A nonsmooth generalized-$α$ scheme for flexible multibody systems with unilateral constraints

Qiong Zhong Chen 1 Vincent Acary 2, * Geoffrey Virlez 1 Olivier Brüls 1
* Auteur correspondant
2 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Mechanical systems are usually subjected not only to bilateral constraints, but also to unilateral constraints. Inspired by the generalized-alpha time integration method for smooth flexible multibody dynamics, this paper presents a nonsmooth generalized-alpha method, which allows a consistent treatment of the nonsmooth phenomena induced by unilateral constraints and an accurate description of the structural vibrations during free motions. Both the algorithm and the implementation are illustrated in detail. Numerical example tests are given in the scope of both rigid and flexible body models, taking account for both linear and nonlinear systems and comprising both unilateral and bilateral constraints. The extended nonsmooth generalized- alpha method is verified through comparison to the traditional Moreau-Jean method and the fully implicit Newmark method. Results show that the nonsmooth generalized-alpha method benefits from the accuracy and stability property of the classical generalized-˛ method with controllable numerical damping. In particular, when it comes to the analysis of flexible systems, the nonsmooth generalized-˛ method shows much better accuracy property than the other two methods.
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Qiong Zhong Chen, Vincent Acary, Geoffrey Virlez, Olivier Brüls. A nonsmooth generalized-$α$ scheme for flexible multibody systems with unilateral constraints. International Journal for Numerical Methods in Engineering, Wiley, 2013, 96 (8), pp.487-511. 〈10.1002/nme.4563〉. 〈hal-00858066〉

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