摘要
力密度法通常用于张拉索网结构等不需要考虑稳定性的结构体系的找形分析,但对于树状结构,由于其在竖向荷载作用下所有构件仅受到轴向压力的作用,除了找形以外还需要考虑构件稳定承载能力的问题。利用力密度法对树状结构进行找形分析的基础上,引入欧拉稳定承载力计算理论以考虑构件几何长度对稳定承载力的影响,并提出了相应的迭代算法。推导了适用于树状结构的修正迭代力密度理论计算式,通过改变每一个分枝的力密度进而达到优化分枝长度的目标。通过与已有计算结果的对比验证所提对于平面树状结构算法的可靠性,对空间树状结构进行分析验证所提算法对于复杂树状结构的适用性。算例分析表明:采用所提算法迭代100次即可得到收敛的结果,耗时5 min左右;与数值逆吊法找形相比,避免了双单元法抗弯刚度不恰当而导致的计算不收敛问题。
The force density method has always been adopted for the form-finding analysis of cable net structures for which the buckling capacity of all components need not to be considered. All components of the branching structures are subjected to axial compression load under the action of vertical load, the buckling capacity of each branch must be considered besides the form-finding issue. The force density method is adopted for the form-finding analysis of branching structures and the Euler buckling theory is combined with the force density method to consider the influence of branch length on buckling capacity. The iteration algorithm for the combination of the force density method and the Euler buckling theory is proposed. The theoretical formula of modified iteration force density method which is suitable for branching structures is deduced. The geometrical length of the branch can be optimized by adjusting the force density of each branch. The reliability of the proposed method is validated by comparing the results derived in this paper with those presented in the existing literature. The applicability of the proposed method for branching structures on a large scale is also validated. The converged results can be derived after 100 iterations and the time needed is about 5 minutes. In addition, the un-convergence caused by the inappropriate bending stiffness of double elements can be avoided compared with the numerical inverse hanging method.
作者
赵中伟
于铎
简相洋
吴谨伽
严仁章
ZHAO Zhongwei;YU Duo;JIAN Xiangyang;WU Jinjia;YAN Renzhang(School of Civil Engineering,Liaoning Technical University,Fuxin 123000,China;School of Civil Engineering,Southeast University,Nanjing 211189,China;School of Civil Engineering,Chongqing Jiaotong University,Chongqing 400074,China)
出处
《建筑结构学报》
EI
CAS
CSCD
北大核心
2022年第9期260-268,共9页
Journal of Building Structures
基金
中国博士后科学基金项目(2021T140116)
辽宁省教育厅基础研究项目(LJ2020 JCL036)。
关键词
树状结构
力密度法
找形算法
长度优化
稳定承载力
branching structure
force density method
form-finding analysis
length optimization
buckling capacity
