implicit; explicit; dynamics; finite element; large strains
Abstract :
[en] In order to simulate an industrial process, an explicit method, which is conditionally stable, is the most adapted while the non-linearities evolve rapidly (impact phase, stamping process, etc.). But when the dynamics becomes quasi-linear (post-impact analysis, springback simulation, etc.), an implicit method, which is iterative, presents the advantage of unconditional stability. The optimal solution is then to have both implicit and explicit methods readily available in the same code and to be able to switch automatically from one to the other. Criteria that decide to switch from one method to another, depending on the current dynamics, have been developed. Implicit restarting conditions are also proposed that annihilate numerical oscillations resulting from an explicit calculation. (C) 2004 Elsevier Ltd. All rights reserved.
Disciplines :
Mechanical engineering
Author, co-author :
Noels, Ludovic ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Milieux continus et thermomécanique
Stainier, Laurent ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Milieux continus et thermomécanique
Ponthot, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Language :
English
Title :
Combined implicit/explicit algorithms for crashworthiness analysis
Publication date :
2004
Journal title :
International Journal of Impact Engineering
ISSN :
0734-743X
Publisher :
Pergamon-Elsevier Science Ltd, Oxford, United Kingdom
Yang D., Jung D., Song I., Yoo D., Lee J. Comparative investigation into implicit, explicit, and iterative implicit/explicit schemes for the simulation of sheet-metal forming processes. J Mater Process Technol. 50:1995;39-53.
Gelin J., Boulmane L., Boisse P. Quasi-static implicit and transient explicit analyses of sheet-metal forming using a. C° three-nodes shell element J Mater Process Technol. 50:1995;54-69.
Sun J., Lee K., Lee K. Comparison of implicit and explicit finite element methods for dynamic problem. J Mater Process Technol. 105:2000;110-118.
Jung D., Yang D. Step-wise combined implicit-explicit finite-element simulation of autobody stamping process. J Mater Process Technol. 83:1998;245-260.
Finn M., Galbraith P., Wu L., Hallquist J., Lum L., Lin T.-.L. Use of a coupled explicit-implicit solver for calculating spring-back in automotive body panels. J Mater Process Technol. 50:1995;395-409.
Narkeeran N., Lovell M. Predicting springback in sheet metal forming: an explicit to implicit sequential solution procedure. Finite Elements Anal Des. 33:1999;29-42.
Noels L, Stainier L, Ponthot J-P. Combined implicit/explicit time integration algorithms for the numerical simulation of sheet metal forming. J Comput Appl Math, in press.
Belytschko T., Hughes T. Computational methods for transient analysis. 1983;North-Holland, Amsterdam.
Hughes T. The finite element method. 1987;Prentice-Hall, Englewood Cliffs, NJ.
Ponthot J-P, Hogge M. On relative merits of implicit schemes for transient problems in metal forming simulation. In: International Conference on Numerical Methods for Metal Forming in Industry, vol. 2, Baden-Baden, Germany, 1994. p. 128-48.
Chung J., Hulbert J. A time integration algorithms for structural dynamics with improved numerical dissipations. the generalized- α method J Appl Mech. 60:1993;371-375.
Géradin M., Cardona A. Flexible multibody dynamics (A finite element approach). 2000;Wiley, New York.
Noels L., Stainier L., Ponthot J. Self-adapting time integration management in crash-worthiness and sheet metal forming computations. Int J Vehicle Des. 30(2):2002;67-114.
Noels L., Stainier L., Ponthot J.-.P., Bonini J. Automatic time stepping algorithms for implicit numerical simulations of non-linear dynamics. Adv Eng Software. 33(10):2002;581-595.
Hulbert G., Chung J. Explicit time integration algorithms for structural dynamics with optimal numerical dissipation. Comput Methods Appl Mech Eng. 137:1996;175-188.