Ss. Chen et al., Unconditionally energy stable implicit time integration: application to multibody system analysis and design, INT J NUM M, 48(6), 2000, pp. 791-822
Citations number
42
Categorie Soggetti
Engineering Mathematics
Journal title
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
This paper focuses on the development of an unconditionally stable time-int
egration algorithm for multibody dynamics that does not artificially dissip
ate energy. Unconditional stability is sought to alleviate any stability re
strictions on the integration step size, while energy conservation is impor
tant for the accuracy of long-term simulations. In multibody system analysi
s, the time-integration scheme is complemented by a choice of coordinates t
hat define the kinematics of the system. As such, the current approach uses
a non-dissipative implicit Newmark method to integrate the equations of mo
tion defined in terms of the independent joint co-ordinates of the system.
In order to extend the unconditional stability of the implicit Newmark meth
od to non-linear dynamic systems, a discrete energy balance is enforced. Th
is constraint, however, yields spurious oscillations in the computed accele
rations and therefore, a new acceleration corrector is developed to elimina
te these instabilities and hence retain unconditional stability in an energ
y sense. An additional benefit of employing the non-linearly implicit time-
integration method is that it allows for an efficient design sensitivity an
alysis. In this paper, design sensitivities computed via the direct differe
ntiation method are used for mechanism performance optimization. Copyright
(C) 2000 John Wiley & Sons, Ltd.