根据索杆张力结构体系特征,建立了一种修正的力密度平衡形态分析方法;基于单纯索网体系力密度法,推导出了索杆自平衡体系力密度平衡方程;根据索杆张力结构的自应力模态、机构位移模态、无约束自平衡条件和力密度矩阵数值特征,推导出了力密度矩阵的秩亏条件,并引入力密度和节点向量线性条件约束索杆结构的几何模型;通过高斯变换降秩法得到满足秩亏的降秩力密度矩阵,并由M—P广义逆矩阵更新了力密度,迭代计算后得到可行力密度;根据一组独立无关坐标和拓扑关系计算了平衡形态位形,最后采用VC++编程实现了算法。结果表明:该方法适用于索杆张力结构的找形分析,具有一定的正确性和有效性。
A modified force density method (MFDM) was developed for form-finding analysis due to the inherent characteristics of cable-strut tension structure systems. On the basis of conventional force density method of pure cable-net system, the force density equilibrium equation was formulated for the cable-strut self-equilibrated assembly. Since the cable-strut assembly had self-equilibrium unstressed mechanism, stress mode, free body and the properties of force density matrix, the rank deficiency of the matrix was deduced. The linear constraint of force density and nodal coordinate vector were applied to the analytical model. The deficiency force density matrix could be obtained with the Gaussian transformation deficiency, the updated force density could be got with M-P generalized inverse matrix, and the feasible force density was solved iteratively. The final equilibrated form was calculated with non-dependable nodal coordinate and topology. Finally, the program was developed with VC++. The results show that the proposed method can applied to form-finding analysis of cable-strut tension structure, and the algorithm is correct and available.