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Form-finding of tensegrity structures via rank minimization of force density matrix

机译：通过力密度矩阵的秩最小化形成矩形结构的形成

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摘要

This study proposes a general computational framework for the form-finding of tensegrity structures. The procedure is divided into two stages in which the member force densities and nodal coordinates are obtained respectively. In the first stage, the determination of force densities is transformed into a rank minimization problem regarding the force density matrix and then formulated into a semi-definite programming. The unilaterality condition of member forces and the positive semi-definiteness condition of force density matrix are incorporated as constraints. In the second stage, the determination of nodal coordinates is formulated into a constrained nonlinear programming model. The nodal positions and member lengths are assigned as constraints and auxiliary variables are introduced to homogenize the member lengths. The proposed formulation bypasses the number of self-stress states in a tensegrity structure thus applies to both tensegrity structures with single and multiple self-stress states. Different from existing studies that are based on the minimum required rank deficiency condition of force density matrix, the proposed method can handle tensegrity structures that have a force density matrix with rank deficiency greater than the required minimum number. Several examples are presented to verify the effectiveness of the proposed method on different types of tensegrity structures.
机译：本研究提出了一种用于形成矩阵结构的一般计算框架。该过程分为两个阶段，分别获得成员力密度和节点坐标。在第一阶段，将力密度的确定转变为力密度矩阵的秩最小化问题，然后配制成半定编程。成员力的单侧状况和力密度矩阵的正半明确条件纳入约束。在第二阶段，将节点坐标的确定配制成受限的非线性编程模型。节点位置和成员长度被分配为约束，引入辅助变量以使构件长度均匀化。因此，所提出的制剂以矩阵结构绕过自压力状态的数量，从而适用于具有单个和多个自重应力状态的TenseGrity结构。与现有的研究不同，基于力密度矩阵的最小所需级别缺陷条件，所提出的方法可以处理具有比所需最小数量的力量缺乏的力密度矩阵的静态结构。提出了几个例子以验证所提出的方法对不同类型的矩形结构的有效性。

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  • 来源
    《Engineering Structures》 |2021年第15期|111419.1-111419.20|共20页
  • 作者

    Wang Yafeng; Xu Xian; Luo Yaozhi;

  • 作者单位

    Zhejiang Univ Coll Civil Engn Architecture 866 Yuhangtang Rd Hangzhou 310058 Zhejiang Peoples R China|Swiss Fed Inst Technol EPFL Sch Architecture Civil & Environm Engn ENAC Appl Comp & Mech Lab IMAC CH-1015 Lausanne Switzerland;

    Zhejiang Univ Coll Civil Engn Architecture 866 Yuhangtang Rd Hangzhou 310058 Zhejiang Peoples R China;

    Zhejiang Univ Coll Civil Engn Architecture 866 Yuhangtang Rd Hangzhou 310058 Zhejiang Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Tensegrity structure; Form-finding; Force density method; Rank minimization; Semi-definite programming; Constrained nonlinear programming;

    机译：Tensegrity结构;形成;力密度法;排名最小化;半定规编程;约束非线性编程;

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