One-dimensional finite element formulation with node-dependent kinematics

Abstract

The present paper presents a refined one-dimensional finite element model with node-dependent kinematics. When this model is adopted, the beam theory can be different at each node of the same element. For instance, in the case of a 2-node beam element the Euler-Bernoulli theory could be used for node 1 and the Timoshenko beam theory could be used for node 2. Classical and higher-order refined models have been established with the Carrera Unified Formulation. Such a capability would allow the kinematic assumptions to be continuously varied along the beam axis, that is, no ad hoc mixing techniques such as the Arlequin method would be required. Different combinations of structural models have been proposed to account for different kinematic approximations of beams, and, beam models based on the Taylor and the Lagrange expansions have in particular been used. The numerical model has been assessed, and a number of applications to thin-walled structures have been proposed. The results have been compared with those obtained from uniform kinematic models and convergence analyses have been performed. The results show the efficiency of the proposed model. The high accuracy of refined one-dimensional models has been preserved while the computational costs have been reduced by using refined models only in those zones of the beam that require them.