Construction of One-Dimensional Elements with B-Spline Wavelet
Xiang Jiawei,Chen Xuefeng,Li Bing,He Yumin,He Zhengjia
(School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China)

Abstract: Adopting the scaling function of BSWI as trial functions, a new finite element method of B-Spline wavelet on the interval (FEM BSWI) is presented. Instead of traditional polynomial interpolation, scaling functions at the cert ain scale was utilized to form the shape functions and construct wavelet-based elements. Unlike the process of direct wavelets adding in the previous work, the elemental displacement field represented by the coefficients of wavelets expansions was transformed into edges and internal modes via the constructed transformation matrix which serves as the key to constructing elements freely as the nonsigularity gets ensured to construct a class of one-dimensional elements. The  numerical examples indicate that the BSWI elements have higher efficiency and accracy in solving problems with variable boundary conditions and structural shapes than the traditional finite element methods.
Keywords: BSWI, transformation matrix, wavelet finite elements.