An adaptive time-step energy-preserving variational integrator for flexible multibody system dynamics

An adaptive time-step variational integrator for simulating flexible multibody system dynamics is proposed. The integrator can adapt the time-step based on the variation of the system's energy. The flexible components in the system can undergo large overall motions and large deformations and are modelled by elements of absolute nodal coordinate formulations. In addition, a three-stage Newton-Raphson iteration method is developed to accurately solve the nonlinear discrete Euler-Lagrange equations in each time-step. Finally, three dynamic examples are presented to validate performance of the proposed integrator. Numerical results indicate that the proposed three-stage method has fast convergence rate. For the nonlinear flexible double pendulum system and the slider-crank mechanism, compared with constant time-step integrators, the proposed integrator can preserve the system's total energy more accurately and lead to more accurate dynamic responses. For the contact problem, the proposed integrator can quickly change the time-step size based on the sudden changes of energy to precisely compute the contact force and dynamic responses. Moreover, the proposed integrator can exactly preserve the displacement constraints and the velocity constraints simultaneously. In addition, it is noted that the computation efficiency of the proposed integrator needs to be further improved.