View in EDS HTML Full Text PDF Full Text

Validity of using noncommutative finite-rotation deformation measures in the large-displacement analysis: a simple counter example.

Saved in:
Bibliographic Details
Title: Validity of using noncommutative finite-rotation deformation measures in the large-displacement analysis: a simple counter example.
Authors: Shabana, Ahmed A.1 (AUTHOR) shabana@uic.edu
Source: Computational Mechanics. Sep2025, Vol. 76 Issue 3, p789-796. 8p.
Subjects: Deformations (Mechanics), Euler angles, Algorithms, Finite element method, Rotational motion, Engineering systems
Abstract: Rotations are used in the deformations analysis of mechanical-system components such as beams, plates, and shells. Nonetheless, concerns have been raised regarding the use of finite rotations in mechanics, particularly as nodal coordinates in the finite-element discretization. This technical note demonstrates that using noncommutative finite rotations can lead to misinterpretation of commutative deformation modes. To this end, two sequences of Euler-angle rotations are used to demonstrate that a configuration that can be attained by one sequence of two rotations is not attainable by another sequence that consists of the same angles of the first sequence with a reversed order. To obtain the same configuration using the second sequence, a third non-zero angle must be added at the expense of introducing a new deformation mode not considered by the first sequence. The analysis presented demonstrates that the noncommutative finite rotations do not preserve the physical interpretation of commutative deformation modes. The analysis and discussion in this paper are relevant to computational algorithms that are based on non-incremental-rotation solution procedures. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mechanics is the property of Springer Nature 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.)
Database: Engineering Source
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
Text:
  Availability: 1
Header DbId: egs
DbLabel: Engineering Source
An: 188150926
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Validity of using noncommutative finite-rotation deformation measures in the large-displacement analysis: a simple counter example.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Shabana%2C+Ahmed+A%2E%22">Shabana, Ahmed A.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> shabana@uic.edu</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Computational+Mechanics%22">Computational Mechanics</searchLink>. Sep2025, Vol. 76 Issue 3, p789-796. 8p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Deformations+%28Mechanics%29%22">Deformations (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Euler+angles%22">Euler angles</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Rotational+motion%22">Rotational motion</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering+systems%22">Engineering systems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Rotations are used in the deformations analysis of mechanical-system components such as beams, plates, and shells. Nonetheless, concerns have been raised regarding the use of finite rotations in mechanics, particularly as nodal coordinates in the finite-element discretization. This technical note demonstrates that using noncommutative finite rotations can lead to misinterpretation of commutative deformation modes. To this end, two sequences of Euler-angle rotations are used to demonstrate that a configuration that can be attained by one sequence of two rotations is not attainable by another sequence that consists of the same angles of the first sequence with a reversed order. To obtain the same configuration using the second sequence, a third non-zero angle must be added at the expense of introducing a new deformation mode not considered by the first sequence. The analysis presented demonstrates that the noncommutative finite rotations do not preserve the physical interpretation of commutative deformation modes. The analysis and discussion in this paper are relevant to computational algorithms that are based on non-incremental-rotation solution procedures. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computational Mechanics is the property of Springer Nature 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.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=188150926
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s00466-025-02626-0
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 8
        StartPage: 789
    Subjects:
      – SubjectFull: Deformations (Mechanics)
        Type: general
      – SubjectFull: Euler angles
        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Rotational motion
        Type: general
      – SubjectFull: Engineering systems
        Type: general
    Titles:
      – TitleFull: Validity of using noncommutative finite-rotation deformation measures in the large-displacement analysis: a simple counter example.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Shabana, Ahmed A.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 09
              Text: Sep2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 01787675
          Numbering:
            – Type: volume
              Value: 76
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: Computational Mechanics
              Type: main
ResultId 1