Shell finite elements with arbitrary displacement fields along the thickness

This paper introduces an innovative approach for developing shell structural theories with an arbitrary kinematic field. In this study, each displacement component may be analysed using an independent expansion function. This method allows for the incorporation of both classical and higher-order theories within a unified framework. The Carrera Unified Formulation is employed to describe the thickness kinematics. In this paper, the structural theories are built by using polynomial terms. The finite element method is employed to discretize the structure in the reference mid-surface of the structure, utilizing Lagrange-based elements. The governing equations for the linear analysis are derived using the principle of virtual displacements. Also, the Mixed Interpolation of Tensorial Components is adopted inside the formulation to limit the locking issues. Cylindrical and spherical shells are studied here. Several radius-to-thickness ratios are taken into account. Both point and distributed loads are considered. Whenever possible, the present results are compared with the existing literature. The accuracy of the models presented is assessed for both displacements and stress outputs. The results illustrate that the selection of the most appropriate model is highly contingent on the specific parameters of the particular problem.