BUCKLING OF THICK ORTHOTROPIC CYLINDRICAL-SHELLS UNDER EXTERNAL-PRESSURE BASED ON NONPLANAR EQUILIBRIUM MODES

A formulation based on the three dimensional theory of elasticity is e mployed to study the buckling of an orthotropic cylindrical shell unde r external pressure. In this paper, a non-zero axial displacement and a full dependence of the buckling modes on the three coordinates is as sumed, as opposed to the ring approximation employed in the earlier st udies. The results from this elasticity solution are compared with the critical loads predicted by the orthotropic Donnell and Timoshenko no n-shallow shell formulations. Two cases of end conditions are consider ed; one with both ends of the shell fixed, and the other with both end s capped and under the action of the external pressure. Moreover, two cases of orthotropic material are considered with stiffness constants typical of glass/epoxy and graphite/epoxy. For the isotropic material case, the predictions of the simplified (single expression) Donnell an d the Flugge and the Danielson and Simmonds theories are also compared . In all cases, the elasticity approach predicts a lower critical load than the shell theories, the percentage reduction being larger with i ncreasing thickness. The degree of non-conservatism depends strongly o n the material properties, being smaller for the isotropic case. Furth ermore. although it is a commonly accepted notion that the critical po int in loading under external pressure occurs for n = 2 and m = 1 (num ber of circumferential waves and number of axial half-waves, respectiv ely), it was found that this is not the case for the strongly orthotro pic graphite/epoxy material and the moderately thick construction; for this case, the value of m at the critical point is greater than 1 (ye t, in all cases n = 2).