Structural Engineering and Mechanics

  • 제59권3호
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  • Pages.503-526
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  • 2016
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Isogeometric method based in-plane and out-of-plane free vibration analysis for Timoshenko curved beams

  • Liu, Hongliang (Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology) ;
  • Zhu, Xuefeng (School of Automobile Engineering, Dalian University of Technology) ;
  • Yang, Dixiong (Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology)
  • 투고 : 2015.07.15
  • 심사 : 2016.05.05
  • 발행 : 2016.08.10
⟨ 이전 논문 다음 논문 ⟩

초록

In-plane and out-of-plane free vibration analysis of Timoshenko curved beams is addressed based on the isogeometric method, and an effective scheme to avoid numerical locking in both of the two patterns is proposed in this paper. The isogeometric computational model takes into account the effects of shear deformation, rotary inertia and axis extensibility of curved beams, and is applicable for uniform circular beams, and more complicated variable curvature and cross-section beams as illustrated by numerical examples. Meanwhile, it is shown that, the $C^{p-1}$-continuous NURBS elements remarkably have higher accuracy than the finite elements with the same number of degrees of freedom. Nevertheless, for in-plane or out-of-plane vibration analysis of Timoshenko curved beams, the NURBS-based isogeometric method also exhibits locking effect to some extent. To eliminate numerical locking, the selective reduced one-point integration and $\bar{B}$ projection element based on stiffness ratio is devised to achieve locking free analysis for in-plane and out-of-plane models, respectively. The suggested integral schemes for moderately slender models obtain accurate results in both dominated and non-dominated regions of locking effect. Moreover, this strategy is effective for beam structures with different slenderness. Finally, the influence factors of structural parameters of curved beams on their natural frequency are scrutinized.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

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  13. Finite element model of circularly curved Timoshenko beam for in-plane vibration analysis vol.49, pp.3, 2016, https://doi.org/10.5937/fme2103615n
  14. Isogeometric Free Vibration Analysis of Curved Euler-Bernoulli Beams with Particular Emphasis on Accuracy Study vol.21, pp.1, 2021, https://doi.org/10.1142/s0219455421500115