Several papers dealing with the mathematical formulations, including exact solutions for Mindlin-Levy plates resting on elastic foundations have been presented. These analytical solutions, although exact in some cases, or very accurate in other cases, are not suitable to the analysis of complex plate systems like: skew plates, stiffened plates, continuous plates, etc. This drawback can be overcome with the use of numerical solutions provided, for instance, by the finite element method. However, very few papers concerning to the vibration analysis of laminated composite plates resting on elastic foundation, by the finite element method, are found in the literature.

This paper is being proposed to surmount such inconvenience. Among several finite elements that have been proposed to analyse laminated composite plates, a six-node triangle element with five nodal degrees of freedom, developed by Kosmatka [1], was chosen. This finite element was formulated using Hamilton's principle along with a first-order shear deformation theory. This element has correct rank and is free of shear locking. The author of this paper later implemented elastic foundation, following the Winkler approach proposed by Chilton and Wekezer[2].

Three examples are presented to validate the formulation and its convergence capabilities in comparison with exact analytical solutions. Another example compares the results presented in this paper with ones given by Omurtag et al.[3], who used a mixed finite element formulation employing the Gâteaux Differential Method and a plate element capable of modeling the Kirchhoff type orthotropic plate resting on Winkler and Pasternak elastic foundation.

From these examples it is possible to conclude that the approach presented in this paper allows its extension to other types of analysis such as buckling and vibration with initial stresses.

1

J.B. Kosmatka, "An Accurate Shear-Deformable Six-Node Triangular Plate Element", International Journal for Numerical Methods in Engineering, 37, 431-455, John Wiley & Sons, Ltd., 1994.

2

D.S. Chilton, J.W. Wekezer, "Plates on Elastic Foundation", Journal of Structural Enginering, ASCE, 16(11), 3236-3241, 1990. doi:10.1061/(ASCE)0733-9445(1990)116:11(3236)

3

M.H. Omurtag, A. Özütok, Y.A. Ahmet, "Free Vibration Analysis of Kirchhoff Plates Resting on Elastic Foundation by Mixed Finite Element Formulation Based on Gâteaux Differential ", International Journal for Numerical Methods in Engineering, 40, 295-317, John Wiley & Sons, Ltd., 1997. doi:10.1002/(SICI)1097-0207(19970130)40:2<295::AID-NME66>3.0.CO;2-2

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