Buckling of open cylindrical shells under combined compression and bending stress

Abstract

In this paper, a procedure is developed to overcome the mathematical difficulty in solving the Donnell equations for a curved panel subject to circumferential variation of axial stress. The present paper deals with the small deflection theory where the axial deformation is predominant. The problem of a simply supported open shell subjected to linear variation of axial stress across the cross section, which can be expressed in terms of an infinite series along the circumferential coordinate, is solved in detail. The expressions for the displacements are given in terms of arbitrary undetermined constants, which can be made to satisfy prescribed longitudinal edge conditions. The solutions for displacement in this paper are given as a sum of two parts, the first part representing the contribution due to a constant axial stress and the second part representing the contribution due to the deviation function.