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谭述君, 侯健, 吴志刚, 杜剑明. 索网天线的参变量变分及非线性有限元方法[J]. 力学学报, 2014, 46(5): 770-775. DOI: 10.6052/0459-1879-14-126
引用本文: 谭述君, 侯健, 吴志刚, 杜剑明. 索网天线的参变量变分及非线性有限元方法[J]. 力学学报, 2014, 46(5): 770-775. DOI: 10.6052/0459-1879-14-126
Tan Shujun, Hou Jian, Wu Zhigang, Du Jianming. THE PARAMETRIC VARATIONAL PRINCIPLE AND NON-LINEAR FINITE ELEMENT METHOD FOR ANALYSIS OF ASTROMESH ANTENNA STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5): 770-775. DOI: 10.6052/0459-1879-14-126
Citation: Tan Shujun, Hou Jian, Wu Zhigang, Du Jianming. THE PARAMETRIC VARATIONAL PRINCIPLE AND NON-LINEAR FINITE ELEMENT METHOD FOR ANALYSIS OF ASTROMESH ANTENNA STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5): 770-775. 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

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

  • 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.

     

    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.

     

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