Validity of using noncommutative finite-rotation deformation measures in the large-displacement analysis: a simple counter example.
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| Title: | Validity of using noncommutative finite-rotation deformation measures in the large-displacement analysis: a simple counter example. |
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| 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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 01787675 |
| DOI: | 10.1007/s00466-025-02626-0 |
