BIFURCATION OF EQUILIBRIUM IN THICK ORTHOTROPIC CYLINDRICAL-SHELLS UNDER AXIAL-COMPRESSION

The bifurcation of equilibrium of an orthotropic thick cylindrical she ll under axial compression is studied by an appropriate formulation ba sed on the three-dimensional theory of elasticity. The results from th is elasticity solution are compared with the critical loads predicted by the orthotropic Donnell and Timoshenko nonshallow shell formulation s. As an example, the cases of an orthotropic material with stiffness constants typical of glass/epoxy and the reinforcing direction along t he periphery or along the cylinder axis are considered. The bifurcatio n points from the Timoshenko formulation are always found to be closer to the elasticity predictions than the ones from the Donnell formulat ion. For both the orthotropic material cases and the isotropic one, th e Timoshenko bifurcation point is lower than the elasticity one, which means that the Timoshenko formulation is conservative. The opposite i s true for the Donnell shell theory, i.e., it predicts a critical load higher than the elasticity solution and therefore it is nonconservati ve. The degree of conservatism of the Timoshenko theory generally incr eases for thicker shells. Likewise, the Donnell theory becomes in gene ral more nonconservative with thicker construction.