Buckling Analysis of Mindlin Plates Under the Green–Lagrange Strain Hypothesis

In the present paper, the influence of Green–Lagrange nonlinear strain-displacement terms, usually considered negligible under the von Kármán hypothesis, on the buckling of isotropic, moderately thick plates and shells, is investigated. The first order shear deformation plate theory is applied and the governing equations, containing nonlinear terms related to both in-plane displacement and out-of-plane rotations usually ignored in the literature, are derived using the principle of minimum of the strain energy. The general Levy type solution method is employed, and exact buckling loads and mode shapes are derived. To verify the accuracy of the solution obtained, comparisons with existing data are first made. Then, through graphics and tables, the effect of the nonlinear strain-displacement terms for a range of boundary and load conditions, variations of aspect ratio, thickness ratio and changes in geometry is presented. The results obtained show that the von Kármán's model can sensibly overestimate the critical load for structures characterized by the modes involving comparable in-plane and out-of-plane displacements.