互承式空间网格结构找形方法研究

互承式空间网格结构是一种以杆件相互搭接为特征的杆系结构,具有连接构造简单、富于韵律美感的特点。由于互承式空间网格结构的形状受杆件搭接关系的影响,因此该类结构设计中的关键问题是找到同时满足杆件搭接关系和建筑造型要求的结构形状。为此,推导了杆件搭接系数,实现了对杆件搭接关系的量化描述,采用二分法实现了杆件搭接过程的数值模拟。基于结构实际搭建过程,提出一种互承式空间网格结构找形方法。该方法按照一定顺序依次提升平面互承网格的每个杆件节点,通过反复迭代使所有节点满足设定的杆件搭接系数,从而实现互承式空间网格结构的循环搭接找形。算例分析表明：所提方法的计算效率明显优于已有基于结构优化算法的找形方法,杆件搭接系数、旋转角度和网格疏密程度是影响互承式空间网格结构形状的主要参数,调整这些参数能够使结构整体形状趋近建筑造型要求。

A form-finding method for reciprocal spatial grid structure

Reciprocal spatial grid structure is a truss structure with mutually lapping bars and simple connection, which is full of rhythm beauty. It is the chief problem in reciprocal spatial grid structural design to find a proper structural configuration that can both satisfy mutually supporting relationship and architectural shape because of the limit of lapping relationship. Bar lapping factor is proposed to realize the mathematical description of lapping status and the lapping process of connection is realized numerically by bisection method. A form-finding method is put forward based on simulating the real building process. The method lifts the nodes of reciprocal grid by a fixed order until all connections satisfy the target bar lapping factor, realizing the form-finding by iterations. Numerical examples show that computing efficiency of proposed method is superior to those based on structural optimization algorithm. Bar lapping factor, rotation angle and grid density are the main influential parameters of reciprocal structural shape. Adjusting these parameters can make structural shape close to the architectural target and realize the form-finding of structures effectively.