Adopting the scaling functions of B-spline wavelet on the interval (BSWI) as trial functions, a new finite element method (FEM) of BSWI is presented. Instead of traditional polynomial interpolation, scaling functions at the certain scale have been adopted to form the shape functions and construct wavelet-based elements. Unlike the process of wavelets added directly in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix. The transformation matrix is the key to construct wavelet-based elements freely as long as we can ensure its non-singularity. Then, classes of C 0 and C 1 type elements are constructed. And the lifting scheme of BSWI elements is also discussed. The numerical examples indicate that the BSWI elements have higher efficiency and precision than traditional finite element method in solving 1D structural problems especially for geometric nonlinear, variable cross-section and loading cases.

ABSTRACT--In this paper we present an experimental investigation of the identification of crack location and size. By providing the first three natural frequencies through vibration measurements, curves of crack equivalent stiffness versus crack location are plotted, and the intersection of the three curves predicts the crack location and size. In the experiments, the cracked specimens were made using a wire-cut electrical discharge machine, and the cantilever beams were excited next to the free end by means of an impulse force hammer. In order to obtain the accurate natural frequencies from the transient signal measured, the method of zoom fast Fourier transform is adopted to improve frequency resolution. From experimental results, it is observed that the identification errors of crack location and size are less than 2% and 4%, respectively. The effectiveness of crack identification through vibration measurements is verified.

( Ba 0.65 Sr 0.35 ) 1 − x La x TiO 3 (BSLT) thin films with different La concentrations have been deposited on Si field emitter arrays (FEAs) using sol-gel technology for field electron emission applications. The films exhibit the perovskite structure at low La substitution level (x≤0.5) and the pyrochlore phase at high La concentration (x≥0.75). The 30-nm-thick BSLT (x=0.25) thin film has higher crystallinity of perovskite structure in the surface region. An x-ray photoelectron spectroscopy study indicates that the oxygen vacancy concentration decreases with La substitution. With respect to the undoped Ba0.65Sr0.35TiO3 thin film, the Fermi level shifts down for the BSLT sample with x=0.1 ascribed to the decreasing oxygen vacancy concentration, and then shifts up for the BSLT sample with x=0.25 attributed to the increasing La substitution level. In highly doped films with an x value over 0.5, it shifts down again associated with the second pyrochlore phase formation. The best enhancement in field emission is found for the BSLT-coated (x=0.25) Si FEAs due to the improved perovskite structure in the surface region and up-moved Fermi level of the coating.

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