Allowance for prebuckling deformations in buckling load relationship between Mindlin and Kirchhoff simply supported plates of general polygonal shape

The elastic buckling of simply supported Mindlin plates under an isotropic inplane loading is considered. In addition to the effect of shear deformation, the analysis also considers the effects of curvature terms and the prebuckling inplane deformations. First considering rectangular plates, the equilibrium equations in terms of the deflection and the cross-section rotations are solved exactly for the buckling load. The buckling load of the Mindlin plate may be expressed in terms of the corresponding Kirchhoff buckling solution of the same plate dimensions. Although this relationship between the Mindlin and Kirchhoff solutions was derived from considering a rectangular plate shape, it can be proved on the basis of work by Irschik that the relationship is valid even for simply supported plates of arbitrary polygonal shape. The closed form relationship presented herein should be useful; firstly, for generating Mindlin buckling solutions for any polygonal plate shape; secondly, for studying the effects of curvature terms and prebuckling deformation; thirdly, in providing benchmark values in checking the validity, convergence and accuracy of numerical buckling solutions; and finally, for the development of simple buckling formulae for Mindlin plates of other boundary conditions. Problems analogous to the buckling problem of Mindlin plates are also highlighted