Beam finite element models with node dependent kinematics and arbitrary displacement fields over the cross-section

The present paper proposes new, improved one-dimensional finite elements that use the node-dependent kinematics method, i.e. each node may adopt a different expansion over the cross-section without using a special coupling method. Furthermore, the presented method is able to choose independent models for each of the three displacement variables. In particular, Taylor-based and Lagrange-based functions have been chosen as expansions for the cross-sections. These two outcomes are possible through the use of the Carrera Unified Formulation, which subdivides the three-dimensional displacement field into a cross-section domain and an axis domain. Starting from the principle of virtual displacements, the governing equations and finite element matrices are obtained. In numerical results, compact and thin-walled beams have been studied and subjected to various loading conditions, including bending and torsion-bending. The selected cases are compared with existing literature or with high-refined CUF-based solutions. The accuracy of the models presented is assessed for both displacements and stress components. The results show that the choice of the ‘best’ computational models in terms of accuracy vs degree of freedom is problem-dependent. Finally, the Node-dependent kinematics method permits the selection of the most suitable expansions for each cross-section.