索穹顶结构非线性分析的杆索有限元法

FINITE MEMBER-CABLE ELEMENT METHOD FOR NONLINEAR ANALYSIS OF CABLE DOMES

索穹顶结构是大变形柔性组合结构，其受力分析属于几何非线性问题，求解较复杂。本文应用有限元法，结合索穹顶结构特征，提出三节点等参数索单元与两节点杆单元相结合的混合有限元模式。基于Lagrangian坐标描述法和虚功原理推导了空间拉索和杆单元的大位移刚度矩阵，并建立了索穹顶结构非线性分析的增量平衡方程，利用NewtonRaphson法进行了实例计算。结果表明，本文方法精度很高，适合于索穹顶结构的空间非线性分析。

Cable dome is a large deformation composite structure consisted of flexible cables.Its analysis is a geometric nonlinear problem and is difficult in its solution.In thes paper, a mixedfinite element model combining the three-node isoparametric cable elements and straight member elements was presented based on the structural characters of cable domes and the nonlinear element method was applied. Based on the Lagrangian coordinates and the virtual displacement principle, the large deflection stiffness matrices of space member and cable elements were derived,and the nonlinear incremental equilibriUm equation of cable domes was established. Using the Newton-Raphson method,one example was analyzed, and the result showed that the model presented in this paper was accurate and efficient for nonlinear static analysis of cable domes.