A robust nonsmooth generalized-alpha scheme for flexible systems with impacts

Cosimo, Alejandro; Galvez Buezo, Javier; Cavalieri, Federico J.; Cardona, Alberto; Bruls, Olivier

doi:10.1007/s11044-019-09692-2

Download

Article (Scientific journals)

A robust nonsmooth generalized-alpha scheme for flexible systems with impacts

Cosimo, Alejandro; Galvez Buezo, Javier; Cavalieri, Federico J. et al.

2020 • In Multibody System Dynamics, 48 (2), p. 124-149

Peer reviewed

Permalink
https://hdl.handle.net/2268/248037

DOI
10.1007/s11044-019-09692-2

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

CosimoEtal2020_ARobustNSGA_AuthorVersion.pdf

Author preprint (644.47 kB)

Download

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Nonsmooth contact dynamics; Flexible multibody system; Generalized-alpha method; Time-stepping schemes

Abstract :

[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

Galvez Buezo, Javier ; Université de Liège - ULiège > A&M

Cavalieri, Federico J.; Universidad Nacional del Litoral / CONICET > CIMEC

Cardona, Alberto; Universidad Nacional del Litoral / CONICET > CIMEC

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

Language :

English

Title :

A robust nonsmooth generalized-alpha scheme for flexible systems with impacts

Publication date :

2020

Journal title :

Multibody System Dynamics

ISSN :

1384-5640

eISSN :

1573-272X

Publisher :

Springer, Switzerland

Volume :

Issue :

Pages :

124-149

Peer reviewed :

Peer reviewed

Available on ORBi :

since 05 June 2020

Statistics

Number of views

81 (9 by ULiège)

Number of downloads

175 (8 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

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