Open Access

ARTICLE

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

X.Y. Cui^1,2, G. R. Liu^2,3, G. Y. Li^1,4, G. Zheng¹

1 State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, PR China
2 Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117576 Singapore
3 Singapore-MIT Alliance (SMA), E4-04-10, 4 Engineering Drive 3, 117576, Singapore
4 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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Keywords

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