An Analytical Insight into the Buckling Paradox for Circular Cylindrical Shells under Axial and Lateral Loading

Abstract

A large number of authors in the past have concluded that the flow theory of plasticity tends to overestimate significantly the buckling load for many problems of plates and shells in the plastic range, while the deformation theory generally provides much more accurate predictions and is consequently used in practical applications. Following previous numerical studies by the same authors focused on axially compressed cylinders, the present work presents an analytical investigation which comprises the broader and different case of nonproportional loading. The analytical results are discussed and compared with experimental and numerical findings and the reason for the apparent discrepancy on the basis of the so-called “buckling paradox” appears once again to lay in the overconstrained kinematics on the basis of the analytical and numerical approaches present in the literature.

An investigation into the plastic buckling paradox for circular cylindrical shells under non-proportional loading

“…Shamass et al (2014) concluded that the main root of the discrepancy between the two plasticity theories can be found in the assumptions made in many analytical treatments with regard to the shape of the buckling modes, a simplification which gives origin to an excessively constrained kinematics, in turn counterbalanced by the material description of the deformation theory of plasticity. This fact has also been confirmed to a certain extent by analytical investigations (Shamass et al, 2015).…”

“…The root of the discrepancy can be thought to lay, once again (see Shamass et al, 2014Shamass et al, , 2015, in the harmonic buckling shapes assumed in the circumferential direction.…”

Plastic Buckling Paradox: An Updated Review

“…Again, he found that the flow theory was more sensitive to the interactive loading than the deformation theory, although the critical loads predicted by flow theory were smaller than those predicted by the deformation theory in some loading regions. Shamass et al (2014;2015a;2015b;2017) investigated numerically the plastic buckling of cylindrical shells subjected to axial compressive load ( Figure 8A) or to combined external pressure and axial tensile load ( Figure 8B). The numerical results were compared with accurate physical test results conducted by Lee (1962) and Batterman (1965) for cylinders under axial compressive load and Blachut et al (1996) and Giezen et al (1991) for cylinders subjected to combined actions.…”

“…On the other hand, the kinematic was free in the finite element analysis. Overall, the analytical analyses of the elastic-plastic buckling of cylinders subjected to non-proportional loading (i.e., combined external pressure and tensile load) studied by Shamass et al (2015a) showed that the discrepancies in the analytical plastic buckling pressures predicted from both the flow and deformation theories of plasticity take place when the buckling modes predicted by the plasticity theories do not coincide. This was also noticed by Guarracino and Simonelli (2018), who pointed out FIGURE 9 | Comparison between the buckling stresses obtained numerically with and without kinematic constraints (Shamass et al, 2014(Shamass et al, , 2015a(Shamass et al, ,b, 2017.…”

“…Several researchers accepted this fact and made reference only to the deformation theory in their analytical analysis (Mao and Lu, 2002;Zhang et al, 2015). The main aim of this paper is thus to present a critical review of the available literature and to illustrate the most recent explanations proposed by Shamass et al (2014;2015a;2015b;2017) and Simonelli (2017, 2018). The review is directed to a broad audience and, for this reason, many concepts are recalled and simplified as much as possible in order to be palatable to nonspecialists in the field.…”