A new floating frame of reference formulation for flexible multibody dynamics

For the dynamic analysis of flexible multibody systems, three conceptually different descriptions are available and commonly used: the inertial frame formulations, the corotational formulations and the floating frame formulations. The differences between these formulations are mainly in the way they describe a body’s elastic behavior or, in particular, in the degrees of freedom used to describe this elastic behavior. As a consequence, differences occur in the way kinematic constraints between bodies are enforced.

The inertial frame and corotational frame formulations can both be interpreted as nonlinear finite element methods. As such, they have in common that they use the absolute nodal coordinates as degrees of freedom. Constraints between bodies can be enforced by simply equating the relevant degrees of freedom that both bodies share at an interface point. On the other hand, the floating frame formulations use the absolute floating frame of reference coordinates together with a set of local generalized coordinates that describe a body’s local elastic displacement field as degrees of freedom. Because the absolute interface coordinates are not part of the degrees of freedom, constraints are enforced using Lagrange multipliers. This increases the total number of unknowns and causes the constrained equations of motion to be of the differential-algebraic type.

In this presentation, an overview is given of a newly developed floating frame of reference formulation of which the details are explained in [1]. In this new method, the absolute interface coordinates are used as degrees of freedom. To this end, coordinate transformations are developed that express the absolute floating frame coordinates and the local generalized coordinates in terms of the absolute interface coordinates.

Not only does the new method not require the use of Lagrange multipliers for enforcing constraints, it also offers the possibility to reduce geometric nonlinear systems by applying important model order reduction techniques in a body’s local frame. Using the well-developed Craig-Bampton method, it is possible to create so-called superelements in a flexible multibody formulation. That is, for each flexible body, the tangent mass and stiffness matrices, reduced to the interface points, can be obtained from linear finite element models and can directly be applied in the dynamic analysis of the entire system.

Reference
[1] M.H.M. Ellenbroek, J.P. Schilder: On the use of absolute interface coordinates in the floating frame of reference formulation for flexible multibody dynamics. Multibody System Dynamics, submitted 03-05-2017.