Buckling of laminated cylindrical shells in terms of different theories and formulations

Bifurcation buckling analysis of laminated cylindrical shells is presented on the basis of three different shell theories: Donnell's (Donnell, L. H., "Stability of Thin-Walled Tubes under Torsion," NACA TR-479, 1933), Sanders's (Sanders, J. L., Jr., "Nonlinear Theories of Thin Shells," Quarterly journal on Applied Mathematics, Vol. 21, No. 1, 1963, pp. 21-36), and Timoshenko's (Timoshenko, S., Theory of Elastic Stability, McGraw-Hill, New York, 1961). Formulations in terms of the displacement components and of the Airy stress function and normal displacement are examined. The partial differential equations are derived via the variational principle and solved with variables expanded in Fourier series in the circumferential direction and presented as finite differences in the axial direction. The buckling behavior of an angle-ply laminated cylindrical shell under different modes of loading was investigated parametrically, showing-in contrast to its isotropic counterparts-a discrepancy between the two formulations.