Vibration analysis of curved shell using B-spline Wavelet on the interval (BSWI) finite elements method and general shell theory

The implementation of the B-spline Wavelet on the Interval (BSWI) for curved shell elements with rectangular planform is presented in this paper. By aid of the general shell theory, cylinder shells, doubly-curved shallow shells and hyperbolic paraboloidal shells BSWI elements are formulated. Instead of traditional polynomial interpolation, scaling functions at certain scale have been adopted to form the shape functions and construct wavelet-based elements. Because of the good character of BSWI scaling functions, the BSWI curved shell elements combine the accuracy of wavelet-based elements approximation and the character of B-spline functions for structural analysis. Different from the flat shell elements, the curved shell elements obtain a better geometrical fitting property in idealizing the practical curved structures. This paper focuses on the dynamic analysis of shell. The study covers wide combinations of boundaries such as cantilever, simply supported and clamped boundary. Numerical results have been established to validate the efficiency and accuracy of the presented elements through comparison with published data from the open literature and some commercial finite element method software.