Modelling Smart Structures With Segmented Piezoelectric Sensors and Actuators

Abstract

In this paper, a number of "nite element models have been developed for comprehensive modelling of smart structures with segmented piezoelectric sensing and actuating patches. These include an eight-node solid-shell element for modelling homogeneous and laminated host structures as well as an eight-node solid-shell and a four-node piezoelectric membrane elements for modelling surface bonded piezoelectric sensing and actuating patches. To resolve the locking problems in these elements and improve their accuracy, assumed natural strain and hybrid stress formulations are employed. Furthermore, piezoelectric patches are often coated with metallization. The concept of electric nodes is introduced that can eliminate the burden of constraining the equality of the electric potential for physical nodes lying on the same metallization. A number of problems are studied by the developed "nite element models and comparisons with other ad hoc element models are presented.

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

“…Therefore, we have recalculated their results for E = 210 GPa by multiplying their numbers by the factor √ 210/68.95 and put them in the right order (see Table 2). After these modifications, the results of Sze and Yao [88] and Sze et al [89] are in reasonable agreement with our results. It can be also observed (Fig.…”

“…5 that the results of Tzou and Ye [8] are probably obtained with an element which exhibits some locking effect and with a mesh which is too coarse. Additionally, we have included in Table 2 results which can be found in Sze and Yao [88] and Sze et al [89], obtained by a hybrid-stress-assumed natural strain 8-node solid-shell element and by the 4-node generalpurpose (thin and thick) curved shell element of ABAQUS S4. Based on these results, these two papers criticize the element of Tzou and Ye [23] as too stiff.…”

“…To this end, two problems are studied extensively. In Chapter 4, we consider a clamped semicircular ring shell with piezoelectric actuator and sensor patches bonded to its upper and lower surfaces that was originally treated by Tzou and Ye [23] and has been used as a benchmark problem for linear vibration control in several recent papers, for example, by Sze and Yao [88], Sze et al [89], Balamurugan and Nayaranan [90]. The refereed results are critically reviewed and extended to account for the effects of structural nonlinearity.…”

Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors

“…To model this condition, particularly for sensing, it would be necessary to impose the constraint of equality on the electric DOF of the nodes on the same electroded surface. To avoid this tedious task, the concept of electric nodes has been used by Sze and Yao [2000], wherein the electric DOF are separated from the kinetic (physical) nodes with which only mechanical DOF are associated. It results in significant reduction in the number of electric DOF.…”

A piezoelectric solid shell element based on a mixed variational formulation for geometrically linear and nonlinear applications

“…One may distinguish between element formulations, which model a reference surface of the shell structure, see e.g. [1,2,3,4,5,6], and solid shell elements which model the top and bottom surfaces of structures, see e. g. [7,8,9,10,11,12]. Some of these element formulations are restricted to shallow shell structures, [5,6], where the initial shell curvature is assumed to be small.…”