Modal analysis of delaminated plates and shells using Carrera Unified Formulation-MITC9 shell element

The present paper considers the modal analysis of delaminated composite shell structures with double-curvature geometry. The finite element for shell with variable through-the-thickness kinematic is adopted for the analysis. The refined models are grouped in the Unified Formulation by Carrera (CUF) and they permit the distribution of displacements 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 alleviate the membrane and shear locking phenomenon. The governing equations are derived from the Principle of Virtual Displacement (PVD) and the Finite Element Method (FEM) is employed to solve them. From the analysis, one can conclude that the shell element based on the CUF is very efficient and the results obtained match closely with three-dimensional finite element simulations. The effect of delamination size, curvature, stacking sequence, and boundary conditions is studied. The results from different ordered theories are tabulated and compared. It is observed that there is reduction in frequencies in the presence of delamination; however, for a given size of delamination, stacking sequence, and boundary conditions, the effect of delamination on shell structure is more predominant in comparison with respect to the plates structures.