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

The main objective of the present work is to give the systematic way for derivation of Kirchho¤ plate-elastic foundation interaction by mixed-type formulation using the GaLteaux di¤erential instead of well-known variational principles of HellingerÐReissner and HuÐWashizu. Foundation is a Pasternak foundation, and as a special case if shear layer is neglected, it converges to ¼inkler foundation in the formulation. Uniform variation of the thickness of the plate is also included into the mixed Þnite element formulation of the plate element PLTVE4 which is an isoparametric C0 class conforming element discretization. In the dynamic analysis, the problem reduces to solution of the standard eigenvalue problem and the mixed element is based upon a consistent mass matrix formulation. The element has four nodes and at each node transverse displacement two bending and one torsional moment is the basic unknowns. Proper geometric and dynamic boundary conditions corresponding to the plate and the foundation is given by the functional. Performance of the element for bending and free vibration analysis is veriÞed with a good accuracy on the numerical examples and analytical solutions present in the literature.