DOI QR코드

DOI QR Code

Adaptive Wavelet-Galerkin Method for Structural Ananlysis

구조해석을 위한 적응 웨이블렛-캘러킨 기법

  • Published : 2000.08.01

Abstract

The object of the present study is to present an adaptive wavelet-Galerkin method for the analysis of thin-walled box beam. Due to good localization properties of wavelets, wavelet methods emerge as alternative efficient solution methods to finite element methods. Most structural applications of wavelets thus far are limited in fixed-scale, non-adaptive frameworks, but this is not an appropriate use of wavelets. On the other hand, the present work appears the first attempt of an adaptive wavelet-based Galerkin method in structural problems. To handle boundary conditions, a fictitous domain method with penalty terms is employed. The limitation of the fictitious domain method is also addressed.

Keywords

Wavelet-Galerkin;Adaptive Analysis;Multi-Resolution;Thin-Walled Box Beain

References

  1. Kim, J. H. and Kim, Y. Y., 1999, 'Analysis of Thin-Walled Closed Beams with General Quadrilateral Cross Sections,' ASME Journal of Applied Mechanics, Vol. 66, pp. 904-912
  2. 김윤영, 김진홍, 송상헌, 1998, '비틀림을 받는 직사각 폐단면 박판보 유한요소 개발,' 대한기계학회논문집 A권 제22권 제6호, pp. 947-954
  3. Latto, A., Resnikoff, H. K. and Tenenbaum, E., 1991, 'The Evaluation of Connection Coefficients of Compactly Supported Wavelets,' In Proce edings of the USA-French Workshop on Wavelets and Turbulance, Princeton University
  4. Vasilyev, O. V., Yuen, D. A. and Paolucci, S., 1997, 'Solving PDEs Using Wavcelets,' Computers in Physics, Vol. 11, No. 5
  5. DeRuse, G. Jr, 1998, 'Solving Topology Optimization Problems Using Wavelet-Galerkin Techniques,' PhD thesis, Michigan State University
  6. Diaz, A. R., 1999, 'A Wavelet-Galerkin Scheme for Analysis of Large-Scale Problems on Simple Domains,' Int. J. Numer. Meth. Engng. Vol. 44, pp. 1599-1616 https://doi.org/10.1002/(SICI)1097-0207(19990420)44:11<1599::AID-NME556>3.0.CO;2-P
  7. Cohen, A., Dahmen, W. and DeVore, R., 1998, 'Adaptive Wavelet Methods for Elliptic Operator Equations - Convergence Rates,' RWTH Aachen, 1GPM Preprint No. 165
  8. Wells, R. O. Jr and Zhou, X., 1993, 'Wavelet Solutions for the Dirichlet Problem,' Technical Report Computational Mathematics Lab. Technical Report, Rice University
  9. Kim, Y. Y. and Kim, J. H., 1999, 'Thin-Walled Closed Box Beam Element for Static and Dynamic Analysis,' Int. J. Num. Methods Eng. Vol. 45, pp. 473-490 https://doi.org/10.1002/(SICI)1097-0207(19990610)45:4<473::AID-NME603>3.0.CO;2-B
  10. Mallat, S., 1998, A Wavelet Tour of Signal Processing, Academic Press
  11. Wells, R. O. Jr, Rieder, Glowinski, A. and Zhou, X., 1993, 'A Wavelet Multi-grid Preconditioner for Dirichlet Boundary Value Problems in General Domains,' Technical Report Computational, Mathematics Laboratory. TR93-06, Rice University
  12. Kunoth, A., 1995, 'Multilevel Preconditioning - Appending Boundary Conditions by Largrange Multipliers,' Advances in Computational Mathematics, Vol. 4, pp. 145-170 https://doi.org/10.1007/BF02123477