索网天线的参变量变分及非线性有限元方法

发布时间：2019-03-26 15:22

【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]:In view of the constitutive nonlinearity caused by different tensile modulus and geometric nonlinearity caused by large deformation of large-scale peripheral truss cable-mesh antenna, a geometric nonlinear finite element method based on the variational principle of parametric variables is presented. Firstly, a unified description form based on parametric variables and complementary equations is derived by introducing parametric variables for constitutive relations with different segments of tensile and compressive modulus of pre-stressed cable elements. The traditional algorithm needs to predict the tension / relaxation state of cable element according to the current deformation, and improves the convergence of the algorithm. Then the Lagrangian strain is used to describe the large deformation of cable-net antenna structure and the nonlinear equilibrium equation and linear complementary equation based on parametric variables are established by means of geometric nonlinear finite element method. The Newton-Raphayson iteration method and the Lyme algorithm are also given in this paper. Numerical examples show that the proposed algorithm has more stable convergence and higher accuracy than the traditional algorithm, and is especially suitable for high-precision deformation analysis and prediction of large-scale cable-net antenna structures.
【作者单位】：大连理工大学工业装备结构分析国家重点实验室;大连理工大学航空航天学院;
【基金】：国家自然科学基金(11372056,11002032) 高等学校博士点基金(20110041130001)资助项目~~
【分类号】：TN820

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