Buckling of inhomogeneous anisotropic cylindrical shells by bending.

Abstract

A theoretical analysis of the buckling of inhomogeneous anisotropic cylindrical shells by bending combined with pressure, axial load, and torsion is presented. Numerical results are given for contemporary composite cylinders. These results show that the pure bending buckling stress is nearly equal to the uniform axial compression buckling stress and that the bending plus uniform axial compression interaction is almost linear. T HIS study is concerned with the stability of radially inhomogeneous, anisotropic, circular cylindrical shells under bending combined with uniform axial load, torsion, and pressure. The buckling of homogeneous isotropic cylindrical shells under bending was investigated by Fliigge.1 He calculated the critical bending stress for a particular longitudinal buckle wavelength parameter and found that it was 1.3 times the critical stress for pure axial compression. Seide and Weingarten2 calculated critical bending stresses for isotropic cylinders by means of Batdorfs modified DonnelFs equations and the Galerkin method. They minimized the buckling load with respect to the longitudinal buckle wavelength and found that the critical bending stress is, for all practical purposes, equal to the critical compressive stress. Hedgepeth and Hall3 studied the stability of stiffened cylinders. They found that the resistance to bending was 25% greater than the resistance to compression for a corrugated cylinder with internal rings. Mah, Almroth, and Pittner4 have investigated the buckling of orthotropic cylinders under combined bending, axial compression, and external pressure. They found that the critical bending stress is substantially higher than critical compression when they are interacting with external pressure. A combined analytical and experimental investigation of the buckling of filament-woun d cylinders under axial compression has been reported by Tasi, Feldman, and Stang.5 Their experimental buckling loads were from 65 to 85% of predicted values, and they found the differences between clamped end and simple support solutions to be negligible. Tasi6 studied the effect of heterogeneity on the stability of composite cylinders under axial compression. He considered composites whose in-plane, coupling, and bending stiffness matrices were orthotropic and found that heterogeneity generally reduced the axial buckling load. Experiments to determine the strength of filament-wound cylinders loaded in axial compression have been reported by Card. 7 In some of his tests, failures were induced by buckling and these buckling loads were from 65 to 90% of predicted values. Holston8 investigated the effects of a soft elastic core on the buckling of inhomogeneous anisotropic cylindrical shells. He showed numerical results for filament-wound cylinders under pressure, axial compression, and torsion. He found that the increment in buckling load associated with an increment in the core parameter is largest for pressure buckling and smallest for axial compression. An analytical and experimental investigation of the stability of filament wound cylinders under combined loads has been presented by Holston, Feldman, and Stang.9 Their experimental buckling loads were from 67 to 90% of theoretical values for loadings without torsion. Ugural and Cheng10 have presented an analysis of the buckling of composite cylinders under pure bending and numerical results for plywood cylinders. In this study an analysis of the buckling of radially inhomogeneous, anisotropic cylindrical shells by bending combined with pressure, uniform axial load, and torsion is presented. Linear anisotropic shell theory is used and the effects of end conditions are not considered. The Donnell type of approximation is included, and these equations reduce to those given by Seide and Weingarten2 for isotropic materials. Numerical results are given for contemporary filamentwound cylinders. The bending-buckling stresses of these cylinders are, for all practical purposes, equal to their uniform axial compression buckling stresses, and the bending plus axial compression interactions are nearly linear. II. Stability Analysis