Plate elements with node dependent kinematics and arbitrary displacement fields for free edge analysis

This paper presents enhanced two-dimensional finite elements based on the Node Dependent Kinematics approach, in which each finite element node may employ a distinct thickness expansion, while kinematic models can be independently selected for each displacement variable using both Taylor- and Lagrange-based expansions over the thickness. The formulation, developed within the Carrera Unified Formulation, permits the generation of generic structural theories in the same framework. The present method is validated by studying the free-edge problem and comparing results with literature data and high-fidelity reference solutions. The results confirm that the optimal computational model for balancing accuracy and efficiency depends on the specific problem under consideration.