Application of Radau IIA algorithms to flexible multibody system with holonomic constraints
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The paper designs new 2- and 3-stage Radau IIA algorithms to integrate the dynamic responses of flexible multibody system with holonomic constraints. The total translation, the incremental rotation and associated velocities are selected as unknowns to avoid the linearization of angular acceleration which makes it possible to parameterize the finite rotation by using the Wiener–Milenković parameters. The new algorithms release the heavy computational burden through the simplified Newton iterations and are stabilized by the preferable h-scaling technique. Contributions of the paper include: (1) For 2-stage algorithm, the resulting block triangular equations are solved efficiently by an inner iteration scheme. (2) For 3-stage algorithm, the full-size linear system is decoupled into a real and a complex subsystems which reduces the size of the system dramatically. (3) A new scheme is designed to predict the truncation error from the associated deferred correction equations without overestimation. Finally, numerical simulations show the 2- and 3-stage Radau IIA algorithms have excellent stability and convergence properties and behavior in a computationally efficient manner.
KeywordsRadau IIA Multibody dynamics DAE of index 3 Finite rotation
The paper is under the supports of both “2011 China overseas personnel science and technology activities supporting project” and “2011 Beijing overseas personnel science and technology activities supporting project”.
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