Beam bending analysis using wavelet finite element

Although wavelets have become efficient tool in signal and image processing, the utility of wavelets in computational mechanic is still in the primary stage, and far less progress has been made so far. This paper introduces Daubechies wavelets into finite element analysis of mechanical structures, then develops wavelet finite element (WFE). In order to overcome the integral difficulty that the scaling functions have no explicit expression, a new two-term connection coefficient for stiffness matrix is present in the procedure. We describe an algorithm for its computation. Furthermore, we derive the equations of the bend of beam based on WFE. A simple bending problem of Euler beam is selected as test case to show that the WFE approach gives accurate results.