摘要
为解决指定节点坐标下张拉整体结构拓扑形态问题,提出一种将关联矩阵编码后组成方案矩阵的拓扑找形方法。基于张拉整体结构形态分析理论,以各节点连接构件的数量为约束指标,通过合理地选取构成方案矩阵中的若干元素以确定各单元所在的空间位置,由此构建0,-1整数变量与结构体系几何稳定之间的关系,结合稳定性判定条件以实现张拉整体结构的拓扑找形。最后以2个空间张拉整体结构为例,结合对称性指标,找到若干拓扑形态高度对称的张拉整体结构,从而验证该算法的可行性及准确性。结果表明,该方法为确定指定节点坐标下张拉整体结构的拓扑形态提供了一条有效的解决途径,对于空间二十六单元张拉整体结构,可寻找到17个压杆数量不同的拓扑形态,力密度对称指标临界值为0.3846。对于空间三十六单元张拉整体结构中,可获取5个压杆数量一致的拓扑形态,且可通过调整性能评价指标中不同设计参数的权重比例寻找到满足工程特定需求的可行形态。
To study the topological morphology of tensegrity structures with specified node coordinates,a topology shape finding method is proposed to form the scheme matrix by directly coding the connectivity matrix.Based on the morphology analysis of tensegrity structures,the number of components that connected to node is taken as the constraint index.The placement of element can be determined by reasonably selecting certain elements in the scheme matrix.The topology finding of tensegrities is completely realized by combining the stability judgement condition with the relationship established from the variables(0,-1)and the structural geometric stability.Several tensegrity structures with high symmetry of topological morphology are found in two spatial tensegrity structure examples using the symmetric index,demonstrating the feasibility and validity of the proposed algorithm in searching the topological morphology of tensegrities with specified nodes.For the case of a spatial tensegrity structure comprising of 26 elements,17 topological morphologies with different number of struts are found,and the critical value of force density symmetric index is determined as 0.3846.For the space tensegrity structure with 36 components,5 topological configurations with same number of struts are obtained.It is worth noting that the feasible configurations meeting the specific requirements of practical projects can be achived by adjusting the weight ratio of different design parameters in the performance-evaluation index.
作者
冯晓东
章万鹏
罗尧治
撒剑波
陈灿
Feng Xiaodong;Zhang Wanpeng;Luo Yaozhi;Sa Jianbo;Chen Can(Shaoxing University,Shaoxing 312000,China;Zhejiang University,Hangzhou 310000,China)
出处
《土木工程学报》
EI
CSCD
北大核心
2021年第8期75-86,共12页
China Civil Engineering Journal
基金
国家自然科学基金(51908356)
中国博士后科学基金(2019M662056)
浙江省自然科学基金(LQ19E080013)。
关键词
张拉整体结构
拓扑变量
方案矩阵
对称性指标
tensegrity structures
topological variables
scheme matrix
symmetric index
