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

Abstract

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.

Node-dependent kinematic elements for the dynamic analysis of beams with piezo-patches

“…The free vibrations of both short- and closed-circuit configurations have been investigated, and the electromechanical coupling coefficient ( EMCC ), has been used to compare the results with those from literature. The second example considers the piezo-patched beam investigated in the works by Benjeddou et al (1997) and Carrera et al (2018a). In this case, the free vibration and the frequency response of the beam, using the piezo-patches as sensors, have been considered.…”

Advanced modeling of embedded piezo-electric transducers for the health-monitoring of layered structures

“…where D is the matrix of the differential operators. The complete form of the matrix can be found in [36].…”

“…The NDK approach is used, in the present paper, to refine locally the numerical model and to impose compatible kinematic models at the interface between one-, two-and threedimensional elements. The theoretical derivation of the NDK modeling approach has been presented in [35] and has been used for the analysis of piezoelectric structure in [36]. A simple, two node, beam element is here used to present the approach.…”

“…This numerical tool can be used to derive any order structural models in a unified fashion. Recently, the formulation has been extended to multidimensional models [34] and, thanks to the node-dependent kinematic, NDK, formulation [35] the order of expansion of the structural model can be considered as a property of the node [36]. These capabilities have originated a powerful framework for global-local analysis [37] since the numerical model can be refined only in those areas of the structure where complex phenomena are expected.…”

“…These capabilities have originated a powerful framework for global-local analysis [37] since the numerical model can be refined only in those areas of the structure where complex phenomena are expected. An application of the NDK formulation to piezo-electric beams can be found here [36]. In the present work, these techniques have been extended at the analysis of surface-mounted and embedded piezoelectric sensors as the basis for the design of health-monitoring system.…”