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Structural Engineering and Mechanics Volume 59, Number 3, August10 2016 , pages 503-526 DOI: https://doi.org/10.12989/sem.2016.59.3.503 |
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Isogeometric method based in-plane and out-of-plane free vibration analysis for Timoshenko curved beams |
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Hongliang Liu, Xuefeng Zhu and Dixiong Yang
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| Abstract | ||
| 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 Cp–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 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. | ||
| Key Words | ||
| Timoshenko curved beams; in-plane and out-of-plane free vibration; isogeometric analysis; NURBS elements; numerical locking | ||
| Address | ||
| Hongliang Liu and Dixiong Yang: Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology, Dalian 116023, China Xuefeng Zhu: School of Automobile Engineering, Dalian University of Technology, Dalian 116023, China | ||