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

This paper focuses on the development of an unconditionally stable time-integration algorithm for multibody dynamics that does not artificially dissipate energy. Unconditional stability is sought to alleviate any stability restrictions on the integration step size, while energy conservation is important for the accuracy of long-term simulations. In multibody system analysis, the time-integration scheme is complemented by a choice of coordinates that define the kinematics of the system. As such, the current approach uses a non-dissipative implicit Newmark method to integrate the equations of motion defined in terms of the independent joint co-ordinates of the system. In order to extend the unconditional stability of the implicit Newmark method to non-linear dynamic systems, a discrete energy balance is enforced. This constraint, however, yields spurious oscillations in the computed accelerations and therefore, a new acceleration corrector is developed to eliminate these instabilities and hence retain unconditional stability in an energy sense. An additional benefit of employing the non-linearly implicit time-integration method is that it allows for an efficient design sensitivity analysis. In this paper, design sensitivities computed via the direct differentiation method are used for mechanism performance optimization.