On the development of shell buckling knockdown factors for imperfection sensitive conical shells under pure bending

Abstract

Thin-walled cylindrical shells are used as adapters between cylindrical shells of different diameters in launch-vehicle systems or as tailbooms in helicopters. A major loading scenario for cylindrical shells is bending. The buckling moment of these shells is very sensitive to imperfections (geometry, loading conditions) which results in a critical disagreement between theoretical and experimental results for axially loaded cylindrical shells. The design of these stability critical shells is based on classical buckling loads obtained by a linear analysis which are corrected by a single knockdown factor (0.41-NASA SP-8019) for all cone geometries. This practice is well established among designers and hasn't changed for the past 50 years because the buckling behavior is till today not very well understood. Within this paper a reduced stiffness analysis for cylindrical shells under pure bending is performed. Data of previous experimental testing campaigns are used to validate the new design criteria for different cylindrical shell geometry configurations. The results show that the application of the new design recommendation for cylindrical shell structures results in increased knockdown factors for the buckling moment which in turn may lead to a significant weight reduction potential. All ABAQUS-Python scripts and the results generated for this article are deposited in the Elsevier repository.

Experimental studies on snaking in 3D-printed cylindrical shells under axial compression using photogrammetry

“…As the dimple exacerbates, the first limit point decreases to a minimum and then increases to a certain load, which corresponds to the limit point of a fully localized single-dimple mode in the post-buckling regime. These observations are in line with the single perturbation load approach studies by Wagner [44], where it is shown that the shell structures collapse at this lower load. Friedrich & Schröder [45] also reported a similar observation that the local buckling in a displacement-controlled study corresponds to the global buckling in a load-controlled analysis.…”

“…In §2, the snaking sequence of the shell is traced using the modified Riks solver, but it is impossible experimentally to trace the fingers of the load–displacement graph. Hence, to match the experimental buckling and post-buckling response, a nonlinear analysis is performed using a Newton–Raphson solver with artificial damping in ABAQUS [44,49]. Using the inverse distance weighted interpolation method, the measured geometrical imperfection is incorporated into the FE mesh [48,50].…”

Impact resistance and energy absorption ability of bio-mimetic thin-walled structures with hollow columns under impact loading

“…15 Some more optimized finite-element methods have been further proposed to divide the mesh of complex shell structures accurately with cutouts, to ensure the high efficiency and precision for numerical simulation. 16,17 The protective shield is another type of typical spherical–cylindrical thin-walled shell structure, which is widely used in underwater vehicles. 18 The buckling and post-buckling behaviors of the unstiffened or stiffened spherical dome are regarded as a classic and challenging topic.…”

A direct approach to progressive buckling design considering ratcheting deformation

“…This method, however, is limited to these structures with small initial geometrical imperfections. In fact, buckling failure, usually caused by large displacement, is very sensitive to initial geometrical imperfections [38][39][40][41]. So the Clement's method could not predict the progressive buckling load for structures with large initial geometrical defects.…”