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