Analysis of Laminated Plates and Shells Using B-Spline Wavelet on Interval Finite Element

Abstract

Composite materials, with characteristics of light weight and high strength, are useful in manufacturing. Therefore, precise design and analysis is the first key procedure in composite applications, improper analysis or use of composite materials may cause serious failures. In this paper, wavelet finite element method (WFEM) based on B-spline wavelet on the interval (BSWI) is constructed for precise analysis of laminated plates and shells, which gives a guidance in design and application of composite structures. First, FEM formulations are derived from the generalized potential energy function based on the generalized variational principle and virtual work principle. Then, BSWI scaling functions are used as interpolation function to discretize the solving displacement field variables. At the same time, transformation matrix is constructed and used to translate the meaningless wavelet coefficients into physical space. At last, the static analysis results can be obtained by solving the FEM formulations. Due to the excellent features of BSWI, such as multiresolution, multiscale, localization and excellent numerical approximation characteristics etc., BSWI-based FEM can achieve accurate and efficient analysis by comparing with traditional methods. In the end, the effectiveness of the constructed BSWI WFEM is verified through several numerical examples.