Large-Deflection Theory for Plates With Small Initial Curvature Loaded in Edge Compression

Abstract This investigation of the buckling of a simply supported, rectangular isotropic plate with small initial curvature was undertaken to evaluate current procedures for deducing the true (flat plate) critical load from the measured deflections and strains of a nominally flat plate. The boundary conditions are those that are usually met in test practice but which have not been satisfied by earlier studies, i.e., stress-free supported edges and uniformly displaced loaded edges. Previous solutions require a distribution of transverse stress along the supported edges sufficient to keep them straight and parallel at all times. However, in most test specimens, the freedom of the supported edges to distort in the plane of the plate measurably influences the behavior of the plate and the stress distribution within it. Levy’s solution of von Kármán’s “large deflection” equations is adapted by the author to yield the nonuniform edge displacements that are characteristic of stress-free supported edges. Limited experimental evidence tends to confirm the predictions of this analysis.