欧拉稳定承载力约束下树状结构找形优化研究

Topology optimization of branching structures with constraints on member instabilities

找形是树状结构研究的关键问题之一,为此,首先提出了基于双单元数值模型的找形迭代程序,并利用已有研究结果对所提出方法进行了验证,计算结果表明利用该方法所得到的树状结构形态在给定荷载作用下只受到轴力。在此基础上,基于欧拉稳定压杆理论,对树状结构各分支的几何长度进行了优化,在保证各个构件只受到轴力的同时,确保整体结构的稳定承载力最大化。研究结果表明,所提的找形优化方法可以精确考虑平面及空间树状结构各个构件计算长度系数和截面特性对稳定性的影响,计算效率高,可为复杂树状结构的找形优化工作奠定理论基础。

The branching structures have been widely adopted in large scale building structures and landmark buildings.The main issue about branching structures is form-finding analysis.The iterative program of form-finding based on double element model was firstly proposed,and then validated using the results of existing literatures.The results indicate that the proposed method can be efficiently used for form-finding analysis of branching structures,and the components are only subjected to axial force after form-finding analysis.In light of this,the geometrical length of each component was also optimized for branching structures based on Euler’s theory to guarantee its loading capacity,and the buckling capacity of branching structures was maximized.The results indicated that the sectional property and the effective length factor can be accurately considered and the proposed method is fully capable of form-finding analysis for spatial branching structures.