fulltext0 - Multibody Syst Dyn (2010) 23: 131 DOI...

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Multibody Syst Dyn (2010) 23: 1–31 DOI 10.1007/s11044-009-9168-0 Analysis of multibody systems experiencing large elastic deformations Manabendra Das · Atila Barut · Erdogan Madenci Received: 10 August 2008 / Accepted: 6 April 2009 / Published online: 28 August 2009 © Springer Science+Business Media B.V. 2009 Abstract This study presents an approach based on the foating Frame oF reFerence method to model complex three-dimensional bodies in a multibody system using solid and plate el- ements. Unlike most oF the Formulations based on the foating Frame oF reFerence method, which assume small or moderate deFormations, the present Formulation allows large elastic deFormations within each Frame by using the corotational Form oF the updated Lagrangian description oF motion. The implicit integration scheme is based on the Generalized- α method, and kinematic joints are invoked in the Formulation through the coordinate par- titioning method. A triangular element with three nodes and a solid wedge element with six nodes have been developed to Facilitate the modeling oF three-dimensional bodies with arbitrary geometry. Various numerical examples have been considered to demonstrate the robustness oF the present approach. Keywords ±loating Frame · Large deFormation · Plate and solid elements 1 Introduction Dynamic simulation oF multibody systems, which initially dealt with interconnected rigid bodies, has currently reached a state where fexible bodies undergoing nonlinear elastic de- Formation can be analyzed as well. Schiehlen [ 1 ] presented a detailed review on the subject oF rigid multibody dynamics, and WasFy and Noor [ 2 ] and Shabana [ 3 ] devoted their reviews to fexible multibody dynamics. Based on the choice oF the reFerence Frame, a fexible multi- body dynamic Formulation can broadly be categorized into the foating Frame, co-rotational M. Das · A. Barut · E. Madenci ( B ) Department oF Aerospace and Mechanical Engineering, The University oF Arizona, Tucson, Arizona, USA e-mail: madenci@email.arizona.edu M. Das e-mail: mdas@email.arizona.edu A. Barut e-mail: atila@email.arizona.edu
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2 M. Das et al. frame, or inertia frame approach [ 2 ]. Among these three approaches, the Foating frame ap- proach is by far the most popular in both commercial and research codes. This is due to the fact that it is a direct extension of the concepts used in rigid multibody dynamics. In spite of its popularity, use of the Foating frame of reference has mostly been restricted to small deformation problems. Moreover, the focus has mainly been on developing different types of beam elements to model slender structures. Utilizing the modal reduction technique, sev- eral practical problems that exhibit large reference translation and rotation were solved in the past with limited computational resources. However, it was observed by Kane et al. [ 4 ] that these techniques, based on small elastic deformations assumption, lead to a dynamic softening effect that eventually leads to instability. The events related to the development of
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fulltext0 - Multibody Syst Dyn (2010) 23: 131 DOI...

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