中文摘要：

首先采用区间五次Hermite样条函数,分别构造了三节点梁的边界和内部节点的多小波尺度函数,然后,基于节点尺度函数在区间内伸缩、平移的思想,构建了梁单元相互嵌套、逐级包含的多尺度位移近似空间序列;最后,采用最小势能原理,得到弯曲梁的平衡方程,从而构造了区间五次Hermite样条多小波Euler-Bernoulli梁单元.算例结果表明,该小波单元可通过改变尺度来重新划分网格,从而可自由调节单个小波单元的计算精度,其计算精度与在相同网格划分下采用任意多个传统三节点Hermite梁单元计算梁构件的完全一致.与其它小波单元相比较,该小波单元具有计算简单明了,物理意义明确,易于理解的特点.

英文摘要：

The quintic Hermite spline function on the interval was adopted to formulate multiwavelet scaling functions for the boundary and the inner nodes of a three-node beam. Based on the concept of shifting and dilating on the interval of the scaling functions, the nested approximate displacement space sequence was constituted for this element. The principle of minimum potential energy was used to establish the beam equilibrium equations as a result,the Euler-Bernoulli beam element was formulated with the mul- tiwavelets based on the quintic Hermite spline function on the interval. Numerical examples show that the multi-resolution property enables the proposed element to be re-meshed by changing its scale, and thus can adjust its calculation accuracy freely. Compared with other wavelet beam elements,this wavelet element is more simple, more solid physically and more easy to understand.