FREE-VIBRATION ANALYSIS OF KIRCHHOFF PLATES RESTING ON ELASTIC-FOUNDATION BY MIXED FINITE-ELEMENT FORMULATION BASED ON GATEAUX DIFFERENTIAL

The main objective of the present work is to give the systematic way f or derivation of Kirchhoff plate-elastic foundation interaction by mix ed-type formulation using the Gateaux differential instead of well-kno wn variational principles of Hellinger-Reissner and Hu-Washizu. Founda tion is a Pasternak foundation, and as a special case if shear layer i s neglected, it converges to Winkler foundation in the formulation. Un iform variation of the thickness of the plate is also included into th e mixed finite element formulation of the plate element PLTVE4 which i s an isoparametric C-0 class conforming element discretization. In the dynamic analysis, the problem reduces to solution of the standard eig envalue problem and the mixed element is based upon a consistent mass matrix formulation. The element has four nodes and at each node transv erse displacement two bending and one torsional moment is the basic un knowns. Proper geometric and dynamic boundary conditions corresponding to the plate and the foundation is given by the functional. Performan ce of the element for bending and free vibration analysis is verified with a good accuracy on the numerical examples and analytical solution s present in the literature.