Applications of wavelet Galerkin FEM to bending of beam and plate structures. (English) Zbl 0919.73305

Summary: We propose an approach for calculations of higher order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of boundary value problems of order higher than 2. After this we use the wavelet Galerkin FEM to solve mechanical problems such as bending of beams and plates. The numerical results show that the method has a good accuracy.


74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K20 Plates
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[1] R. L. Motard, and B. Joseph.Wavelet Applications in Chemical Engineering, Kluwer Academic Publishers, Boston (1994).
[2] J. R. Williams and K. Amaratunga, Introduction to vavelets in engineering,Internat. J. Numer. Methods Engrg.,37, 14 (1994), 2365–2388. · Zbl 0812.65144 · doi:10.1002/nme.1620371403
[3] I. Daubechies. Orthonormal bases of compactly supported wavelets,Comm. Pure Appl. Math.,41, 7 (1988), 909–996. · Zbl 0644.42026 · doi:10.1002/cpa.3160410705
[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. · Zbl 0813.65106 · doi:10.1002/nme.1620371602
[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.
[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)
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