Geometrically exact beam equations in the adaptive DCA framework

This work examines the suitability of two popular methods of modeling bodies that undergo large deformation for use in the adaptive divide-and-conquer framework. In this framework, the method used to form and solve the equations-of-motion must handle a mixed set of bodies using different formulations, such as rigid-bodies that use a Newton–Euler formulation or flexible-bodies that use a floating frame of reference. Importantly, the method must treat all bodies indiscriminately of underlying formulation since the goal is to have adaptive changes in body definition, e.g., various rigid-bodies to a highly-flexible body. This work shows that the absolute nodal coordinate formulation is not immediately suitable for this purpose and derives the geometrically exact beam formulation equations that are compatible with these adaptive changes in body definition.