A Closed form solution for the buckling analysis of orthotropic reddy plate and prismatic plate structures

A closed-form solution based on the Reddy third-order shear deformation plate theory is proposed for the buckling of both flat and stiffened plates, with simply supported on two opposite edges. The equations governing the critical behaviour considering the full Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor are derived using the principle of minimum potential energy. The general Levy-type approach is employed, and the accuracy and effectiveness of the proposed formulation is validated through direct comparison with analytical and numerical results available in the literature. The parametric analyses performed for different geometrical ratios show that the von Kármán hypothesis holds only for thin flat plates whereas it can significantly overestimate buckling loads for stiffened plates, for which the buckling mode entails comparable in-plane and out-of-plane displacements