[en] An automatic time step size determination for non-linear problems, solved by implicit schemes, is presented. The time step calculation is based on the estimation of the integration error. This estimation is calculated from the acceleration difference. It is normalised according to the size of the problem and the integration parameters. This time step control algorithm modifies the time step size only if the problem has a long time physical change. On the other hand, Hessian matrix can be kept constant for several iterations however the problem is non-linear. According to the fact that the time step size is constant for some time step, the Hessian matrix shouldn’t be recalculated for each time step. A criterion selecting if Hessian matrix must be calculated or
not is developed. Finally, a criterion of iterations divergence is also proposed. It avoids the determination, by the user, of a maximal iterations number. The iterations number is the smaller. Industrial numerical examples are presented that demonstrated the performances (precision and computational cost) of the algorithms.
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 :
Automatic time step size determination and automatic Hessian matrix actualisation selection for non-linear dynamic problems solved by implicit schemes
Publication date :
2000
Event name :
International Crashworthiness Conference (ICrash 2000)