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Automated form‐finding method of spoke cable net structures using physics‐constrained neural network.

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Title: Automated form‐finding method of spoke cable net structures using physics‐constrained neural network.
Authors: Li, Xuanzhi1 (AUTHOR), Liu, Yue2 (AUTHOR) yueliu@ustb.edu.cn, Xue, Suduo3 (AUTHOR), Tafsirojjaman, Tafsirojjaman4 (AUTHOR)
Source: Computer-Aided Civil & Infrastructure Engineering. 11/28/2025, Vol. 40 Issue 28, p5093-5113. 21p.
Subjects: Cable structures, Deep learning, Tensile architecture, Structural optimization, Strains & stresses (Mechanics), Optimization algorithms
Abstract: The spoke cable‐net structure is a typical flexible tensile structure that relies solely on cables as load‐bearing components. Its unique topological characteristics, composed of ring cables and radial cables, determine that the main challenge in its form‐finding lies in controlling the spatial configuration of the inner ring. Existing computational methods primarily rely on numerical iteration based on empirical trial and error, which makes it difficult to effectively address the multi‐variable coupling problem between the prestress distribution and the geometric configuration of the ring cables. Accordingly, this paper aims to establish a deep learning‐based autonomous form‐finding framework driven by geometric constraints and physical equations to achieve the simultaneous intelligent solution of prestress distribution and spatial configuration. The effectiveness and versatility of the proposed method are validated through case studies with various regular and irregular geometric forms. To enhance the precision of form‐finding for structures with intricate geometries, a dual‐optimizer strategy integrating the adaptive moment estimation and limited‐memory Broyden Fletcher Goldfarb Shanno algorithms is implemented. For a spoke cable‐net structure spanning 100 m, the intelligent form‐finding accuracy can be maintained within 1 cm, ensuring a satisfactory form‐finding outcome. The proposed deep neural network (DNN) method automatically correlates cable force distribution with geometric configuration, offering a novel computational approach and solution pathway for the automated shape determination and configuration design of flexible cable structures. [ABSTRACT FROM AUTHOR]
Copyright of Computer-Aided Civil & Infrastructure Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Automated form‐finding method of spoke cable net structures using physics‐constrained neural network.
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  Data: <searchLink fieldCode="JN" term="%22Computer-Aided+Civil+%26+Infrastructure+Engineering%22">Computer-Aided Civil & Infrastructure Engineering</searchLink>. 11/28/2025, Vol. 40 Issue 28, p5093-5113. 21p.
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  Data: <searchLink fieldCode="DE" term="%22Cable+structures%22">Cable structures</searchLink><br /><searchLink fieldCode="DE" term="%22Deep+learning%22">Deep learning</searchLink><br /><searchLink fieldCode="DE" term="%22Tensile+architecture%22">Tensile architecture</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+optimization%22">Structural optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Strains+%26+stresses+%28Mechanics%29%22">Strains & stresses (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The spoke cable‐net structure is a typical flexible tensile structure that relies solely on cables as load‐bearing components. Its unique topological characteristics, composed of ring cables and radial cables, determine that the main challenge in its form‐finding lies in controlling the spatial configuration of the inner ring. Existing computational methods primarily rely on numerical iteration based on empirical trial and error, which makes it difficult to effectively address the multi‐variable coupling problem between the prestress distribution and the geometric configuration of the ring cables. Accordingly, this paper aims to establish a deep learning‐based autonomous form‐finding framework driven by geometric constraints and physical equations to achieve the simultaneous intelligent solution of prestress distribution and spatial configuration. The effectiveness and versatility of the proposed method are validated through case studies with various regular and irregular geometric forms. To enhance the precision of form‐finding for structures with intricate geometries, a dual‐optimizer strategy integrating the adaptive moment estimation and limited‐memory Broyden Fletcher Goldfarb Shanno algorithms is implemented. For a spoke cable‐net structure spanning 100 m, the intelligent form‐finding accuracy can be maintained within 1 cm, ensuring a satisfactory form‐finding outcome. The proposed deep neural network (DNN) method automatically correlates cable force distribution with geometric configuration, offering a novel computational approach and solution pathway for the automated shape determination and configuration design of flexible cable structures. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computer-Aided Civil & Infrastructure Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1111/mice.13491
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        Text: English
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      – SubjectFull: Tensile architecture
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      – SubjectFull: Structural optimization
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      – SubjectFull: Strains & stresses (Mechanics)
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              Text: 11/28/2025
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              Y: 2025
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