Theory and Tests on the Plastic Stability of Plates and Shells

Buckling of plates and shells superimposes an additional state of stress on the original one. Assuming that is governed only by the amount of elastic shearing energy at the point in question, it is shown that the assumption of plastic deformation leads to smaller buckling stresses than that of plastic flow. Using the assumption of plastic deformation, it is found that the theory is in good agreement with tests by Kollbrunner and by the N.A.C.A. I t is found that the ratio between and elastic buckling stress is highest when the proportions of the deviator components, as superimposed by buckling, differ most from the proportions of the original deviator components. The stress-strain relations are derived by writing the infinitely small excess strains as total differentials and computing the partial derivatives of the strains with respect to the stresses. The differential equation for plate buckling is derived, and results of its application to several kinds of loading and boundary conditions are tabulated. The theory for the buckling of shells is also given. The author presents a comparison of his theory with the theories of Ilyushin, Stowell, and Handelman and Prager.