Simulation of Flexible Multibody Systems Using Linear Graph Theory

This chapter provides a general description of a variational graph-theoretic formulation for simulation of flexible multibody systems (FMS) 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. 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 3-D 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, deployable space structures and micro-nano electro-mechanical systems (MEMS).