Analysis of beams with piezo-patches by node-dependent kinematic finite element method models

This article presents a family of one-dimensional finite element method models with node-dependent kinematics for the analysis of beam structures with piezo-patches. The models proposed are built by applying Carrera unified formulation. Carrera unified formulation permits to obtain finite element method stiffness matrices through so-called fundamental nuclei whose form is independent of the assumptions made for the displacement/electrical field over the cross section of a beam. In the previous works, uniform kinematic assumptions have been applied to all the nodes within the same element. The present contribution proposes to use different kinematics on different nodes, leading to node-dependent kinematic finite element method formulations. In such an approach, non-uniform cross sections introduced by piezo-patches can be considered. With the help of layer-wise models, piezoelectric and mechanical domains each can possess individual constitutive relations. Meanwhile, node-dependent kinematics can integrate equivalent single layer models and layer-wise models to reach an optimal balance between accuracy and use of computational resources. Static governing equations for beam elements with node-dependent kinematics accounting for electromechanical effects are derived from the principle of virtual displacements. The competence of the proposed approach is validated by comparing the obtained results with solutions taken from the literature and ABAQUS three-dimensional modelling. Both extension and shear actuation mechanisms are considered.