西安建筑科技大学学报(自然科学版)

本文提出了一种求解张拉整体结构初始形态的可行预应力找形的新方法.根据已知结构的单元类型和几何拓扑关系,分别采用谱分解和奇异值分解的方法将结构体系的平衡矩阵和力密度矩阵分解,在此基础上进行循环迭代直至满足对应矩阵最小秩缺失的必要条件,以此寻找合适的节点坐标和力密度.基于空间六杆张拉整体结构算例结果,利用棉绞线和PVC管模拟拉压单元成功制作模型进行了结果验证.本文的算例分析和模型结果证实了该空间六杆张拉整体结构体系的合理性,为新型复杂张拉整体结构的构型研究提供了一条新的途径.

A novel form-fining for solving the initial configuration of tensegrity structures is presented.According to the given elemental type and topological relationship of the structure, the structural equilibrium matrix and the force density matrix are decomposed by spectral decomposition and singular value decomposition respectively.In order to find the appropriate node coordinates and force density, the iteration was terminated until the corresponding matrix satisfies the necessary rank deficiency condition.Based on the numerical results of the spatial six-bar tensegrity structure, a simulate model is successfully fabricated by using cotton strands and PVC pipes.The results obtained in this paper confirm the rationality of the space six-bar tensegrity structure theorically and practically, which also provide a new path for investigating configurations of more complicated tensegrity structure.

引言
1 力密度找形法及相应的秩亏条件
2 基于矩阵分析的找形步骤
3 算例
4 张拉整体结构模型制作
5 结论

图1 自由形态张拉整体结构找形流程图<br/>Fig.1 Process of the proposed form-finding procedure for free-form tensegrity structures

图1 自由形态张拉整体结构找形流程图
Fig.1 Process of the proposed form-finding procedure for free-form tensegrity structures

图2 6杆24索张拉整体结构拓扑连接图<br/>Fig.2 Topological connection of tensegrity structure with 6 struts and 24 cables

图2 6杆24索张拉整体结构拓扑连接图
Fig.2 Topological connection of tensegrity structure with 6 struts and 24 cables

图3 无指定节点坐标下得到的6杆24索张拉整体结构的几何形态<br/>Fig.3 The obtained geometric configuration of tensegrity structure(6 struts and 24 cables)without specified node coordinates

图3 无指定节点坐标下得到的6杆24索张拉整体结构的几何形态
Fig.3 The obtained geometric configuration of tensegrity structure(6 struts and 24 cables)without specified node coordinates

图4 找形得到的6杆24索张拉整体结构(状态1)<br/>Fig.4 The obtained tensegrity structure with 6 struts and 24 cables(configuration 1)

图4 找形得到的6杆24索张拉整体结构(状态1)
Fig.4 The obtained tensegrity structure with 6 struts and 24 cables(configuration 1)

表1 图 4所示结构的各节点坐标<br/>Tab.1 The nodal coordinates of the structure displayed in Fig. 4

表1 图 4所示结构的各节点坐标
Tab.1 The nodal coordinates of the structure displayed in Fig. 4

表2 图 4所示结构各构件的自应力<br/>Tab.2 The self-stresses of all components ofthe structure displayed in Fig. 4

表2 图 4所示结构各构件的自应力
Tab.2 The self-stresses of all components ofthe structure displayed in Fig. 4

图5 找形得到的6杆24索张拉整体结构(状态2)<br/>Fig.5 The obtained tensegrity structure with 6 struts and 24 cables(configuration 2)

图5 找形得到的6杆24索张拉整体结构(状态2)
Fig.5 The obtained tensegrity structure with 6 struts and 24 cables(configuration 2)

表3 图 5所示结构的各节点坐标<br/>Tab.3 The nodal coordinates ofthe structure displayed in Fig. 5

表3 图 5所示结构的各节点坐标
Tab.3 The nodal coordinates ofthe structure displayed in Fig. 5

表4 图 5所示结构各构件的自应力<br/>Tab.4 The self-stresses of all components ofthe structure displayed in Fig. 5

表4 图 5所示结构各构件的自应力
Tab.4 The self-stresses of all components ofthe structure displayed in Fig. 5

图6 安装杆件的前期准备<br/>Fig.6 Preparation for installation of members

图6 安装杆件的前期准备
Fig.6 Preparation for installation of members

图7 张拉成型后的六杆张拉整体结构<br/>Fig.7 The formed configuration of tensegrity structure with 6 struts

图7 张拉成型后的六杆张拉整体结构
Fig.7 The formed configuration of tensegrity structure with 6 struts

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备注

引言

1 力密度找形法及相应的秩亏条件

2 基于矩阵分析的找形步骤

3 算例

4 张拉整体结构模型制作

5 结论

期刊信息