基于群论的预应力索杆体系刚度解析与形态优化研究

Prestressed cable-strut structures are novel and efficient, and could obtain/improve structural rigidity through initial self-balancing prestresses. Therefore, they possess exuberant vitality and have promising engineering applications. However, the stiffness of a novel prestressed cable-strut structure is generally indeterminate; the geometric configuration is mutually coupled with the structural performance. To overcome these difficulties, novel stiffness analysis and form-finding of prestressed cable-strut structures using group theory are proposed. The static and kinematic indeterminacy of cable-strut structures is studied, to evaluate symmetry representations of internal mechanism modes and self-stress states. Accordingly, the approach for determining prestress stability of cable-strut structures could be further improved. Subsequently, the elastic stiffness, the geometric stiffness, and the tangent stiffness of a general cable-strut structure are investigated, respectively. It turns out that, through the stiffness analysis, sufficient and necessary stability conditions for symmetric cable-strut structures can be obtained. On the basis of group theory and irreducible representations for equivalent transformations, an automated recognition technique for structural symmetry is also proposed. Furthermore, to consider the effect of structural performance, economy and inherent symmetry, two independent constrained optimization models are respectively established, where the initial prestresses and connectivity of members are taken as independent variables. Then, the ant colony optimization method is adopted to find the optimum for the form-finding analysis on prestressed cable-strut structures. It could be concluded that this project would enrich and develop basic theory and computation method for cable-strut structures. Besides, the project could provide new techniques and reference for developing large-scale prestressed cable-strut structures.

预应力索杆结构构型新颖、高效，借助体内自平衡预应力形成或改善结构刚度，具有很强的生命力和良好的工程应用前景。针对新型预应力索杆体系设计中的刚度不确定性问题及结构构型与结构性能相互耦合的问题，本项目引入群论方法，开展预应力索杆体系刚度解析及形态优化研究。主要内容包括：（1）研究索杆体系静动不定性及其机理，定性分析机构位移和自应力模态的对称表示，并完善索杆结构预应力稳定性的判定方法；（2）对索杆体系的弹性刚度、几何刚度、结构刚度进行解析，给出评判对称索杆结构稳定性的充分和必要条件；（3）根据等效变换的不可约表示，提出基于群论的结构对称性自动识别方法；（4）分别以预应力和拓扑关系为自变量，并考虑结构性能、经济性和对称性，采用两种独立的约束优化模型，提出基于蚁群算法的预应力索杆体系形态优化方法。本项目一方面丰富和发展索杆体系研究的理论与方法；另一方面为开发大型预应力索杆体系提供新的技术手段与参考。

预应力索杆结构构型新颖、高效，借助体内自平衡预应力形成或改善结构刚度，具有很强的生命力和良好的工程应用前景。针对新型预应力索杆体系设计中的刚度不确定性问题及结构构型与结构性能相互耦合的问题，本项目引入了群集理论方法，开展了预应力索杆体系刚度解析及形态优化研究。主要包括：（1）研究了索杆体系静动不定性及其演变机理，定性分析了节点偏差、构件拓扑、外荷载等多种因素影响下机构位移模态和自应力模态的对称表示及其变化机制，并完善了索杆结构预应力稳定性的判定方法；（2）分别从对称子空间、节点与构件层次对索杆体系的弹性刚度、几何刚度、结构整体刚度进行解析，给出了评判对称索杆结构稳定性的充分和必要条件；（3）归纳了百余种对称群及五类对称操作，开发了群论工具箱，根据对称操作的等效变换以及相应矩阵的不可约表示，提出了基于群论的结构对称性自动识别方法，有效拓展群论方法在工程领域的应用范围；（4）利用全对称子空间的物理意义，提出了高效求解结构整体自应力模态的方法；在此定性分析基础上，分别以预应力和拓扑关系为自变量，并充分考虑了结构对称性、结构刚度及初始预应力分布特点，采用两种独立的约束优化模型，提出了基于蚁群算法的预应力索杆体系形态优化方法。本项目培养研究生4名，已发表SCI论文14篇（其中JCR Q1论文7篇、ASCE论文3篇）；围绕索杆结构找形、结构对称性识别等方面解决了数个关键技术问题，申请了发明专利10项，已授权6项。项目研究成果一方面丰富和发展了索杆体系研究的理论与方法；另一方面为开发大型预应力索杆体系提供新的技术手段与参考。