An implicit asynchronous variational integrator for flexible multibody dynamics

To accurately capture the dynamic responses of flexible multibody systems with complex geometric shapes or with contact and collision problems, extremely fine meshes have to be used. However, most previous algorithms for simulating these systems adopt a single integration time step size. A way to improve computation efficiency is to use different integration time steps for different elements with different sizes. In this study, a novel implicit AVI (asynchronous variational integrator) is originally proposed to study dynamics of complex flexible multibody systems. The proposed integrator allows different integration time step sizes for different elements with different mesh sizes. The multipoint constraint method is utilized to glue non-matching elements. To establish the system's discrete Euler–Lagrange equations (DELs), the diagonal-scaling method is used to construct the lumped mass matrix of elements. Finally, seven numerical examples are presented to comprehensively validate accuracy and efficiency of the proposed integrator. Numerical results indicate that the proposed AVI is capable of accurately capturing the dynamic response of flexible multibody systems and preserving systems’ energy and momentum. Compared with the generalized-α algorithm with a single time step size, the proposed AVI can significantly improve the computation efficiency for the dynamic simulation of complex flexible multibody systems with clearance joints.