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索网天线找形分析的参变量变分有限元法
引用本文:刘涛,王碧,李昊,周鑫,张亮.索网天线找形分析的参变量变分有限元法[J].计算力学学报,2021,38(1):73-77.
作者姓名:刘涛  王碧  李昊  周鑫  张亮
作者单位:复旦大学航空航天系,上海200433;上海宇航系统工程研究所,上海201109;上海宇航系统工程研究所,上海201109;复旦大学航空航天系,上海200433;重庆大学航空航天学院,重庆400044
基金项目:国家自然科学基金(11872133);上海航天创新基金(SAST2019-023)资助项目.
摘    要:针对柔性空间索网天线的非线性特点,建立了基于参变量变分描述索网拉压非线性和共旋列式描述几何非线性的有限元控制方程,应用Lernke与改进牛顿法进行求解.通过对索网预张力平衡计算,证明改进牛顿法比Newton-Raphson法具有更强的收敛能力.进一步将力密度法迭代原理与有限元法结合应用于索网天线的非线性找形分析中,获得了理想的索网构型.本文的索网找形方法可广泛应用于空间索网天线结构的设计.

关 键 词:索网天线  参变量变分  共旋列式  改进牛顿法  找形分析
收稿时间:2019/7/4 0:00:00
修稿时间:2020/4/28 0:00:00

Parametric variational finite element method for the form-finding of the cable-network antenna
LIU Tao,WANG Bi,LI Hao,ZHOU Xin,ZHANG Liang.Parametric variational finite element method for the form-finding of the cable-network antenna[J].Chinese Journal of Computational Mechanics,2021,38(1):73-77.
Authors:LIU Tao  WANG Bi  LI Hao  ZHOU Xin  ZHANG Liang
Institution:Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China;Aerospace System Engineering Shanghai, Shanghai 201109, China,Aerospace System Engineering Shanghai, Shanghai 201109, China,Aerospace System Engineering Shanghai, Shanghai 201109, China,Aerospace System Engineering Shanghai, Shanghai 201109, China and School of Aerospace Engineering, Chongqing University, Chongqing 400044, China
Abstract:In view of the constitutive nonlinearity and geometric nonlinearity of the cable-network antenna, the parametric variational principle and a co-rotational formation were introduced to establish the finite element governing equation.The improved Newton method was employed to solve the governing equation.Firstly,the method was applied for pretension balance calculation of cable-network antenna.The analysis results show that the improved Newton method has a better convergence than Newton-Raphson method.Further,the iterative principle of force density method combined with this finite element method was applied for nonlinear form-finding analysis of the cable-network antenna and an ideal configuration was obtained.The output of this paper is expected to provide some valuable information for studying other similar structures in the future.
Keywords:cable-network antenna  parametric variational principle  co-rotational formation  improved Newton method  form-finding analysis
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