., 2020, "A Nonsmooth Frictional Contact Formulation for Multibody System Dynamics," Int. J. Numer. Methods Eng., 121(16), pp. 3584-3609.
Arnold, M., and Bruls, O., 2007, "Convergence of the Generalized-a Scheme for Constrained Mechanical Systems," Multibody Syst. Dyn., 18(2), pp. 185-202.
Chung, J., and Hulbert, G., 1993, "Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-a Method," ASME J. Appl. Mech., 60(2), pp. 371-375.
Alart, P., and Curnier, A., 1991, "A Mixed Formulation for Frictional Contact Problems Prone to Newton Like Solution Methods," Comput. Methods Appl. Mech. Eng., 92(3), pp. 353-375.
Zander, R., 2008, "Flexible Multi-Body Systems With Set-Valued Force Laws," Ph.D. thesis, Technische Universitat Munchen, Munich, Germany.
Piatkowski, T., 2014, "Dahl and LuGre Dynamic Friction ModelsThe Analysis of Selected Properties," Mech. Mach. Theory, 73, pp. 91-100.
Uchida, T. K., Sherman, M. A., and Delp, S. L., 2015, "Making a Meaningful Impact: Modelling Simultaneous Frictional Collisions in Spatial Multibody Systems," Proc. R. Soc. A: Math., Phys. Eng. Sci., 471(2177), p. 20140859.
Pfeiffer, F., and Glocker, C., 1996, Multibody Dynamics With Unilateral Contacts, Wiley-VCH Verlag GmbH, Weinheim, Germany.