Effect of Longitudinal Stress Gradients on Elastic Buckling of Thin Plates

Abstract

This paper analyzes the effect of longitudinal stress gradients on the elastic buckling of thin isotropic plates. Two types of thin plates are considered: (1) a plate simply supported on all four edges and rotationally restrained on two longitudinal edges; and (2) a plate simply supported on three edges with one longitudinal edge free and the opposite longitudinal edge rotationally restrained. These two cases illustrate the influence of longitudinal stress gradient on stiffened and unstiffened elements, respectively. A semianalytical method is derived and presented herein to calculate the elastic-buckling stress of both types of rectangular thin plates subjected to nonuniform applied longitudinal stresses. Finite-element analysis using ABAQUS is employed to validate the semianalytical model for plates with fixed and/or simple supports. Empirical formulas are produced to calculate the buckling coefficients of plates with fixed and/or simple supports under longitudinal stress gradients. The results help establish a better understanding of the effect of longitudinal stress gradients on the elastic buckling of thin plates and are intended to aid in the development of design provisions to include these effects in the strength prediction of thin-walled beams under moment gradients.