Keywords: layerwise mixed finite elements, piezolaminated plates.

This paper deals with the development of a Layerwise finite element model for piezo-laminated plate structures. A Reissner mixed variational equation is used to derive the governing equations, using transverse stresses, transverse electrical displacement, displacement components and electrical potential as primary variables. The present model in contrast with the standard Layerwise displacement finite elements fulfils the continuity of all primary variables at the interface between adjacent layers. Only the layers in-plane stress components and corresponding electric displacements are evaluated by post-processing through the piezolaminated constitutive equations. In the present Layerwise theory the transversal shear and normal stresses, the transverse electrical displacement, the mechanical displacements and the electric potential are given by the following expansion:

The integers , ... are the number of analysis layers (not the number of physical layers) considered, for each one of the stresses, electrical displacement, mechanical displacements or electric potential. The shape functions describe the plate behaviour in the direction of thickness and its variation can be linear, quadratic, cubic, etc. Introducing the previous approximations into a modified Reissner variational principle [1] and interpolating the functions with polynomial shape functions yields the finite element formulation.

Three types of interpolations have been considered and results for a benchmark problem of a simply supported piezolaminated plate closed-form solution of Heyliger [2] are presented. Results of primary and secondary variables are also compared and discussed with an alternative Layerwise displacement finite element solution of Mota Soares et al [3]. An excellent agreement is obtained with both solutions. The present model appears as an alternative to the traditional displacement finite element formulations and guarantees the continuity of transverse stresses and transversal electrical displacement. The present finite element formulation models accurately the three-dimensional behaviour of piezolaminated plate structures.

1

Reissner, E., "On a Certain Mixed Variational Theory and Proposed Applications", International Journal of Numerical Methods in Engineering, 20, 1366-1368, 1984. doi:10.1002/nme.1620200714

2

Heyliger, P., "Exact Solutions for Simply Supported Laminated Piezoelectric Plates", Journal of Applied Mechanics, 64, 299-306, 1997. doi:10.1115/1.2787307

3

Mota Soares, C.M., Garção, J.E., Reddy, J.N., "Modeling of Layerwise Piezolaminated Structures" Smart Structures and Integrated Systems, Edited by L. Porter Davies, SPIE, The International Society of Optical Engineering, Vol. 4701, Paper no. 17, 2002. doi:10.1117/12.474665

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