Rodrigo Bird Burgos

Analysis of Beams and Thin Plates Using the Wavelet-Galerkin Method

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.

Solution of Wave Equation in Rods Using the Wavelet-Galerkin Method for Space Discretization

The use of multiresolution techniques and wavelets has become increasingly popular in the development of numerical schemes for the solution of partial differential equations (PDEs) in the last three decades. Therefore, the use of wavelets scale functions as a basis in computational analysis holds some promise due to their compact support, orthogonality, localization and multiresolution properties. The present work discusses an alternative to the usual finite difference (FDM) approach to the acoustic wave equation modeling by using a space discretization scheme based on the Galerkin Method. The combination of this method with wavelet analysis using scale functions results in the Wavelet Galerkin Method (WGM) which has been adapted for the direct solution of the wave differential equation in a meshless formulation. This paper presents an extension of previous works which dealt with linear elasticity problems. This work also introduces Deslauriers-Dubuc scaling functions (also known as Interpolets) as interpolating functions in a Galerkin approach considering wave propagation problems. Examples in 1-D were formulated using a central difference (second order) scheme for time differentiation. Encouraging results were obtained when compared with the FDM using the same time steps. The main improvement in the presented formulation was the recognition of a different dispersion pattern when comparing FDM and WGM results using the same space and time grid.

OBTENÇÃO DE TRAJETÓRIAS DE TENSÕES EM VIGAS DE CONCRETO ARMADO

Este trabalho apresenta um estudo das trajetorias de tensoes obtidas pela solucao analitica de vigas de concreto armado. A analise e feita em regime linear elastico para ambos os materiais, ou seja, considerando o concreto no Estadio I (nao fissurado). A viga estudada possui armadura de tracao e secao do tipo “T”, com carregamento distribuido devido ao peso proprio e cargas concentradas aplicadas a distâncias iguais dos apoios extremos. Primeiramente foram calculadas as tensoes principais e suas direcoes em secoes ao longo de todo o comprimento da viga estudada atraves do Circulo de Mohr. Em seguida, foram determinadas as trajetorias de tensoes (curvas ortogonais cuja tangente em qualquer ponto tem a direcao das tensoes principais). Ao final do trabalho, e feita uma analise comparativa entre os resultados obtidos para diferentes taxas de armadura.