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Wavelet Series Analysis of Axial Members with Stress Singularities  

Woo, Kwang-Sung (영남대학교 건설시스템공학과)
Jang, Young-Min (한국농어촌공사 사업기획팀)
Lee, Dong-Woo (영남대학교 건설시스템공학과)
Lee, Sang-Yun (영남대학교 건설시스템공학과)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.23, no.1, 2010 , pp. 1-8 More about this Journal
Abstract
The Fourier series uses a vibrating wave that possesses an amplitude that is like the one of the sine curve. Therefore, the functions used in the Fourier series do not change due to the value of the frequency and that set a limit to express irregular signals with rapid oscillations or with discontinuities in localized regions. However, the wavelet series analysis(WSA) method supplements these limits of the Fourier series by a linear combination of a suitable number of wavelets. By using the wavelet that is focused on time, it is able to give changes to the range in the cycle. Also, this enables to express a signal more efficiently that has singular configuration and that is flowing. The main objective of this study is to propose a scheme called wavelet series analysis for the application of wavelet theory to one-dimensional problems represented by the second-order elliptic equation and to evaluate theperformance of proposed scheme comparing with the finite element analysis. After a through evaluation of different types of wavelets, the HAT wavelet system is chosen as a wavelet function as well as a scaling function. It can be stated that the WSA method is as efficient as the FEA method in the case of axial bars with distributed loads, but the WSA method is more accurate than the FEA method at the singular points and its computation time is less.
Keywords
wavelet series analysis; wavelet function; scaling function; singular point;
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  • Reference
1 Reddy, J.N. (1993) An Introduction to the Finite Element Method, McGraw-Hill.
2 Sidney Burrus, C., Ramesh A. Gopinath, Haitao Guo (1998) Introduction to Wavelets and Wavelet Transforms, Prentice Hall.
3 Xiang, J.W., Chen, X.F., He, Z.J., Dong, H.B. (2007) The construction of 1D Wavelet Finite Elements for Structural Analysis, Comput. Mech., 40, pp.325-339.   DOI   ScienceOn
4 Basu, P.K., Jorge, A.B., Bardi, S., Lin, J. (2003) Higher-Order Modeling of Continua by Finite- Element, Boundary-Element, Meshless, and Wavelet Methods, Comput. Math., 46, pp.15-33.
5 이승훈, 윤동한 (2000) 알기 쉬운 웨이블렛 변환, 진한도서.
6 강현배, 김대경, 서진근 (2001) Wavelet Theory and its Applications, 아카넷.
7 김충락, 송현종, 장대홍, 홍창곤 (1998) 웨이블렛의 기본 이론과 통계에의 응용, 아르케.