Relationships between buckling loads of Kirchhoff, Mindlin, and Reddy polygonal plates on Pasternak foundation

This paper presents relationships between the buckling loads determined using classical Kirchhoff plate theory and shear deformable plate theories. The latter theories considered are the first-order shear deformation plate theory of Reissner-Mindlin and the third-order plate theory of Reddy. The relationships are exact for isotropic, simply supported polygonal plates under an isotropic inplane load and resting on a Pasternak foundation. Using the relationships, buckling solutions of the Reissner-Mindlin and Reddy plate theories can be readily obtained from known buckling solutions of the Kirchhoff plate theory without the Pasternak foundation.