Free-vibration analysis of laminated shells via refined MITC9 elements

This article presents the free-vibration analysis of composite shell structures with double-curvature geometry by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are grouped in the Unified Formulation by Carrera (CUF) and they permit the distribution of displacements and stresses along the thickness of the multilayered shell to be accurately described. The shell element has nine nodes and the mixed interpolation of tensorial components (MITC) method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacements (PVD). Laminated cylindrical and spherical shells with simply-supported edges are analyzed. Various laminations, orthotropic ratios and thickness ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using the CUF and the Navier's method. The shell element based on the CUF is very efficient, and refined models provide better results than classical ones in the free-vibration analysis of multilayered composite shells. Finally, spherical shells with different boundary conditions are analyzed using various theories in order to provide finite element method benchmark solutions.