Graph-Theoretic Approach for the Dynamic Simulation of Flexible Multibody Systems

This paper provides a general description of a variational graph-theoretic formulation for simulation of flexible multibody systems (FMSs) which includes a brief review of linear graph principles required to formulate this algorithm. The system is represented by a linear graph, in which nodes represent reference frames on flexible bodies, and edges represent components that connect these frames. The method is based on a simplistic topological approach which casts the dynamic equations of motion into a symmetrical format. To generate the equations of motion with elastic deformations, the flexible bodies are discretized using two types of finite elements. The first is a 2 node 3D beam element based on Mindlin kinematics with quadratic rotation. This element is used to discretize unidirectional bodies such as links of flexible systems. The second consists of a triangular thin shell element based on the discrete Kirchhoff criterion and can be used to discretize bidirectional bodies such as high-speed lightweight manipulators, large high precision deployable space structures, and micro/nano-electromechanical systems (MEMSs). Two flexible systems are analyzed to illustrate the performance of this new variational graph-theoretic formulation and its ability to generate directly a set of motion equations for FMS without additional user input.