Buckling of circular cylindrical shells with different moduli in tension and compression

Abstract

An exact solution is derived for buckling of circular cylindrical shells with different elastic moduli in tension and compression under arbitrary combinations of axial and lateral pressure. The combinations include those in which one component of pressure causes tension. Classical buckling theory, by which is implied a membrane prebuckled shape, is used for simply supported edge boundary conditions. General results in a form analogous to Batdorf's classical k-Z form are presented for several ratios of tensile to compressive elastic moduli. Differences in tensile and compressive moduli are observed to cause significant differences in the buckling loads. This situation is particularly acute when only a small tensile loading component exists in conjunction with an apparently dominant compressive loading component. For example, if a small axial tensile loading is present in a principally external pressure loading environment, a reduction of 17% in the external pressure buckling load from the zero axial load case can occur for a tensile modulus that is half the compressive modulus. The present results are important because current composite materials often have significantly different elastic moduli in tension and compression.