Generalisation of reference conditions for the floating frame formulation in terms of global boundary coordinates

Abstract The global boundary coordinates formulation can be used to examine flexible multibody systems in terms of the global coordinates of the boundary nodes. It is formulated by transforming the generalised coordinates of the floating frame formulation to global boundary coordinates. To obtain a unique transformation, a reference condition is required which eliminates the rigid body modes from the elastic deformation. Various existing formulations implement different reference conditions that define the floating frame as: (1) attached to the node in the centre of mass of the undeformed body, (2) attached to a boundary node, (3) a weighted average of the global boundary coordinates, (4) corotational and (5) located in the centre of mass of the deformed body. This work derives the transformation matrices corresponding to these reference conditions required for the global boundary coordinates formulation, showing that the various existing formulations can be generalised. Furthermore, this allows one to implement a different reference condition within the global boundary coordinates formulation by changing the transformation matrix. As the choice of reference condition affects the simulation accuracy, the accuracy of each reference condition is considered.