零弯矩型自由曲面结构找形方法

摘要

To design free-form structures with reasonable mechanical behaviors and rich geometrical shapes, the principles of traditional form-finding methods by physical experiments were referred, and a numerical form-finding method for free-form structures was proposed based on the combination of the Dynamic Relaxation method and the Local Linearization method.As the zero bending moment type free-form structure has the same form with the flexible membrane structure which has the same loading distributions and boundary conditions,the form-finding of free-form shell structures can be realized by membrane structures. In the proposed method,equilibrium forms under different driving forces,such as the gravity, pneumatic pressure, pretension force, were generated by Dynamic Relaxation method,and the form-control problem aiming to meet the requirements of architectural design was explored by adjusting the initial parameters of the model using the Local Linearization method. The poposed form-finding method was applied to the inverse-hanging type shells,the pneumatic type shells and the tension type shells separately. For the inverse-hanging type shells,a model made by Isler was simulated,and the results were compared with the data by 3D scanning to verify the accuracy of the proposed method. For the pneumatic type shells, the multi-region controlling strategy was used to realize the form-finding of complicated shapes. For the tension type shells, the behaviors of a shell genertated by the form-finding method were analized to illustrate the zero bending moment feature. It can be concluded that the proposed method is more effective and applicable, which is helpful to realize the harmonious design of architecture and structure.%为获得受力合理且形式丰富的自由曲面结构,借鉴传统模型试验找形法的原理,提出基于动力松弛法和局部线性化法的零弯矩型自由曲面结构数值找形方法.该方法利用了零弯矩型薄壳结构与相同荷载与边界条件下的柔性膜结构具有相同形状的性质,通过膜结构来实现自由曲面结构的找形.首先采用动力松弛法确定柔性结构在不同驱动力作用下的平衡构形;然后利用局部线性化方法调整结构初始参数,实现对结构形状的精确调控,以满足建筑设计对控制点坐标的要求.利用所提方法分别对逆吊型、充气型和张拉型自由曲面进行了数值模拟分析.通过对Isler逆吊试验模型的模拟,并与实际模型的3D扫描结果进行比较,验证了方法的精确性;通过对一充气型自由曲面的模拟,证明通过多区域分步控制可实现复杂造型结构的多点精确控制;通过对一找形后的张拉型自由曲面结构进行受力分析,证明采用本文方法可获得受力合理的纯压结构.研究表明,本文方法的计算效率更高,适用范围更广,有助于实现建筑与结构设计的协调统一.