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Hamiltonian Nodal Position Finite Element Method for Cable Dynamics

Department of Mechanics and Engineering Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

E-mail Address: ding_huaiping@163.com

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Zheng H. Zhu

Department of Mechanical Engineering, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J1P3

E-mail Address: gzhu@yorku.ca

Corresponding author.

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Xiaochun Yin

Department of Mechanics and Engineering Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

E-mail Address: yinxiaochun2000@aliyun.com

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Lin Zhang

Department of Mechanics and Engineering Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

E-mail Address: 179192591@qq.com

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Gangqiang Li

Department of Earth and Space Science and Engineering, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J1P3

E-mail Address: lgq1984@yorku.ca

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, and

Wei Hu

Department of Mechanics and Engineering Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

E-mail Address: huwei@njust.edu.cn

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https://doi.org/10.1142/S1758825117501095Cited by:7 (Source: Crossref)

Abstract

This paper developed a new Hamiltonian nodal position finite element method (FEM) to treat the nonlinear dynamics of cable system in which the large rigid-body motion is coupled with small elastic cable elongation. The FEM is derived from the Hamiltonian theory using canonical coordinates. The resulting Hamiltonian finite element model of cable contains low frequency mode of rigid-body motion and high frequency mode of axial elastic deformation, which is prone to numerical instability due to error accumulation over a very long period. A second-order explicit Symplectic integration scheme is used naturally to enforce the conservation of energy and momentum of the Hamiltonian finite element system. Numerical analyses are conducted and compared with theoretical and experimental results as well as the commercial software LS-DYNA. The comparisons demonstrate that the new Hamiltonian nodal position FEM is numerically efficient, stable and robust for simulation of long-period motion of cable systems.

Keywords:

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