区间五次Hermite样条多小波Euler-Bernoulli梁单元

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中间节点的多小波尺度函数，然后，基于小波多辨分析思想，构建了梁单元位移多尺度近似空间的基函数系；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传统三节点Hermite梁单元计算的完全一致；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。

EULER-BERNOULLI BEAM ELEMENT FORMULATION USING MULTIWAVELETS BASED ON THE QUINTIC HERMITE SPLINE FUNCTION ON THE INTERVAL

The quintic Hermie spline function on the interval was adopted to formulate multiwavlets scaling functions for the boundary and the middle nodes of a three-node beam respectively. Then, based on the wavelet multiresolution concept, the multiresolution function bases for the approximate spaces of the element displacement were erected. After that, the principle of minimum potential energy was used to establish the beam equilibrium equations, thus a beam element was formulated using multiwavelets based on the quintic Hermie spline function on the interval. The practical example result shows that the accuracy of the element could be automatically adjusted by changing scaling level or grid partitioning, and be the same as the traditional beam element with the equivalent grid. Compared with other wavelet beam elements, this element possesses such advantages as to be more compact clearly, more definite physically and easier to understand.