Keywords: finite element method, plate elements, shell elements, active vibration control, dynamic analysis.

The element proposed in this paper is three-noded in order to keep the finite element models as simple as possible and, it has all six structural DOFs to avoid numerical difficulties when interacting with flexible multibody codes. The formulation of the bending element is based on a generalization of the discrete Kirchhoff technique to include transverse shear effects as proposed by Batoz and Lardeur [1] and, the formulation of the membrane element is based on the compatible displacement field for triangular elements with rotational degrees of freedom as proposed by Allman [2]. In addition to the two-dimensional discretization of the mechanical displacement field in the middle surface, the electric potential field of each piezoelectric sensor and, or actuator layer is further discretized by finite sublayers.

The finite element uses theories that are available in the literature, nevertheless, the mutual interaction of these theories and its effects on the performance of the resulting plate-shell element has been carefully investigated.

The model verification includes static and dynamic analysis of plate-shell structures. A bimorph beam with sensing and actuation capabilities is analyzed. The modal frequencies of a piezoelectric bimorph plate structure studied by Wang are computed [3]. The modal frequencies are evaluated for both open circuit and closed conditions on the top and bottom surfaces of the piezoelectric layers. The second dynamic analysis problem was studied by Chevallier et al. [4] and it consists on a rectangular thick aluminum cantilever plate with a single pair of PIC255 PZT patches.

The numerical results obtained using SDST element correlated well with other published results. Nevertheless, when the element is applied to shell analysis it shows some membrane locking and, therefore, further improvements of the membrane behavior of the SDST element should be considered for the correctness of shell solutions.

1

J.L. Batoz, P. Lardeur, "A discrete shear triangular nine d.o.f. element for the analysis of thick to very thin plates", International Journal for Numerical Methods in Engineering, 28, 533-560, 1989. doi:10.1002/nme.1620280305

2

D.J. Allman, "A compatible triangular element including vertex rotations for plane elasticity analysis", Computers and Structures, 19, 1-8, 1984. doi:10.1016/0045-7949(84)90197-4

3

S.Y. Wang, "A finite element model for the static and dynamic analysis of a piezoelectric bimorph", International Journal of Solids and Structures, 41, 4075-4096, 2004. doi:10.1016/j.ijsolstr.2004.02.058

4

G. Chevallier, S. Ghorbel, A. Benjeddou, "A benchmark for free vibration and effective coupling of thick piezoelectric smart structures", Smart Materials Structures, 17, 11, 2008. doi:10.1088/0964-1726/17/6/065007

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