柔性多体系统接触动力学高效建模方法研究

The project deals with the contact-winding of a large deployable space mesh truss antenna with the scale of 100m during the deployment on orbit and the long service in order to meet the nation’s requirements in the future space technology. The major studies of the project include: (1) the high-precision modeling methods for the deployment dynamics of the mesh-truss antenna under micro-gravity, (2) the efficient modeling methods for the moving contact of the mesh-truss antenna, (3) the design and management technology of the winding preventing for the deployment of the mesh-truss antenna. The project will focus on the integrated research of theoretical and numerical aspects and provide the solutions to the following open problems:(1) how to realize the integration of the deployment dynamics modeling, simulation and analysis of the mesh truss antenna, (2) how to describe and analyze the moving contact and winding dynamics of flexible cable net under micro-gravity, (3) how to design and manage the winding preventing technology of the mesh-truss antenna. Through this project, the achievements will offer the new knowledge and new technology to the nation’s development in large deployable space structures.

以实现十九大提出的航天强国目标为背景，针对未来航天科技发展迫切需求的百米口径量级超大型空间可展开桁架索网天线，研究其展开过程的索网动态接触缠绕问题。该项目的主要研究内容：（1）微重力环境下桁架索网天线展开动力学高精度建模方法；（2）柔性索网大范围运动的动态接触高效建模方法；（3）桁架索网天线展开过程的索网防缠绕设计。该项目主要基于理论、分析和计算，重点解决以下科学问题：（1）如何实现桁架索网天线展开动力学的建模、仿真和分析一体化；（2）如何对微重力环境下松弛状态的柔性索网动态接触进行非线性动力学描述和分析；（3）如何对桁架索网天线展开过程的索网防缠绕进行设计。通过上述研究有望为我国超大型空间可展开桁架索网天线的动力学建模和防缠绕设计提供理论依据，支撑我国未来百米大口径桁架索网天线的研制。

近三十年来，柔性多体系统动力学取得长足进步，尤其是以绝对节点坐标方法（Absolute Nodal Coordinate Formulation, ANCF）为代表的非线性有限元已被用来处理复杂的柔性多体系统动力学问题。但绝对节点坐标方法采用斜率矢量作为广义坐标，导致系统自由度多，计算效率低。针对柔性多体系统，基于非均匀有理B样条（Non-Uniform Rational B-Splines, NURBS）曲线和曲面分别提出了Euler-Bernoulli细长梁单元和Kirchhoff-Love薄壳单元，在完全拉格朗日格式下，根据Green应变张量对单元变形进行描述，结合第二类Piola-Kirchhoff应力张量给出单元应变能公式，推导了单元的弹性力和弹性力雅各比矩阵表达式，最后通过静力学及动力学数值算例对提出的两类单元的性能进行对比和验证，为柔性多体系统建模提供了一种精确高效的新单元。