# Co-rotational Formulations for 3D Flexible Multibody Systems: A Nodal-Based Approach

• Andreas Zwölfer
• Johannes Gerstmayr
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 114)

## Abstract

Rigid body models are only sufficient for rough estimates of the dynamics of real world systems, such as machines, robots and vehicles. Although, deformations are usually small compared to a rigid body motion, they need to be taken into account in many cases; e.g., to determine vibrations, resonance effects and stresses. So far, there are two main approaches to model these so-called flexible multibody systems. Both are based on the idea to decompose the motion of the flexible body into a rigid body motion and a superimposed small deformation. In the traditional approach, i.e., the floating frame of reference formulation, the degrees of freedom of the flexible body are rigid body coordinates and superimposed flexible coordinates, which typically result from a finite element model. In the non-conventional approach, the absolute displacement coordinates are employed as degrees of freedom, which can model both the rigid body motion and flexible deformations. In a previous research, a continuum-mechanics-based derivation and comparison has been presented for both approaches. In the present paper, we consistently derive and compare the two formulations on the semi-discrete nodal level of an underlying finite element model. Despite the novel and concise derivation, the present approach leads to equations that can be implemented easily within program codes and unpleasant evaluations of inertia shape integrals, which are present in the conventional floating frame of reference formulation, become obsolete.

## Keywords

Flexible multibody systems Floating frame of reference formulation Absolute coordinate formulation Finite element methods Geometric non-linearity

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## Authors and Affiliations

1. 1.Department of MechatronicsUniversity of InnsbruckInnsbruckAustria