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ARTICLE

B-Spline Wavelet on Interval Finite Element Method for Static and Vibration Analysis of Stiffened Flexible Thin Plate

Xing Wei^1,2, Wen Chen², Bin Chen^2,3, Bin Chen^1,4, Bin Chen², Bin Chen¹

1 State Key Laboratory for Manufacturing System Engineering, School of Mechanical Engineering,Xi’ an Jiaotong University, Xi’ an 710049, PR China
2 Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleve-land Ohio 44106, USA
3 School of Instrument Science and Engineering, Southeast University, Nanjing 210096, PR China
4 Corresponding author. Tel: +86 29 82667963; fax: +86 29 82663689.E-mail address: chenxf@mail.xjtu.edu.cn (X.F. Chen)

Computers, Materials & Continua 2016, 52(1), 53-71. https://doi.org/10.3970/cmc.2016.052.053

Abstract

A new wavelet finite element method (WFEM) is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed. By means of generalized potential energy function and virtual work principle, the formulations of the bending and free vibration problems of the stiffened plate are derived separately. Then, the scaling functions of the B-spline wavelet on the interval (BSWI) are introduced to discrete the solving field variables instead of conventional polynomial interpolation. Finally, the corresponding two problems can be resolved following the traditional finite element frame. There are some advantages of the constructed elements in structural analysis. Due to the excellent features of the wavelet, such as multi-scale and localization characteristics, and the excellent numerical approximation property of the BSWI, the precise and efficient analysis can be achieved. Besides, transformation matrix is used to translate the meaningless wavelet coefficients into physical space, thus the resolving process is simplified. In order to verify the superiority of the constructed method in stiffened plate analysis, several numerical examples are given in the end.

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