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.

The present article considers the linear static 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 displacement (PVD) and the finite element method (FEM) is employed to solve them. Cross-ply spherical shells with simply-supported edges and subjected to bi-sinusoidal pressure are analyzed. Various laminations, thickness ratios, and curvature 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. From the analysis, one can conclude that the shell element based on the CUF is very efficient and its use is mandatory with respect to the classical models in the study of composite structures. Finally, shells with different lamination, boundary conditions, and loads are also analyzed using high-order layer-wise theories in order to provide FEM benchmark solutions.

In this paper, classical as well as various refined plate finite elements for the analysis of laminates and sandwich structures are discussed. The attention is particularly focussed on a new variable-kinematic plate element. According to the proposed modelling approach, the plate kinematics can vary through the thickness within the same finite element. Therefore, refined approximations and layer-wise descriptions of the primary mechanical variables can be adopted in selected portions of the structures that require a more accurate analysis. The variable-kinematic model is implemented in the framework of the Carrera unified formulation, which is a hierarchical approach allowing for the straightforward implementation of the theories of structures. In particular, Legendre-like polynomial expansions are adopted to approximate the through-the-thickness unknowns and develop equivalent single layer, layer-wise, as well as variable-kinematic theories. In this paper, the principle of virtual displacements is used to derive the governing equations of the generic plate theory and a mixed interpolation of tensorial components technique is employed to avoid locking phenomena. Various problems are addressed in order to validate and assess the proposed formulation, including multi-layer plates and sandwich structures subjected to different loadings and boundary conditions. The results are compared with those from the elasticity theory given in the literature and from layer-wise solutions. The discussion clearly underlines the enhanced capabilities of the proposed variable-kinematic mixed interpolation of tensorial component plate elements, which allows, if used properly, to obtain formally correct solutions in critical areas of the structure with a considerable reduction of the computational costs with respect to more complex, full layer-wise models. This aspect results particularly advantageous in problems where localized phenomena within complex structures play a major role.