[en] The aim of this work is the development of a robust and accurate time integrator for the simulation of the dynamics of multibody systems composed of rigid and/or flexible bodies subject to frictionless contacts and impacts. The integrator is built upon a previously developed nonsmooth generalized-alpha scheme time integrator which was able to deal well with nonsmooth dynamical problems avoiding any constraint drift phenomena and capturing vibration effects without introducing too much numerical dissipation. However, when dealing with problems involving nonlinear bilateral constraints and/or flexible elements, it is necessary to adopt small time-step sizes to ensure the convergence of the numerical scheme. In order to tackle these problems more efficiently, a fully decoupled version of the nonsmooth generalized-alpha method is proposed in this work, avoiding these inconveniences. Several examples are considered to assess its accuracy and robustness.
Disciplines :
Mechanical engineering
Author, co-author :
Cosimo, Alejandro ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire des Systèmes Multicorps et Mécatroniques
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Bibliography
Paoli, L., Schatzman, M.: A numerical scheme for impact problems I: the one-dimensional case. SIAM J. Numer. Anal. 40(2), 702–733 (2002)
Paoli, L., Schatzman, M.: A numerical scheme for impact problems II: the multidimensional case. SIAM J. Numer. Anal. 40(2), 734–768 (2002)
Jean, M., Moreau, J.J.: Dynamics in the presence of unilateral contacts and dry friction: a numerical approach. In: Unilateral Problems in Structural Analysis, vol. 2, pp. 151–196. Springer, Vienna (1987)
Moreau, J.J.: Unilateral contact and dry friction in finite freedom dynamics. In: Nonsmooth Mechanics and Applications, pp. 1–82. Springer, Vienna (1988)
Brüls, O., Acary, V., Cardona, A.: Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized- α scheme. Comput. Methods Appl. Mech. Eng. 281, 131–161 (2014)
Chen, Q., Acary, V., Virlez, G., Brüls, O.: A nonsmooth generalized- α scheme for flexible multibody systems with unilateral constraints. Int. J. Numer. Methods Eng. 96(8), 487–511 (2013)
Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: definition and outlook. Math. Comput. Simul. 95, 180–199 (2014)
Schindler, T., Rezaei, S., Kursawe, J., Acary, V.: Half-explicit timestepping schemes on velocity level based on time-discontinuous Galerkin methods. Comput. Methods Appl. Mech. Eng. 290, 250–276 (2015)
Brüls, O., Acary, V., Cardona, A.: On the constraints formulation in the nonsmooth generalized- α method. In: Advanced Topics in Nonsmooth Dynamics, pp. 335–374. Springer, Berlin (2018)
Acary, V.: Projected event-capturing time-stepping schemes for nonsmooth mechanical systems with unilateral contact and Coulomb’s friction. Comput. Methods Appl. Mech. Eng. 256, 224–250 (2013)
Schoeder, S., Ulbrich, H., Schindler, T.: Discussion of the Gear–Gupta–Leimkuhler method for impacting mechanical systems. Multibody Syst. Dyn. 31(4), 477–495 (2013)
Géradin, M., Cardona, A.: Flexible Multibody Dynamics: A Finite Element Approach. Wiley, Chichester (2001)
Moreau, J.: Numerical aspects of the sweeping process. Comput. Methods Appl. Mech. Eng. 177(3–4), 329–349 (1999)
Gear, C., Leimkuhler, B., Gupta, G.: Automatic integration of Euler–Lagrange equations with constraints. J. Comput. Appl. Math. 12–13, 77–90 (1985)
Arnold, M., Brüls, O.: Convergence of the generalized- α scheme for constrained mechanical systems. Multibody Syst. Dyn. 18(2), 185–202 (2007)
Chung, J., Hulbert, G.M.: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized- α method. J. Appl. Mech. 60(2), 371–375 (1993)
Alart, P., Curnier, A.: A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput. Methods Appl. Mech. Eng. 92(3), 353–375 (1991)
Cardona, A., Géradin, M.: Numerical integration of second order differential—algebraic systems in flexible mechanism dynamics. In: Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, pp. 501–529. Springer, Netherlands (1994)
Cardona, A., Klapka, I., Géradin, M.: Design of a new finite element programming environment. Eng. Comput. 11, 365–381 (1994)
Brüls, O., Cardona, A., Arnold, M.: Lie group generalized- α time integration of constrained flexible multibody systems. Mech. Mach. Theory 48, 121–137 (2012)
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