An efficient wavelet finite element method in fault prognosis of incipient crack

Typical structural damage is evidenced by emergence and expansion of incipient crack that is not easy to detect1]. The crack fault is one of the major causes for damage of the large-scale complicated structure. A serious consequence of expanding crack is frequent occurrence of grave accidents. As a consequence, one of the important orientations in the field of fault diagnosis is to monitor and prognose the location and depth of incipient crack. Prognosis of the incipient fault is a new subjec…

An efficient wavelet finite element method in fault prognosis of incipient crack

The method of constructing any scale wavelet finite element (WFE) based on the one-dimensional or two-dimensional Daubechies scaling functions was presented, and the corresponding WFE adaptive lifting algorithm was given. In order to obtain the nested increasing approximate subspaces of multiscale finite element, the Daubechies scaling functions with the properties of multi-resolution analysis were employed as the finite ele-ment interpolating functions. Thus, the WFE could adaptively mesh the singularity domain caused by local cracks, which resulted in better approximate solutions than the traditional finite element methods. The calculations of natural frequencies of cracked beam were used to check the accuracy of given methods. In addition, the results of cracked cantilever beam and engineering application were satisfied. So, the current methods can provide effective tools in the numerical modeling of the fault prognosis of incipient crack.