Higher order cylindrical panel relationships considering general ply layups

Abstract

An analytical study was performed to determine the critical buckling loads and natural frequencies for composite cylindrical shells, including transverse shear effects and constant through-the-thickness direct strain ε z . A linearized form of Sander's shell equations are derived, including a parabolic transverse shear strain distribution. Higher order laminate constitutive relations are developed. Hamilton's Principle is applied to derive five partial differential equations of motion and the associated boundary conditions, which are then solved using the Galerkin technique. Ply layups of [ 0 90 ] and [ 45 −45 ] were investigated under three boundary conditions, simply supported, clamped, and a combination simple-clamped. Symmetric and nonsymmetric laminates were investigated. Curvature is shown to have an important effect on all panels investigated due to membrane and bending coupling. Buckling loads for deeper shells are significantly higher than for flat plates. The effect on frequencies is not as great. The behavior of the nonsymmetric laminates was somewhat unexpected. Some results indicate the nonsymmetric laminates to be stiffer than the corresponding symmetric layup.