物理学报2016，Vol.65Issue(9)：094501-0-094501-10,11.DOI:10.7498/aps.65.094501
基于绝对节点坐标法的大变形柔性梁几种动力学模型研究∗
Several dynamic mo dels of a large deformation flexible b eam based on the absolute no dal co ordinate formulation
摘要
Abstract
With the development of space technology, flexible appendages such as lightweight manipulators and satellite an-tennas, 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 π 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 π increases. Considering the calculating efficiency of the dynamic model, whenπis small, simplified model I is chosen preferentially;whenπis big, simplified model II is adopted preferentially.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Key words
absolute nodal coordinate formulation/large deformation/Green-Lagrangian strain tensor/Lagrange identical equation引用本文复制引用
章孝顺,章定国,陈思佳,洪嘉振..基于绝对节点坐标法的大变形柔性梁几种动力学模型研究∗[J].物理学报,2016,65(9):094501-0-094501-10,11.基金项目
国家自然科学基金(批准号:11272155,11302192,11132007)和江苏省333工程(批准号：BRA2011172)资助的课题 （批准号:11272155,11302192,11132007）
