Riccati discrete time transfer matrix method for elastic beam undergoing large overall motion

An efficient method for dynamics simulation for elastic beam with large overall spatial motion and nonlinear deformation, namely, the Riccati discrete time transfer matrix method (Riccati-DT-TMM), is proposed in this investigation. With finite segments, continuous deformation field of a beam can be decomposed into many rigid bodies connected by rotational springs. Discrete time transfer matrices of rigid bodies and rotational springs are used to analyze the dynamic characteristic of the beam, and the Riccati transform is used to improve the numerical stability of discrete time transfer matrix method of multibody system dynamics. A predictor-corrector method is used to improve the numerical accuracy of the Riccati-DT-TMM. Using the Riccati-DT-TMM in dynamics analysis, the global dynamics equations of the system are not needed and the computation time required increases linearly with the system's number of degrees of freedom. Three numerical examples are given to validate the method for the dynamic simulation of a geometric nonlinear beam undergoing large overall motion.