Elastic stability of thin-walled cylindrical and conical shells under axial compression

Rigorous Derivation of the Formula for the Buckling Load in Axially Compressed Circular Cylindrical Shells

“…This result justifies the generally accepted assumption that the paradoxical behavior of cylindrical shells in buckling is due to the high sensitivity of the buckling load to imperfections [1,13,15]. This phenomenon is commonly explained by the instability of equilibrium states in the vicinity of the buckling point on the bifurcation diagram [9,15,2]. However, the exact mechanisms of imperfection sensitivity are not fully understood, nor is there a reliable theory capable of predicting experimentally observed buckling loads [10,17,7].…”

“…In this paper, we apply our theory and obtain a mathematically rigorous proof of the classical formula for buckling load [11,14]. This result justifies the generally accepted assumption that the paradoxical behavior of cylindrical shells in buckling is due to the high sensitivity of the buckling load to imperfections [1,13,15]. This phenomenon is commonly explained by the instability of equilibrium states in the vicinity of the buckling point on the bifurcation diagram [9,15,2].…”

Cylinder Buckling: The Mountain Pass as an Organizing Center

“…A variety of different explanations has been put forward, but with the experimental work of Tennyson [30] and the theoretical work of Almroth [1] it became clear that this discrepancy is mostly due to imperfections in loading conditions and in the shape of the specimens. Further experimental and theoretical work by many others has confirmed this conclusion [14,33,36].…”

Stacking sequence influence on imperfection sensitivity of cylindrical composite shells under axial compression

“…To overcome this issue, empirical knock down factors, which are the ratios of experimental buckling loads to theoretical buckling loads of the perfect shell structure, are applied to reduce the buckling load determined theoretically. Early empirical knock down factors established during the 1960s, such as the knock down factor suggested by Seide [3], which is recommended in the NASA SP-8007 Space vehicle design guideline [4] and Almroth [5] are meant to be applied to isotropic shell structures. When these knock-down factors are applied to composite shells, an equivalent shell wall thickness t eq is used to consider different imperfection sensitivities due to various laminate stacking sequences.…”

“…The empirical knock down factors according to [5], according to NASA SP-8007 [4], which is derived by Seide [3], and according to [7] are illustrated in Fig. 1.…”