Applied Mathematics and Mechanics

, Volume 19, Issue 8, pp 745–755

# Applications of wavelet galerkin fem to bending of beam and plate structures

• Zhou Youhe
• Wang Jizeng
• Zheng Xiaojing
Article

## Abstract

In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-value problems with order higher than 2. After that, it is realized that the wavalet Galerkin FEM is used to solve mechanical problems such as bending of beams and plates. The numerical results show that this method has good precision.

### Key words

applications of wavelet theory scaling functions operation of high-order derivations Galerkin FEM bending of beams and plates

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### References

1. [1]
R. L. Motard, and B. Joseph.Wavelet Applications in Chemical Engineering, Kluwer Academic Publishers, Boston (1994).Google Scholar
2. [2]
J. R. Williams and K. Amaratunga, Introduction to vavelets in engineering,Internat. J. Numer. Methods Engrg.,37, 14 (1994), 2365–2388.
3. [3]
I. Daubechies. Orthonormal bases of compactly supported wavelets,Comm. Pure Appl. Math.,41, 7 (1988), 909–996.
4. [4]
K. Amaratunga and J. William, Wavelet-Galerkin solution for one-dimensional partial differential equations,Internal. J. Numer. Methods in Engrg.,37, 16 (1994), 2703–2716.
5. [5]
J. Ko, A. J. Kurdila and M. Pilant, A class of wavelet-based finite element methods for computational mechanics.Proc. 35th Structures, Structural Dynamics and Materials Conference, Hilton Head, South Carolina, May (1994), 665–675.Google Scholar
6. [6]
Y. H. Zhou and J. Z. Wang. Generalinzed Gaussian method and its application in solving nonlinear boundary-value problems of ordinary differential equations.Proc. 7th National Modern Math. Mech. of China, Shanghai, Nov. (1997) 464–467 (in Chinese)Google Scholar

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## Authors and Affiliations

• Zhou Youhe
• 1
• Wang Jizeng
• 1
• Zheng Xiaojing
• 1
1. 1.Department of MechanicsLanzhou UniversityLanzhouP. R. China