On the Analysis of Stress Concentration Problems Using Wavelet Galerkin Method (1st Report, Mathematical Formulations and Treatments on External Boundaries)

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. These basis functions have the so called multiresolution property. B-spline scaling function and wavelet have simple forms and are easy to integrate and differentiate. 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 superposition of the other basis functions. Numerical results are presented for the problems of tensile plate with a circular hole.