Efficient dynamics analysis of large-deformation flexible beams by using the absolute nodal coordinate transfer matrix method
- 602 Downloads
This paper describes an efficiently computational method for dynamics simulating of planar multibody system with flexible beams undergoing large deformations by combining the absolute nodal coordinate formulation (ANCF) and the transfer matrix method (TMM). Firstly, according to ANCF and the geometrically nonlinear theory, the two-dimensional shear-deformable beam element and its dynamic equations of motion are presented. Then according to TMM and the dynamic equations of beam elements, by defining the new state vectors and deducing the new transfer equations of elements, an efficient computational method named as ANC–TMM, is presented for dynamics of planar multibody system with flexible beams undergoing large deformations. Compared with the ordinary dynamics methods, the proposed method combines the strengths of TMM and ANCF. It does not need the global dynamic equations of system and has the low order of the system matrix and high computational efficiency. This method can be extended to solve the nonlinear dynamics problems of general flexible multibody systems undergoing large deformations. Formulations as well as a numerical example of a flexible four-bar linkage mechanism are given to validate the method.
KeywordsMultibody system Geometric nonlinearity Computational method Shear-deformable beam element Large rotation
The research was supported by the Natural Science Foundation of China Government (Grant No. 10902051) and the Program for New Century Excellent Talents in University (Grant No. NCET-10-0075). We owe special thanks to Professor Jorge A.C. Ambrósio (Instituto Superior Técnico, Lisbon, Portugal) and Professor Werner Schiehlen (University of Stuttgart, Germany) for their heuristic suggestions.
- 6.Matikainen, M.: Development of beam and plate finite elements based on the absolute nodal coordinate formulation. Ph.D. dissertation, Lappeenranta University of Technology, Finland (2009) Google Scholar
- 7.Tian, Q., Zhang, Y.Q., Chen, L.P., Qin, G.: Advances in the absolute nodal coordinate method for the flexible multibody dynamics. Adv. Mech. 40(2), 189–202 (2010) Google Scholar
- 9.Gerstmayr, J., Shabana, A.A.: Efficient integration of the elastic forces and thin three-dimensional beam elements in the absolute nodal coordinate formulation. In: ECCOMAS Thematic Conference, Madrid, Spain, 21–24 June 2005, pp. 21–24 (2005) Google Scholar
- 10.Liu, C., Tian, Q., Hu, H.Y.: Efficient computational method for dynamics of flexible multibody systems based on absolute nodal coordinate. Theor. Appl. Mech. Lett. 42(6), 1197–1204 (2010) Google Scholar
- 12.Chijie, L.: Dynamic and thermal analyses of flexible structures in orbit. Ph.D. dissertation, University of Connecticut, Storrs (2006) Google Scholar
- 13.Pestel, E.C., Leckie, F.A.: Matrix Method in Elastomechanics. McGraw-Hill, New York (1963) Google Scholar
- 15.Dokanish, M.A.: A new approach for plate vibration: combination of transfer matrix and finite element technique. J. Mech. Des. 94(2), 526–530 (1972) Google Scholar
- 19.Rong, B., Rui, X.T., Wang, G.P.: New method for dynamics modeling and analysis on flexible plate undergoing large overall motion. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 224(K1), 33–44 (2010) Google Scholar
- 21.Horner, G.C.: The Riccati transfer matrix method. Ph.D. dissertation, University of Virginia, USA (1975) Google Scholar