The present paper extends the Koiter-type initial post-buckling analysis for a prismatic plate in order to evaluate the critical load corresponding to modes that involve unlikely in-plane displacements that cannot be obtained when the von Karman strain displacement relationship is used. In-plane displacements cannot be neglected with respect to out-of-plane displacements when stiffened plates undergo global buckling. The consistency of the model is discussed, and several numerical tests are reported. It appears that meaningful reduction of critical load in comparison with the classical von Karman model can occur; moreover the use of a semi-analytical model makes the perturbation approach insensitive to numerical instabilities occurring in the evaluation of the post-buckling behaviour and allows the use of very low-cost discretization meshes.
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