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Calculation of Euler angle of matrix displacement method for space reticulated shell.

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Title: Calculation of Euler angle of matrix displacement method for space reticulated shell.
Authors: Xia, Yong-Qiang1,2 (AUTHOR), Xu, Chao1,3 (AUTHOR), Hui, Xu1 (AUTHOR), Ni, Ke-yi4 (AUTHOR), Xiao, Nan5 (AUTHOR), Zou, Bao-Ping1 (AUTHOR) zoubp@zust.edu.cn
Source: International Journal of Space Structures. Dec2025, Vol. 40 Issue 4, p199-207. 9p.
Subjects: Euler angles, Structural shells, Mathematical optimization, Structural design, Cylindrical shells, Displacement (Mechanics), Finite element method, Euler, Leonhard, 1707-1783, Spherical shells (Engineering)
Abstract: In order to accurately describe the position of the main inertia axis of the rod in the finite element analysis, and determine the direction of the bolt when machining the spatial rigid frame rod, the Euler angle calculation method of the spatial rigid frame displacement method of the reticulated shell rod is established, and the Euler angle calculation formulas of the cylindrical reticulated shell and the spherical reticulated shell are derived. Unlike conventional approaches in commercial software (e.g., 3DCAD and BIM) that require labor-intensive extraction processes, our method provides precise analytical solutions that significantly improve computational efficiency for large complex structures. The formula shows that the Euler angles of cylindrical reticulated shell members is related to the azimuths and longitudinal distances between the two ends, and the Euler angles of spherical reticulated shell members is related to the difference between the azimuth angle of the two ends of the member and the inclination angle of the two ends. The Euler angle is calculated by the proposed formula, and the finite element models of cylindrical reticulated shell, spherical reticulated shell and hyperbolic paraboloid reticulated shell are established respectively. It can be found that the proposed formula makes the reticulated shell members and the curved surface fit well, and the position of section of spatial beam element can be conveniently determined. This analytical approach overcomes the limitations of existing software solutions by providing direct, accurate Euler angle determination without iterative calculations, particularly beneficial for complex structural designs. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Space Structures is the property of Sage Publications Inc. 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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  Label: Title
  Group: Ti
  Data: Calculation of Euler angle of matrix displacement method for space reticulated shell.
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  Data: <searchLink fieldCode="AR" term="%22Xia%2C+Yong-Qiang%22">Xia, Yong-Qiang</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xu%2C+Chao%22">Xu, Chao</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hui%2C+Xu%22">Hui, Xu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ni%2C+Ke-yi%22">Ni, Ke-yi</searchLink><relatesTo>4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xiao%2C+Nan%22">Xiao, Nan</searchLink><relatesTo>5</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zou%2C+Bao-Ping%22">Zou, Bao-Ping</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zoubp@zust.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Space+Structures%22">International Journal of Space Structures</searchLink>. Dec2025, Vol. 40 Issue 4, p199-207. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Euler+angles%22">Euler angles</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+shells%22">Structural shells</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+design%22">Structural design</searchLink><br /><searchLink fieldCode="DE" term="%22Cylindrical+shells%22">Cylindrical shells</searchLink><br /><searchLink fieldCode="DE" term="%22Displacement+%28Mechanics%29%22">Displacement (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Euler%2C+Leonhard%2C+1707-1783%22">Euler, Leonhard, 1707-1783</searchLink><br /><searchLink fieldCode="DE" term="%22Spherical+shells+%28Engineering%29%22">Spherical shells (Engineering)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In order to accurately describe the position of the main inertia axis of the rod in the finite element analysis, and determine the direction of the bolt when machining the spatial rigid frame rod, the Euler angle calculation method of the spatial rigid frame displacement method of the reticulated shell rod is established, and the Euler angle calculation formulas of the cylindrical reticulated shell and the spherical reticulated shell are derived. Unlike conventional approaches in commercial software (e.g., 3DCAD and BIM) that require labor-intensive extraction processes, our method provides precise analytical solutions that significantly improve computational efficiency for large complex structures. The formula shows that the Euler angles of cylindrical reticulated shell members is related to the azimuths and longitudinal distances between the two ends, and the Euler angles of spherical reticulated shell members is related to the difference between the azimuth angle of the two ends of the member and the inclination angle of the two ends. The Euler angle is calculated by the proposed formula, and the finite element models of cylindrical reticulated shell, spherical reticulated shell and hyperbolic paraboloid reticulated shell are established respectively. It can be found that the proposed formula makes the reticulated shell members and the curved surface fit well, and the position of section of spatial beam element can be conveniently determined. This analytical approach overcomes the limitations of existing software solutions by providing direct, accurate Euler angle determination without iterative calculations, particularly beneficial for complex structural designs. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Space Structures is the property of Sage Publications Inc. 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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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1177/09560599251358722
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 9
        StartPage: 199
    Subjects:
      – SubjectFull: Euler angles
        Type: general
      – SubjectFull: Structural shells
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Structural design
        Type: general
      – SubjectFull: Cylindrical shells
        Type: general
      – SubjectFull: Displacement (Mechanics)
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Euler, Leonhard, 1707-1783
        Type: general
      – SubjectFull: Spherical shells (Engineering)
        Type: general
    Titles:
      – TitleFull: Calculation of Euler angle of matrix displacement method for space reticulated shell.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Xia, Yong-Qiang
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            NameFull: Xu, Chao
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            NameFull: Hui, Xu
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            NameFull: Ni, Ke-yi
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            NameFull: Xiao, Nan
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            – D: 01
              M: 12
              Text: Dec2025
              Type: published
              Y: 2025
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              Value: 09560599
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              Value: 40
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              Value: 4
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            – TitleFull: International Journal of Space Structures
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