On the Analysis of Stress Concentration Problems Using Wavelet Galerkin Method (3rd Report, Adaptive Analysis)

Abstract

In present research, B-spline wavelet Galerkin method is applied to solid/structural mechanics analyses. B-spline scaling function and wavelet are used as the basis functions. The basis functions have the so-called multiresolution properties. The spatial resolutions of interpolation functions can be enhanced in the regions of high stress/strain gradients by superposing finer basis functions. B-spline wavelet Galerkin method can discretize a solid by structured cells. There are no finite element meshes in a classical sense. Then, it can be classified to be a kind of meshfree method. To control the spatial resolution of the discretization, an adaptive analysis strategy is developed based on a posteriori error estimation. The solution can be refined by superposing different wavelets of finer length scales. In this paper, the developed methodology and some numerical demonstrations are presented.