—The use of wavelets has become increasingly
popular in the development of numerical schemes for the
solution of partial differential equations (PDEs), especially for
problems with local high gradient. In this work, the Galerkin
Method has been adapted for the direct solution of differential
equations in a meshless formulation using Daubechies wavelets
and Deslauriers-Dubuc interpolating functions (Interpolets).
This approach takes advantage of wavelet properties like
compact support, orthogonality and exact polynomial
representation, which allow the use of a multiresolution analysis.
Several examples based on typical differential equations for
beams and thin plates were studied successfully.
—Wavelets, interpolets, wavelet-galerkin
method, beam on elastic foundation, thin plates.
R. B. Burgos is with the State University of Rio de Janeiro (UERJ),
Department of Structures and Foundations, RJ, Brazil (e-mail:
M. A. Cetale Santos is with Fluminense Federal University (UFF), ISIS
Group, Department of Geology and Geophysics, RJ, Brazil (e-mail:
R. R. Silva is with Pontifical Catholic University of Rio de Janeiro,
Department of Civil Engineering, RJ, Brazil (e-mail: firstname.lastname@example.org).
Cite: Rodrigo Bird Burgos, Marco Antonio Cetale Santos, and Raul Rosas e Silva, "Analysis of Beams and Thin Plates Using the
Wavelet-Galerkin Method," International Journal of Engineering and Technology vol. 7, no. 4, pp. 261-266, 2015.