Buckling of thick orthotropic cylindrical shells under combined external pressure and axial compression

Abstract

A formulation based on the three-dimensional theory of elasticity is employed to study the buckling of an orthotropic cylindrical shell under combined external pressure and axial compression. A properly defined load interaction parameter expresses the ratio of axial compression and external pressure loading, and critical loads are thus derived for a given load interaction. The results from this elasticity solution are compared with the critical loads predicted by the orthotropic Donnell and Timoshenko nonshallow classical shell formulations. Two cases of orthotropic material are considered with stiffness constants typical of glass/epoxy and graphite/epoxy. Furthermore, two cases of load interaction are considered, representing a relatively high and a relatively low axial load. For both load interaction cases considered and for both materials, the Donnell and the Timoshenko bifurcation points are higher than the elasticity solution, which means that both shell theories are nonconservative. However, the bifurcation points from the Timoshenko formulation are always found to be closer to the elasticity predictions than the ones from the Donnell formulation. An additional common observation is that, for a high value of the load interaction parameter (relatively high axial load), the Timoshenko shell theory is performing remarkably well, approaching closely the elasticity solution, especially for thick construction. Finally, a comparison with some available results from higher order shell theories for pure external pressure indicates that these improved shell theories seem to be adequate for the example cases that were studied.