Study on Weight Function of Meshless Method Based on B-spline Wavelet Function

Abstract

The Moving Least Square(MLS) is used to solve as approximate function in meshless methods. The accuracy of solution will be affected by the right selected of the weight function. The Cubic B-spline wavelet function has many good natures, such as recursion, local positive supported, multi-scale and the smallest compact supported. This paper attempted to study it as the weight function and design a practical algorithm of meshless. With the one-dimensional pole and two-dimensional plate structures as example, three functions which are Gauss function, the constructed Cubic B-spline wavelet function and Cubic spline function are studied as weight function in meshless methods. Through the comparison of approximate and exact solutions of displacement and stress, results show that the proposed Cubic B-spline wavelet function possesses high fitting solution based on multi-scale and good stability, while exploiting application area to select the weight function in meshless methods.