索网天线的参变量变分及非线性有限元方法

谭述君; 侯健; 吴志刚; 杜剑明

doi:10.6052/0459-1879-14-126

索网天线的参变量变分及非线性有限元方法

doi: 10.6052/0459-1879-14-126

1.
大连理工大学工业装备结构分析国家重点实验室, 大连116024
2. 大连理工大学航空航天学院, 大连116024

基金项目: 国家自然科学基金（11372056，11002032）和高等学校博士点基金（20110041130001）资助项目.

详细信息

作者简介:
吴志刚，教授，主要研究方向：飞行器动力学与控制，鲁棒控制与最优控制的理论、算法及应用.E-mail：wuzhg@dlut.edu.cn

中图分类号: O343.5;V414.1
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出版历程
- 收稿日期: 2014-05-07
- 修回日期: 2014-08-11
- 刊出日期: 2014-09-18

THE PARAMETRIC VARATIONAL PRINCIPLE AND NON-LINEAR FINITE ELEMENT METHOD FOR ANALYSIS OF ASTROMESH ANTENNA STRUCTURES

1.
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China

Funds: The project was supported by the National Natural Science Foundation of China (11372056, 11002032) and the Research Fund for the Doctoral Program of Higher Education (20110041130001).

摘要

摘要: 针对大型周边桁架式索网天线由拉索拉压模量不同引起的本构非线性和结构大变形引起的几何非线性问题，给出了基于参变量变分原理的几何非线性有限元方法. 首先针对含预应力索单元拉压模量不同分段描述的本构关系，通过引入参变量，导出了基于参变量及其互补方程的统一描述形式，避免了传统算法需要根据当前变形对索单元张紧/松弛状态的预测，提高了算法收敛性. 然后利用拉格朗日应变描述索网天线结构大变形问题，结合几何非线性有限元法，建立了基于参变量的非线性平衡方程和线性互补方程；并给出了牛顿-拉斐逊迭代法与莱姆算法相结合的求解算法. 数值算例验证了本文提出的算法比传统算法具有更稳定的收敛性和更高的求解精度，特别适合于大型索网天线结构的高精度变形分析和预测.
- 索网天线 /
- 本构非线性 /
- 几何非线性 /
- 参变量变分原理 /
- 非线性有限元
Abstract: A new stable algorithm is presented for AstroMesh antenna structure with large deformation based on the parametric variational principle (PVP) and nonlinear finite element method. Firstly, a parametric variable with its related complementary equation is introduced to model the bilinear constitutive relations of cable elements, and so a unified description of bilinear constitutive model is obtained, which avoids the prediction that the cable is tensioned or relaxed for traditional algorithms. Then, the Lagrangian strain is applied to tackle the large deformation problem of the AstroMesh structure. The nonlinear equilibrium equations and complementary equations are established based on the nonlinear geometric finite element method and parametric variatianal principle. The Newton-Raphson scheme combined with Lemke algorithm is employed to solve the equations. Numerical examples are given to demonstrate the convergence and accuracy of the PVP method in this paper are better than those of the traditional method. The proposed method is particularly suitable for high-precision analysis and prediction for large deformation of AstroMesh antenna structure.
- astroMesh antenna /
- constitutive nonlinearity /
- geometric nonlinearity /
- parametric variational principle /
- nonlinear finite element method

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