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The Wavelet Series Analysis for the Fourth-order Elliptic Differential Equation  

Jo, Jun-Hyung (한국전력공사 전력연구원 녹색성장연구소)
Woo, Kwang-Sung (영남대학교 건설시스템공학과)
Sin, Young-Sik (영남대학교 건설시스템공학과)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.24, no.4, 2011 , pp. 355-364 More about this Journal
Abstract
In this study, the details of WSA(wavelet series analysis) have been demonstrated to solve the 4th-order elliptic differential equation. It is clear to solve the 2nd-order elliptic differential equation with the basis function of Hat wavelet series that is used in the previous study existed in $H^1$-space. However, it is difficult to solve the 4th order differential equation with same basis function of Hat wavelet series because of insufficient differentiability and integrability. To overcome this problem, the linear equations in terms of moment and deflection have been formulated and solved sequentially that are similar to extension of Elastic Load Method and Moment Area Method in some senses. Also, the differences and common points between the proposed method and the meshless method are discussed in the procedure of WSA formulation. As we expect, it is easy to ascertain that the more terms of Hat wavelet series are used, the better numerical solutions are improved. Also the solutions obtained by WSA have been compared with the conventional FEM solutions in case of Euler beam problems with stress singularity.
Keywords
Wavelet Series Analysis; Hat Wavelet Function; $H^1$-space; Elastic Load Method; Moment Area Method; 4th-order Elliptic Differential Equation;
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Times Cited By KSCI : 2  (Citation Analysis)
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