Knockdown factor of buckling load for axially compressed cylindrical shells: state of the art and new perspectives

Necking of thin-walled cylinders via bifurcation of incompressible nonlinear elastic solids

“…The latter constitutive equation mimics the in-loading branch of a plastic solid and allows the eventuality of tensile bifurcations. Remarkably, while the behaviour of cylindrical shells under compression and for compressible materials is a famous topic in mechanics, [18][19][20] the model of Flu ¨gge 21 does not allow Fig. 1 Nominal stress vs. conventional strain obtained from a tensile test on a polypropylene (PP) thin-walled tube (6.5 mm initial diameter, 0.18 mm thickness, 205 mm length).…”

“…The latter constitutive equation mimics the in-loading branch of a plastic solid and allows the eventuality of tensile bifurcations. Remarkably, while the behaviour of cylindrical shells under compression and for compressible materials is a famous topic in mechanics, 18–20 the model of Flügge 21 does not allow tensile instabilities and was never extended neither to tension nor to incompressibility, which is the purpose of the present article. In particular, our theoretical approach retains the thinness of the tube wall through a condensation of the governing equations on the mean surface of the cylinder, thus defining a two-dimensional cylindrical shell.…”

Application of the Variational Method to the Large Deformation Problem of Thin Cylindrical Shells with Different Moduli in Tension and Compression

“…Thus, cylindrical shells have been regarded as an effective structural element, which is widely used in roof construction, pressure vessels and other engineering structures. There are many review works in this field, and they involve various aspects of the analysis and application of cylindrical shells, such as the earlier reviews on the buckling of moderately thick laminated cylindrical shells [ 21 ] and on the development of layered vessels using flat-ribbon-wound cylindrical shells [ 22 ], and recent reviews on the analysis of graphene nanoplatelet-reinforced cylindrical shells subjected to thermo-mechanical loads [ 23 ], on the recent progress in lightweight carbon fiber-reinforced lattice cylindrical shells [ 24 ], on the ring stiffened cylindrical shell structures [ 25 ] and on the knockdown factor of buckling load for axially compressive cylindrical shells [ 26 ], to list but a few. More recently, the natural frequencies optimization of circular cylindrical shells using axially functionally graded materials was investigated [ 27 ].…”

Influence of Initial Imperfections on PMMA Spherical Shell

“…In the research of accurately predicting the lower-bound buckling load under the influence of geometric defects, Bo and Xiangtao [17] found that the improved worst multiple perturbation load approach (WMPLA) can provide an improved knockdown factor(KDF) by examples in the open literature. Subsequently, Wang et al [18] found a new lower-bound curve that approximately produces a series of improved KDFs based on decades collection of test data. In another study, Yang et al [19] proposed a novel bi-stage random field parameter estimation method with limited samples which achieves the best performance in terms of accuracy, efficiency, and stability.…”