On the Analysis of Stress Concentration Problems Using Wavelet Galerkin Method (4th Report, A Technique to Examine Linear Independence of the Basis Functions)

Abstract

B-spline wavelet Galerkin method is adopted to the solid/structural mechanics analyses. B-spline scaling function and wavelet are used as the basis functions. These basis functions have the so-called multiresolution properties. The steep gradients of stresses or strains can be enhanced by superposing different length scale wavelet basis functions. In the authors' previous study, B-spline wavelet Galerkin method adopted an adaptive strategy based on the posterior error estimation. On the other hand, there are some difficulties in dealing with external boundaries for the analyses of complicated shaped structures. There are loss of linear independence of the basis functions. A technique to remove particular basis functions that can be expressed by the linear superposition of the other basis functions is presented. In this paper, some numerical tests are carried out to validate the technique and some numerical examples are shown.