On the Analysis of Stress Concentration Probelm Using Wavelet Galerkin Method (2nd Report, Using Higher Degree B-splines as the Basis Functions)

Abstract

In this paper, discussions on B-spline wavelet Galerkin method are presented for its mathematical formulations and numerical implementations. Scaling function and wavelet are used as the trial and the test functions in Galerkin formulation. Quadratic and Cubic B-spline scaling function/ wavelet are adopted as the basis functions. These basis functions have simple forms and are easy to integrate and differentiate. Furthermore, they have the so called multiresolution properties. The stress and strain solutions are continuous throughout the analysis domain. However, there are some difficulties in dealing with external boundaries. They are due to the loss of linear independence of the basis functions. To circumvent these problems, we introduce the boundary scaling functions/ wavelets or eliminate particular basis functions that can be expressed by the linear superpositions of the other basis functions. Numerical results are presented for the problems of tensile plate with a circular hole.