Elastic stability of elliptical cylindrical shells under axial compression or torsion

Abstract

The shell as a structural form is widely present in nature and extensively applied in various engineering practices. Due to its inherent thinness and curvature, the shell structure boasts an efficient load-carrying capability and a unique aesthetic value in architecture. It is also because of the thinness and curvature the shell structure is well acknowledged to exhibit the greatest complexity of any structural form. For thin-walled shells, buckling failure is commonly recognized as the dominating failure mode and can often lead to catastrophic collapse of the structure. The buckling and post-buckling behavior of circular cylindrical shells (CCSs) is one of the most extensively investigated problems in the last century, and is now reasonably well understood. Research on a more generic geometric form, the elliptical cylindrical shells (ECSs), has however been rather limited. To date, only four types of loading cases, namely uniform axial compression, uniform external pressure, global bending, and torsion, have been examined in a small number of studies with regard to the elastic stability of isotropic ECSs. The majority of these studies focus on the buckling and post-buckling of ECSs under axial compression in a much less systematic way compared with research on CCSs. For the loading case of torsion, only one study has been discovered, which implies this loading condition is extremely underexplored. To this end, the present PhD thesis is dedicated to investigations into the elastic buckling and post-buckling problems of isotropic ECSs under two fundamental loading cases, namely, axial compression and torsion, in a thorough and systematic way using finite element analysis. The elastic buckling of ECSs under axial compression is firstly investigated considering both the effects of shell length and boundary conditions. Length parameters similar to the well-known Batdorf parameter in CCSs are proposed to characterize the full range buckling behavior. Formulae predicting the critical elastic buckling loads are also proposed. The elastic post-buckling of perfect and imperfect ECSs under axial compression is subsequently examined. The influences of both imperfection amplitude and imperfection form are systematically explored. The envelope of lowest buckling loads for medium-length ECSs with the introduction of three different types of initial geometric imperfections is finally approximated by two algebraic formulae. The elastic buckling of ECSs under torsion is finally studied. Due to the presence of the warping effect in ECSs under restrained torsion, this study starts from an investigation of the stress distributions of ECSs under restrained torsion in the pre­buckling stress state. The results demonstrate the inappropriateness of the rigid body rotation assumption in the classical restrained torsion theory when applied to ECSs. After obtaining a clear understanding of the pre-buckling stress distributions of ECSs under torsion, the elastic buckling behavior of ECSs under torsion is eventually examined by considering both the length effect and the boundary condition effect as in the study on axially compressed ECSs. Length parameters are devised to characterize the full range elastic buckling behavior. Formulae predicting the critical elastic buckling torques are proposed as well.