Duabechies小波基梁单元的构造及应用研究

以Daubechies小波尺度函数作为单元插值函数，构造了一类小波基梁单元，由于采用节点挠度和转角作为单元自由度，单元连接和约束条件处理能够像传统单元一样方便地进行，从而使该小波基梁单元可有效地用于变截面、局部承载等复杂梁弯曲问题分析，数值算例表明，本文构造的小波基梁单元对不同约束条件、不同结构形式梁弯曲问题均有较高分析精度，为有限元方法提出了一种新的研究途径．

Study of the Construction and Application of Duabechies Wavelet-based Beam Element

In this paper, a class of wavelet based beam elements is constructed by using Daubechies scaling functions as interpolating function. Because the nodal lateral displacements and angles are used as element degree of freedom, the connection between neighboring elements and boundary conditions can be processed simply as done in 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.