Plate finite elements with arbitrary displacement fields along the thickness

The present paper introduces a methodology for formulating two-dimensional structural theories featuring arbitrary kinematic fields. In the proposed approach, each displacement variable can be examined through an independent expansion function, enabling the integration of both classical and higher-order theories within a unified framework. The Carrera Unified Formulation is used to derive the governing equations in a unified form, independent of the expansion adopted for each displacement component. In this paper, plate structural theories are constructed by using polynomial expansions. The finite element method is used to discretize the structure in the reference plane of the plate, utilizing Lagrange-based elements. The Mixed Interpolation of Tensorial Components is adopted to alleviate the shear locking issues. In this study, isotropic plate structures are investigated under various loadings, boundary conditions, and different length-to-thickness ratios. Whenever possible, the present results are compared with analytical and literature solutions. The accuracy of the presented models is evaluated for both displacements and stress components. The findings indicate that the selection of the most appropriate model is strongly dependent on the specific parameters of the individual problem, however, choosing the right model can significantly enhance the efficiency of the numerical analysis.