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A Novel Two-Step Tensegrity Topology-Finding Method Based on Mixed Integer Programming and Nonlinear Programming

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Abstract

A two-step topology-finding method based on mixed integer programming and nonlinear programming is proposed for tensegrity structures. In the first step, feasible and symmetric strut connectivities are obtained through a ground structure method combined with mixed integer programming; in the second step, the cable connectivities are optimized through nonlinear programming to obtain a feasible tensegrity structure. The same ground structure used in the first step is adopted in the second step, which is beneficial to find a more symmetric cable layout. The independent continuous mapping method is used in the second step to convert the 0–1 binary variables of cable connectivities to continuous variables to transform the combinatorial optimization problem into a nonlinear programming problem. The number of strut lengths is adopted as a control parameter and a symmetry objective function is proposed to generate a variety of regular and symmetric tensegrity structures. A multi-stage computation scheme is proposed to improve the computational efficiency. Typical examples are carried out to validate the proposed method. The computational efficiency of the method is benchmarked with existing methods fully based on mixed integer programming. Results demonstrate that the computational efficiency of the proposed method is significantly improved compared to the existing methods.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 52178175, 52108182), grant from Center for Balance Architecture of Zhejiang University, China Postdoctoral Science Foundation (Grant No. 2021M702867), and funding for postdoctoral research projects of Zhejiang Province (Grant No. ZJ2021009).

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Authors and Affiliations

  1. Space Structure Research Center, College of Civil Engineering and Architecture, Zhejiang University, 866 Yuhangtang Road, Hangzhou, Zhejiang, 310058, China

    Xian Xu, Shaoxiong Huang, Tingting Shu, Yafeng Wang & Yaozhi Luo

  2. Center for Balance Architecture, Zhejiang University, 148 Tianmushan Road, Hangzhou, Zhejiang, 310063, China

    Xian Xu

  3. Department of Civil and Mechanical Engineering, Technical University of Denmark, Nils Koppels Alle 404, 2800, Kongens Lyngby, Denmark

    Yafeng Wang

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  1. Xian Xu
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  2. Shaoxiong Huang
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  3. Tingting Shu
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  4. Yafeng Wang
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  5. Yaozhi Luo
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Correspondence to Yafeng Wang.

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Xu, X., Huang, S., Shu, T. et al. A Novel Two-Step Tensegrity Topology-Finding Method Based on Mixed Integer Programming and Nonlinear Programming. Int J Steel Struct 22, 1266–1282 (2022). https://doi.org/10.1007/s13296-022-00634-x

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