Analysis of Thin Plates Using Deslauriers-Dubuc Scaling Functions
Rodrigo Bird Burgos1; Marco Antonio Cetale Santos2; Raul Rosas e Silva3
1 UERJ; 2 UFF; 3 PUC-Rio
doi:10.20906/CPS/COB-2015-2116
Resumo
The use of multiresolution techniques and wavelets has become increasingly popular in the development of numerical schemes for the solution of partial differential equations. In this work, the widely used Galerkin Method has been adapted for the direct solution of differential equations in a meshless formulation using Deslauriers-Dubuc scaling functions, also known as Interpolets (interpolating wavelets). This approach has an advantage of obtaining interpolation coefficients instead of nodal displacements, allowing the solution representation to be in a different resolution than the system of equations. Another possible advantage is the fact that the calculation of integrals of inner products of wavelet scaling functions and their derivatives can be made by solving an eigenvalue problem, thus avoiding the issue of approximating the integral by some numerical method. These inner products are known as connection coefficients and they are employed in the calculation of stiffness matrices and load vectors. Several examples based on the typical differential equation for thin plates were studied successfully.
Palavras-chave: Wavelets; Deslauriers-Dubuc; Galerkin Method; Thin Plates