Unified wavelet finite element formulation for static and vibration analysis of laminated composite shells

This study presents, for the first time, a unified wavelet finite element formulation for static and free vibration analysis of laminated composite shells, combining the wavelet finite element method and general shell theory. The governing equations of the proposed unified wavelet finite element formulation are derived from general shell theory and first-order shear deformation theory (FSDT) using the principle of minimum total potential energy. The formulated kinematics of laminated shells can be applied to flat plates, cylindrical shells, and doubly-curved shells with the selection of appropriate Lamé coefficients with surface metric tensor and radii of curvature parameters. With the excellent approximation of B-spline wavelets on the interval (BSWI) for structure analysis, BSWI scaling functions are used as interpolating functions to construct wavelet finite elements for laminated shells. The accuracy and efficiency of the proposed BSWI method are assessed through numerical comparisons with analytical 3-D elasticity solutions and other reference solutions in the literature for static and free vibration analysis of laminated composite plates, cylindrical shells, and doubly-curved shells.