Large-deflection theory of curved sheet

Abstract

Equations are given for the elastic behavior of initially curved sheets in which the deflections are not small in comparison with the thickness, but at the same time small enough to justify the use of simplified formulas for curvature. These equations are solved for the case of a sheet with circular cylindrical shape simply supported along two edges parallel to the axis of the generating cylinder. Numerical results are given for three values of the curvature and for three ratios of buckle length to buckle width. The computations are carried to buckle deflections of about twice the sheet thickness. It was concluded that initial curvature may cause an appreciable increase in the buckling load but that, for edge strains which are several times the buckling strain, the initial curvature causes a negligibly small change in the effective width.