%0 Journal Article %1 ZhouEtAl22 %A Zhou, Qinbo %A Fehr, Jörg %A Bestle, Dieter %A Rui, Xiaoting %D 2022 %J Multibody System Dynamics %K PN7 EXC2075 selected %N 3 %P 269-292 %R 10.1007/s11044-022-09869-2 %T Simulation of generally shaped 3D elastic body dynamics with large motion using transfer matrix method incorporating model order reduction %U https://doi.org/10.1007/s11044-022-09869-2 %V 59 %X The multibody system transfer matrix method (MSTMM) is an efficient formalism for systems involving rigid bodies and simple elastic elements like beams. The paper tackles the challenge of setting up transfer matrices as building blocks for generally shaped, three-dimensional elastic bodies, and establishes a novel connection between the transfer matrix method and a large family of model order reduction (MOR) methods. An articulated manipulator arm serves as a demonstration example throughout the paper to first explain the basic concepts of MSTMM. Then, a classical floating frame of reference formulation (FFRF) of flexible bodies is adapted to MSTMM to express their equations of motion in a global inertial frame. The favorable ideas from FFRF are transferred into the typical MSTMM formulation yielding the transfer equation of a general elastic body. These ideas include: (i) splitting the overall motion into a large rigid body motion and a small elastic deformation; (ii) discretization of the deformation field by using the linear finite element (FE) method; (iii) calculating the standard input data from commercial FE data for generally shaped bodies; and (iv) MOR, to find the most suitable shape functions and speed up the simulation. Next, the procedure for solving elastic multibody system dynamics using MSTMM is illustrated. In a final numerical simulation, the proposed elastic MSTMM concept for a coupled rigid-flexible multibody system shows good agreement with a classical Newton-Euler formulation. The algorithm is based on the classical FFRF without additional assumptions and thus can be used with any MOR method available in MatMorembs.

@article{ZhouEtAl22, abstract = {The multibody system transfer matrix method (MSTMM) is an efficient formalism for systems involving rigid bodies and simple elastic elements like beams. The paper tackles the challenge of setting up transfer matrices as building blocks for generally shaped, three-dimensional elastic bodies, and establishes a novel connection between the transfer matrix method and a large family of model order reduction (MOR) methods. An articulated manipulator arm serves as a demonstration example throughout the paper to first explain the basic concepts of MSTMM. Then, a classical floating frame of reference formulation (FFRF) of flexible bodies is adapted to MSTMM to express their equations of motion in a global inertial frame. The favorable ideas from FFRF are transferred into the typical MSTMM formulation yielding the transfer equation of a general elastic body. These ideas include: (i) splitting the overall motion into a large rigid body motion and a small elastic deformation; (ii) discretization of the deformation field by using the linear finite element (FE) method; (iii) calculating the standard input data from commercial FE data for generally shaped bodies; and (iv) MOR, to find the most suitable shape functions and speed up the simulation. Next, the procedure for solving elastic multibody system dynamics using MSTMM is illustrated. In a final numerical simulation, the proposed elastic MSTMM concept for a coupled rigid-flexible multibody system shows good agreement with a classical Newton-Euler formulation. The algorithm is based on the classical FFRF without additional assumptions and thus can be used with any MOR method available in MatMorembs.}, added-at = {2024-03-26T11:56:30.000+0100}, author = {Zhou, Qinbo and Fehr, Jörg and Bestle, Dieter and Rui, Xiaoting}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/206f17dba6f4999218a8a5246510197bc/exc2075}, doi = {10.1007/s11044-022-09869-2}, interhash = {7e399faf5f35931a3f4cd2e824a191f6}, intrahash = {06f17dba6f4999218a8a5246510197bc}, issn = {1573272X}, journal = {Multibody System Dynamics}, keywords = {PN7 EXC2075 selected}, number = 3, pages = {269-292}, refid = {Zhou2022}, timestamp = {2024-03-26T11:56:30.000+0100}, title = {Simulation of generally shaped 3D elastic body dynamics with large motion using transfer matrix method incorporating model order reduction}, url = {https://doi.org/10.1007/s11044-022-09869-2}, volume = 59, year = 2022 }