一种空间缆索结构静力分析的解析元法

Analytical element method on the calculation of three-dimensional cable supported structures

将空间缆索结构简化为具有拉伸刚度的质点系,给出了缆索结构空间解析元法的基本方程和求解方法,单元间的作用力与坐标变化的关系可以用解析法得到,对所得到的反映结构特性的质点系方程组进行力的平衡迭代,求解方程组。采用自动的动态可变步长的迭代方法,能够提高计算效率,保证收敛。这种方法既考虑了几何非线性,又适用于材料非线性的计算,比有限元法优越之处还在于,它不用求解线性方程组,所以适用范围广,允许求解多自由度的几何可变体系,而有限元法在求解此类问题时经常不收敛。

Provided that three-dimensional cable-supported structures were particles system with tension stiffness, primary equilibrium equations of these particles could be established, and these equations could be solved by numerical method. Relationships between the inner forces of elements and the change of their coordinates were obtained by analytical method. Therefore the method is named as analytical element method. Particles system equations, which reflecting the properties of cable structures, were solved by iterative method of force equilibrium. Changeable steps are applied automatically in the iterarive calculation, so that the process is efficient and the results are convergent. Geometrical nonlinearity and material nonlinearity were both taken into account in this method. Compared with finite element method, no linear equations are obliged to solve in this method, so this method is more adaptable in calculating geometrical transformable structures, whereas the solutions of this kind of problems is often not convergent by finite element method.