A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation

• A simple refined theory is proposed for plates resting on elastic foundation.
• The theory contains two unknowns and requires no shear correction factor.
• Closed-form solutions are derived for rectangular plates.
• The theory can accurately predict the deflection, buckling load, and frequency.

A simple refined shear deformation theory is proposed for bending, buckling, and vibration of thick plates resting on elastic foundation. The theory accounts for parabolic distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The number of unknowns of present theory is two as against three in the case of other shear deformation theories. The elastic foundation is modeled as two-parameter Pasternak foundation. Equations of motion are derived from Hamilton's principle. Analytical solutions are obtained for rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are presented to verify the validity of present solutions. It can be concluded that the proposed theory is accurate and efficient in predicting the bending, buckling, and vibration responses of thick plates resting on elastic foundation.