Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method (FEM) of B-spline wavelet on the interval (BSWI) is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the proposed finite elements have higher precision than the traditional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundationmodel excited by external or internal dynamic load. The proposed finite elements can be also used to connect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.