中文摘要：

分析了现有各种求解索杆张力结构初始预应力方法的局限性，充分考虑对称性和整体可行性，从平衡矩阵理论出发利用奇异值分解法提出了一种旨在求解各种张力结构体系的整体自应力模态的求解方法，并对具有多个整体自应力模态的索穹顶结构采用修正单纯形法、以外圈环索初内力最小为优化目标进行了预应力优化。研究表明，充分考虑对称性和整体可行性的奇异值分解法能求解各种体系的整体自应力模态，预应力优化能求得满足条件的合理初始预应力分布。

英文摘要：

After reviewing the limitations of existing methods for solving the prestress modes of cable-strut tension structures, a new method, which is capable of determining the overall selfstress modes for different types of cable-strut tension structures, is proposed. The method is to employ singular value decomposition, considering both the symmetry and feasibility of the structure in question. Taking the minimum initial force of outer hoop cables as the objective function, an optimal prestress design of a selected structure with multi-overall selfstress modes is investigated by a revised simplex algorithm. Numerical results show that the prestress modes can be easily determined by using the singular value decomposition method considering both the symmetry and feasibility of the structure. The proposed optimal method appears to be reasonably effective for finding the optimal initial prestress of a tension structure.