Unconditionally energy stable implicit time integration: application to multibody system analysis and design

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.