向量式有限元在索穹顶静力分析中的应用

APPLICATION OF VECTOR FORM INTRINSIC FINITE ELEMENT METHOD TO STATIC ANALYSIS OF CABLE DOMES

索穹顶结构是一种由预应力拉索与竖杆组成的高效柔性空间结构,易发生较大位移,拉索可能出现松弛现象。该文采用向量式有限元进行了索穹顶的静力分析。向量式有限元是一种向量力学与数值计算相结合的分析方法,不同于传统分析力学方法和其他数值计算方法。向量式有限元基于运动方程求解,不需求解非线性方程组及刚度矩阵,尤其适合于发生刚体位移和几何大变形的结构或机构求解。该文首先介绍了向量式有限元的基本原理,推导了预应力索单元的求解公式,最后采用自编向量式有限元程序,分析了一个单摆模型和一个索穹顶结构模型。结果表明:向量式有限元应用于索穹顶静力分析是可行而且可靠的,在传统有限元计算难以收敛的情况下仍然可以对结构进行精确的非线性分析,为索穹顶的非线性分析提供了一种新的方法和手段。

A cable dome is a new type of efficient spatial structures, which mainly consists of cables and struts. A large displacement even cable slack is easy to happen. In this paper, the static behavior of a cable dome is studied by the Vector Form Intrinsic Finite Element （VFIFE）. VFIFE is a recently proposed method based on the combination of the vector mechanics and numerical calculations, different from traditional analysis mechanics and other numerical computational methods. VFIFE derives from a kinematic equation. There is no need to solve any nonlinear equations by calculating the stiffness matrix, very helpful in the analysis of large rigid body motions and large geometrical changes. The fundamentals of this method are summarized first. And the internal force of a cable element is conducted to model the cable dome. Then a simple the Matlab language program. Numerical results show that VFIFE cable dome structure. Hence, a new approach of nonlinear analyses method is hard to converge. pendulum and a cable dome are analyzed with is useful and reliable in case of analyzing the is provided when the traditional finite element