关键词: 绝对节点坐标法/
大变形/
Green-Lagrangian应变张量/
拉格朗日恒等式
English Abstract
Several dynamic models of a large deformation flexible beam based on the absolute nodal coordinate formulation
Zhang Xiao-Shun1,Zhang Ding-Guo1,
Chen Si-Jia2,
Hong Jia-Zhen3
1.School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China;
2.Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
3.Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200240, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 11272155, 11302192, 11132007), and the 333 Project of Jiangsu Province, China (Grant No. BRA2011172).Received Date:10 December 2015
Accepted Date:27 December 2015
Published Online:05 May 2016
Abstract:With the development of space technology, flexible appendages such as lightweight manipulators and satellite antennas, often appear in spacecrafts. Usually, the large overall motion of the flexible appendage will bring about large deformation problem. And there is a strong nonlinear coupling between the large overall motion and deformation of the flexible appendage, which brings about a large challenge to the precise control of the spacecraft. Dynamics of a rotating flexible planar beam with large deformation is investigated in this paper. A new nonlinear dynamic model of a flexible beam with large deformation is established based on an absolute node coordinate formulation (ANCF). The longitudinal and bending deformations of the flexible beam are both considered in the model. The longitudinal strain energy and bending strain energy of the beam can be calculated by using Green-Lagrangian strain tensor and the exact expression of the flexible beam curvature, respectively. A new concise expression of the bending deformation energy can be obtained by using the Lagrange identical equation. The new elastic force model is derived from the new expression of the deformation energy. The dynamic equations of the present model can precisely deal with the large deformation problem of flexible beams. Then, simulation results from three dynamic models, including the ANCF model, the high order coupling model (HOC model), and the BEAM188 model in ANSYS, are compared to prove the validity of the ANCF model proposed in this paper. And we can also find the deficiency of the HOC model from the simulation. Further study shows that the new generalized elastic force model can be simplified properly. Two simplified models are presented in this paper. The applicabilities of the simplified models are pointed out from the viewpoints of computational efficiency and accuracy. A dimensionless parameter denoted as is introduced to describe the extent to which a flexible beam pendulum undergoing free falling motion is deformed. The deformation of the flexible beam increases as increases. Considering the calculating efficiency of the dynamic model, when is small, simplified model I is chosen preferentially; when is big, simplified model Ⅱ is adopted preferentially.
Keywords: absolute nodal coordinate formulation/
large deformation/
Green-Lagrangian strain tensor/
Lagrange identical equation
