Based on two-dimensional tensor product B-spline wavelet on the interval (BSWI), a class of C0 type plate elements is constructed to solve plane elastomechanics and moderately thick plate problems. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to form the shape functions and construct BSWI elements. Unlike the process of direct wavelets adding in the previous work, the elemental displacement field represented by the coefficients of wavelets expansions is transformed into edges and internal modes via the constructed transformation matrix in this paper. The method combines the versatility of the conventional finite element method (FEM) with the accuracy of B-spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the closed-form or traditional FEM solutions

小波有限元是一类新的有限元逼近方法，将信号处理领域中小波函数的多分辨思想引入有限元法中，以小波函数作为插值函数，构造出嵌套递进的多尺度广义有限元逼近空间，使得求解问题可以先用较粗的网格分析，特定奇异区域通过自适应多分辨剖分获得更好的逼近，该算法数值稳定性好、适宜求解奇异性问题。从小波加权残值法、小波有限元理论以及自适应小波有限元三个方面，综述了小波有限元国内外研究现状，并介绍了小波有。限元在大梯度非线性、裂纹定量预示等方面的工程应用进展，指出了其关键技术、存在问题以及工程实用前景。

A new time-domain analysis method that uses second generation wavelet transform (SGWT) for weak fault feature extraction is proposed. To extrata incipient fault feature, a biorthogonal wavelet with the characteristics of impact is constructed by using SGWT. Processing detail signal of SGWT with a sliding window devised on the basis of rotating operation cycle, and extracting modulus maxi-mum from each window, fault features in time-domain are highlighted. To make fitrther analysis on the reason of the fault, wavelet package transform based on SGWT is used to process vibration data again. Calculating the energy of each frequency-band, the energy distribution features of die signal are at- tained. Then taking account of the fault features and the energy distribution, the reason of die fault is worked out. An early impact-rob fault caused by axis misalignment and rotor imbalance is successfully detected by using this method in an oil refinery.