A study of the construction and application of a Daubechies wavelet-based beam element
Wavelet theory provides various basis functions and multi-resolution methods for finite element method. In this paper, a wavelet-based beam element is constructed by using Daubechies scaling functions as an interpolating function. Since the nodal lateral displacements and rotations are used as element degrees of freedom, the connection between neighboring elements and boundary conditions can be processed simply as done for traditional elements. Then, it is realized that the complicated beams such as those with unequal cross section, local load and so on, can be analyzed by this wavelet-based element. The numerical examples illustrate that the wavelet-based element has high analytical accuracy for beam bending problems with various boundary conditions and structures. A new approach is presented for finite element method.
wavelet-based beam element scaling functions daubechies wavelet un-uniform beam