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Effects of Discretization Schemes on Free Vibration Analysis of Planar Beam Structures Using Isogeometric Timoshenko-Ehrenfest Beam Formulations
Several Timoshenko-Ehrenfest beam formulations have been presented in the literature for analysis of planar beam structures. In general, the displacements of the beam axis and the cross-sectional rotation are taken as kinematic unknowns. Two discretization schemes are available, namely discretization of local displacements and discretization of global displacements. In the case of linear static analysis, it has been shown that discretization of local displacements fails to accurately represent rigid transformations, whereas discretization of global displacements does not. Consequently, numerical instability is observed in analysis using discretization of local displacements. This paper investigates the effects of the two discretization schemes on free vibration analysis of planar beam structures using isogeometric Timoshenko-Ehrenfest beam formulations. Several numerical experiments on a free-form cubic beam are used for the investigation. In terms of accuracy, better performance from a formulation that employs discretization of global displacements is noticed.
Effects of Discretization Schemes on Free Vibration Analysis of Planar Beam Structures Using Isogeometric Timoshenko-Ehrenfest Beam Formulations
Several Timoshenko-Ehrenfest beam formulations have been presented in the literature for analysis of planar beam structures. In general, the displacements of the beam axis and the cross-sectional rotation are taken as kinematic unknowns. Two discretization schemes are available, namely discretization of local displacements and discretization of global displacements. In the case of linear static analysis, it has been shown that discretization of local displacements fails to accurately represent rigid transformations, whereas discretization of global displacements does not. Consequently, numerical instability is observed in analysis using discretization of local displacements. This paper investigates the effects of the two discretization schemes on free vibration analysis of planar beam structures using isogeometric Timoshenko-Ehrenfest beam formulations. Several numerical experiments on a free-form cubic beam are used for the investigation. In terms of accuracy, better performance from a formulation that employs discretization of global displacements is noticed.
Effects of Discretization Schemes on Free Vibration Analysis of Planar Beam Structures Using Isogeometric Timoshenko-Ehrenfest Beam Formulations
Lecture Notes in Civil Engineering
Geng, Guoqing (editor) / Qian, Xudong (editor) / Poh, Leong Hien (editor) / Pang, Sze Dai (editor) / Van Nguyen, Duc (author) / Vo, Duy (author) / Nanakorn, Pruettha (author)
2023-03-14
8 pages
Article/Chapter (Book)
Electronic Resource
English
Isogeometric analysis (IGA) , Free vibration analysis , Planar Timoshenko-Ehrenfest beam formulations , Discretization schemes , Convergence tests Engineering , Building Construction and Design , Structural Materials , Solid Mechanics , Sustainable Architecture/Green Buildings , Light Construction, Steel Construction, Timber Construction , Offshore Engineering
| Wiley | 2024
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