复合可展曲面网格结构形态创建方法研究  

Research on morphology creation method of composite developable surface grid structure

作　　者：崔京兰 郑延丰[1] 罗尧治[1] CUI Jinglan;ZHENG Yanfeng;LUO Yaozhi(Space Structure Research Center of Zhejiang University,Hangzhou 310058,China)

机构地区：[1]浙江大学空间结构研究中心,浙江杭州310058

出　　处：《建筑结构学报》2022年第12期290-299,共10页Journal of Building Structures

基　　金：国家自然科学基金项目(51778568,51908492)。

摘　　要：空间网格结构的形态创建需要同时考虑建筑外形的美观性、结构受力的合理性和施工建造的便捷性。基于可展曲面的几何特性提出了一种复合可展曲面网格结构形态创建方法。首先基于Bézier函数给出了单一可展曲面的几何描述,并通过引入G0(两个曲线端点连续的连接)、G1(一阶微分连续的连接)连接条件提出了复合可展曲面的构建方法;其次,基于曲面表面积最小化的优化数学模型给出了复合可展曲面形态存在的判定方法;将曲面离散为网格结构后,利用结构系统应变能最小化的优化数学模型,建立了复合可展曲面网格结构的形态创建方法。从设计变量变化范围、导线拼接方式、初始直纹面等方面,通过算例验证了所提出的复合可展曲面网格结构形态创建方法的有效性。研究结果表明,不同的初始结构会优化得到不同的受力合理的网格结构形态。通过不同的连接方式,可以实现满足建筑意图的各种形式可展曲面结构形态。所提出的复合可展曲面网格结构形态创建方法,在保证施工建造便捷性的同时兼顾了结构受力合理性。The morphology of spatial lattice structures should be created considering the aesthetics of building shape,the rationality of structural forces and the convenience of construction.Based on the geometric properties of the developable surface,a morphology creation method was proposed based on the composite developable surfaces.Firstly,the geometric description of a single developable surface was given based on the Bézier function,and the construction method of the composite developable surfaces was given by introducing the G0 and G1 connection conditions.Secondly,the determination method of the existence of the composite developable surfaces’morphology was derived based on the optimized mathematical model for minimizing the surface area.After discretizing the surface into a mesh structure,an optimization mathematical model for minimizing the strain energy of the structural system was applied to establish the morphology creation method of mesh structure of the composite developable surfaces.The effectiveness of the proposed method for creating the grid structure morphology of composite developable surfaces was verified in terms of the variation range of design variables,connection method of directing curve,and initial ruled surface through examples.The results show that different initial structures will be optimized to obtain different force-reasonable grid structure morphologies.Through different connection ways,it is possible to achieve various shapes of developable surface morphology satisfying the architectural intent.The proposed method of creating composite developable surface grid structure morphology can ensure the convenience of construction while providing reasonable structural forces.

关 键 词：空间网格结构 复合可展曲面 BÉZIER曲线曲面 结构形态 形状优化 

分 类 号：TU356[建筑科学—结构工程]