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A rotation free formulation for static and free vibration analysis of thin beams using gradient smoothing technique

X.Y. Cui1,2, G. R. Liu2,3, G. Y. Li1,4, G. Zheng1

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, PR China
Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117576 Singapore
Singapore-MIT Alliance (SMA), E4-04-10, 4 Engineering Drive 3, 117576, Singapore
Corresponding author. Tel: 86-731-8821717; Fax: 86-731-8822051; Email: gyli@hnu.cn

Computer Modeling in Engineering & Sciences 2008, 38(3), 217-230. https://doi.org/10.3970/cmes.2008.038.217

Abstract

In this paper, a gradient smoothed formulation is proposed to deal with a fourth-order differential equation of Bernoulli-Euler beam problems for static and dynamic analysis. Through the smoothing operation, the C1 continuity requirement for fourth-order boundary value and initial value problems can be easily relaxed, and C0 interpolating function can be employed to solve C1 problems. In present thin beam problems, linear shape functions are employed to approximate the displacement field, and smoothing domains are further formed for computing the smoothed curvature and bending moment field. Numerical examples indicate that very accurate results can be yielded when a reasonable number of nodes are used.

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Cite This Article

Cui, X., Liu, G. R., Li, G. Y., Zheng, G. (2008). A rotation free formulation for static and free vibration analysis of thin beams using gradient smoothing technique. CMES-Computer Modeling in Engineering & Sciences, 38(3), 217–230.



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