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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 93
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
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Paper 83

Assessment of a Layerwise Mixed Least-Squares Model for Analysis of Multilayered Piezoelectric Composite Plates

F. Moleiro1, C.M. Mota Soares1, C.A. Mota Soares1 and J.N. Reddy2

1Department of Mechanical Engineering, IDMEC/IST - Instituto Superior Técnico, Technical University of Lisbon, Portugal
2Department of Mechanical Engineering, Texas A&M University, College Station, United States of America

Full Bibliographic Reference for this paper
F. Moleiro, C.M. Mota Soares, C.A. Mota Soares, J.N. Reddy, "Assessment of a Layerwise Mixed Least-Squares Model for Analysis of Multilayered Piezoelectric Composite Plates", in , (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 83, 2010. doi:10.4203/ccp.93.83
Keywords: layerwise mixed formulation, least-squares formulation, finite element model, piezoelectric layers, composite layers.

Summary
A new layerwise mixed finite element model is developed based on a least-squares formulation for the coupled electromechanical static analysis of multilayered plates with piezoelectric and composite layers. The model assumes a layerwise variable description for displacements, transverse stresses and in-plane strains, along with the electrostatic potential, transverse electric displacement and in-plane electric field components, taken as independent variables. This original choice for the layerwise mixed formulation is intended to ensure the a priori and complete fulfilment of the requirements that compatibility and equilibrium conditions at the layers interfaces pose on both mechanical and electrical fields, namely the interlaminar C0 continuity of all chosen independent variables. This is demonstrated by the three-dimensional exact solutions developed by Heyliger [1]. In addition, this model preserves the benefits of least-squares formulation as shown by previous works [2], specifically, it is able to by-pass inf-sup conditions, and leads to a symmetric positive definite system of linear equations. Moreover, this model takes full advantage of the mixed formulation since post-computation requires no numerical differentiation.

Numerical applications are shown for assessment of the present model predictive capabilities by a thorough comparison with the three-dimensional exact solutions. In particular, a simply supported (PVDF/90/0/90/PVDF) piezoelectric composite plate is considered with different side-to-thickness ratios, namely a/h = 4, 10, 100 i.e. thick, moderately thick and thin plates, under an applied sinusoidal load or surface potential. Actually, the extensive number of results shown by the present model used 3×3 elements of fourth-order in-plane and 5 layers of either third- or fourth-order z-expansion through the layer thickness. Altogether, it is demonstrated that the layerwise mixed least-squares model is able to predict highly accurate results for all the mechanical and electrical variables, in very good agreement with the three-dimensional exact solutions, for both cases of applied load or potential, and for all side-to-thickness ratios. In fact, convergence of the predicted results to the three-dimensional exact solutions is verified by through the thickness refinement (and by in-plane refinement also, although not included here). For thick plates in particular, it is shown that through the thickness refinement, from third- to fourth-order z-expansion through the layer thickness, is indeed useful to achieve more accurate through-thickness predictions. Furthermore, it should be emphasized that the present layerwise mixed least-squares model is shown to be insensitive to shear locking, similarly to previous models [2].

References
1
P.R. Heyliger, "Exact solutions for simply supported laminated piezoelectric plates", Journal of Applied Mechanics, 64, 299-306, 1997. doi:10.1115/1.2787307
2
F. Moleiro, C.M. Mota Soares, C.A. Mota Soares, J.N. Reddy, "Layerwise mixed least-squares finite element models for static and free vibration analysis of multilayered composite plates", Composite Structures, 92(9), 2328-2338, 2010. doi:10.1016/j.compstruct.2009.07.005

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