Daubechies Wavelet Meshless Method for 2-D Elastic Problems

This paper introduces a meshless method based on Daubechies (DB) wavelets for 2-D elastic problems. The scaling and wavelet functions of the DB wavelet are used as basis functions to approximate the unknown field functions, so there is no need to construct costly shape functions as in the finite element method (FEM) and other meshless methods. In addition, the properties of the DB wavelets facilitate implementation of the method. The new method is used to analyze the elastic problem of a plain plate with a circle hole, and the numerical results agree well with the FEM. This method is effective and can be extended to solve complicated two or three dimensional problems.