Comparison of different formulations of 2D beam elements based on Bond Graph technique

Bond Graphs are well suited for modelling multibody systems. In this paper modelling of planar flexible beams undergoing large overall motions are studied based on finite element (FE) technique. Two well-known approaches are used – the co-rotational (CR) and absolute nodal coordinate (ANC) formulation. Two ANC formulations are analyzed – one in which elastic forces is described using classical beam theory in a local coordinate frame, and another based on a global continuum mechanics approach. Starting from these classical formulations velocity formulations are developed and used to develop Bond Graph FE components. The effect of gravity has been considered as well. These components can be put in libraries and used for systematic Bond Graph flexible body model development. It is shown that Bond Graph technique is capable of dealing with different flexible body formulations and can be used as a general approach in parallel to other modelling approaches. Models are developed and simulations are performed using the object oriented environment of BondSim. Owing to the object oriented approach, transformation from one to the other model is relatively simply. The results are illustrated by suitable examples and they confirm accuracy of the developed models. It was shown that the CR approach offers much better performance than the both ANC formulations.