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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. L. Motard, and B. Joseph.Wavelet Applications in Chemical Engineering, Kluwer Academic Publishers, Boston (1994).
J. R. Williams and K. Amaratunga, Introduction to vavelets in engineering,Internat. J. Numer. Methods Engrg.,37, 14 (1994), 2365–2388.
I. Daubechies. Orthonormal bases of compactly supported wavelets,Comm. Pure Appl. Math.,41, 7 (1988), 909–996.
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.
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.
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)
Author information
Authors and Affiliations
Additional information
Communicated by Yeh Kaiyuan
Project supported by the National Natural Science Foundation of China and Science Foundation of the National Education Committee of China for the Scholars Returned from Abroad and for the Exellent Young Teachers in Universities
Rights and permissions
About this article
Cite this article
Youhe, Z., Jizeng, W. & Xiaojing, Z. Applications of wavelet galerkin fem to bending of beam and plate structures. Appl Math Mech 19, 745–755 (1998). https://doi.org/10.1007/BF02457749
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02457749