“…This occurs because the changing planar geometry leads to a changing aspect ratio of the discretized finite elements with associated variations in numerical accuracy. We thus conjecture that the small root-mean-square error of the fitted power laws is by no means a statistical accident but reveals some of the underlying physics of the problem; at the very least, 2000 3000 4000 5000 6000 7000 8000 9000 10 000 0 Tennyson [49] Yamaki [43] Flügge [50] Arbocz [51] Almroth [52] Eßlinger & Geier [12] Hutchinson et al [53] Tennyson & Muggeridge [54] Wang et al [55] Jiao et al [56] Krishnakumar & Foster [57] Arbocz & Abramovich [58] Harris et al [59] Donnell [60] Lundquist [61] Verduyn & Elishakoff [62] Ankalhope & Jose [63] Abramian et al [23] Weingarten et al [1] 1 the importance of the Batdorf parameter in characterizing the probing stability landscape and imperfect buckling loads.…”
Section: (B) Cylinder Buckling Knockdown Factors From the Stability L...mentioning
confidence: 97%
“…3 Also included in this figure are 514 data points taken from 20 studies spanning more than 100 years of cylinder buckling experiments [ 1 , 12 , 23 , 43 , 48 – 63 ]. As such, the data shown include modern experiments on tightly dimensioned cylinders [ 57 ], as well as earlier, less accurate experiments on cylinders manufactured by rolling sheet metal around a mandrel with a single axial weld line [ 60 ]. Figure 4 Dataset of 514 experimental buckling results from [ 1 , 12 , 23 , 43 , 48 – 63 ] plotted in terms of recorded KDF versus Batdorf parameter, .…”
“…To test the four design guidelines against experimental data, each curve is plotted on one set of axes of Batdorf parameter, Z, against KDF (u * /u cl ) in figure 4. 3 Also included in this figure are 514 data points taken from 20 studies spanning more than 100 years of cylinder buckling experiments [1,12,23,43,[48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. As such, the data shown include modern experiments on tightly dimensioned cylinders [57], as well as earlier, less accurate experiments on cylinders manufactured by rolling sheet metal around a mandrel with a single axial weld line [60].…”
Section: (B) Cylinder Buckling Knockdown Factors From the Stability L...mentioning
confidence: 99%
“…3 Also included in this figure are 514 data points taken from 20 studies spanning more than 100 years of cylinder buckling experiments [1,12,23,43,[48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. As such, the data shown include modern experiments on tightly dimensioned cylinders [57], as well as earlier, less accurate experiments on cylinders manufactured by rolling sheet metal around a mandrel with a single axial weld line [60]. In general, the design curves can be split into three categories.…”
Section: (B) Cylinder Buckling Knockdown Factors From the Stability L...mentioning
The buckling response of axially compressed cylindrical shells is well known for its imperfection sensitivity. Mapping out a stability landscape by localized probing has recently been proposed as a rational means for establishing shell buckling knockdown factors. Probing using a point force directed radially inwards and perpendicular to the cylinder wall is based on the insight that a localized single dimple exists as an edge state in the basin boundary of the stable prebuckling equilibrium. Here, we extend the idea of probing to bi-directional inwards and outwards forces to trigger both single-dimple and double-dimple edge states. We identify key features of the ensuing probing stability landscape and generalize these to derive three design curves of varying conservatism that are a function of the non-dimensional Batdorf parameter only. Interestingly, the most conservative of the three knockdown curves bounds a large dataset of experimental buckling results from below, despite being derived from probing features of geometrically perfect cylinders. Overall, the three design curves permit a more nuanced design approach than legacy knockdown factors, as different levels of conservatism can be chosen based on expected manufacturing quality. For instance, the most and least conservative of the three design guidelines differ by a factor of 3 for the most slender cylinder geometries, and the associated reduction in safety factor has profound implications for efficient structural design.
This article is part of the theme issue ‘Probing and dynamics of shock sensitive shells’.
“…This occurs because the changing planar geometry leads to a changing aspect ratio of the discretized finite elements with associated variations in numerical accuracy. We thus conjecture that the small root-mean-square error of the fitted power laws is by no means a statistical accident but reveals some of the underlying physics of the problem; at the very least, 2000 3000 4000 5000 6000 7000 8000 9000 10 000 0 Tennyson [49] Yamaki [43] Flügge [50] Arbocz [51] Almroth [52] Eßlinger & Geier [12] Hutchinson et al [53] Tennyson & Muggeridge [54] Wang et al [55] Jiao et al [56] Krishnakumar & Foster [57] Arbocz & Abramovich [58] Harris et al [59] Donnell [60] Lundquist [61] Verduyn & Elishakoff [62] Ankalhope & Jose [63] Abramian et al [23] Weingarten et al [1] 1 the importance of the Batdorf parameter in characterizing the probing stability landscape and imperfect buckling loads.…”
Section: (B) Cylinder Buckling Knockdown Factors From the Stability L...mentioning
confidence: 97%
“…3 Also included in this figure are 514 data points taken from 20 studies spanning more than 100 years of cylinder buckling experiments [ 1 , 12 , 23 , 43 , 48 – 63 ]. As such, the data shown include modern experiments on tightly dimensioned cylinders [ 57 ], as well as earlier, less accurate experiments on cylinders manufactured by rolling sheet metal around a mandrel with a single axial weld line [ 60 ]. Figure 4 Dataset of 514 experimental buckling results from [ 1 , 12 , 23 , 43 , 48 – 63 ] plotted in terms of recorded KDF versus Batdorf parameter, .…”
“…To test the four design guidelines against experimental data, each curve is plotted on one set of axes of Batdorf parameter, Z, against KDF (u * /u cl ) in figure 4. 3 Also included in this figure are 514 data points taken from 20 studies spanning more than 100 years of cylinder buckling experiments [1,12,23,43,[48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. As such, the data shown include modern experiments on tightly dimensioned cylinders [57], as well as earlier, less accurate experiments on cylinders manufactured by rolling sheet metal around a mandrel with a single axial weld line [60].…”
Section: (B) Cylinder Buckling Knockdown Factors From the Stability L...mentioning
confidence: 99%
“…3 Also included in this figure are 514 data points taken from 20 studies spanning more than 100 years of cylinder buckling experiments [1,12,23,43,[48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. As such, the data shown include modern experiments on tightly dimensioned cylinders [57], as well as earlier, less accurate experiments on cylinders manufactured by rolling sheet metal around a mandrel with a single axial weld line [60]. In general, the design curves can be split into three categories.…”
Section: (B) Cylinder Buckling Knockdown Factors From the Stability L...mentioning
The buckling response of axially compressed cylindrical shells is well known for its imperfection sensitivity. Mapping out a stability landscape by localized probing has recently been proposed as a rational means for establishing shell buckling knockdown factors. Probing using a point force directed radially inwards and perpendicular to the cylinder wall is based on the insight that a localized single dimple exists as an edge state in the basin boundary of the stable prebuckling equilibrium. Here, we extend the idea of probing to bi-directional inwards and outwards forces to trigger both single-dimple and double-dimple edge states. We identify key features of the ensuing probing stability landscape and generalize these to derive three design curves of varying conservatism that are a function of the non-dimensional Batdorf parameter only. Interestingly, the most conservative of the three knockdown curves bounds a large dataset of experimental buckling results from below, despite being derived from probing features of geometrically perfect cylinders. Overall, the three design curves permit a more nuanced design approach than legacy knockdown factors, as different levels of conservatism can be chosen based on expected manufacturing quality. For instance, the most and least conservative of the three design guidelines differ by a factor of 3 for the most slender cylinder geometries, and the associated reduction in safety factor has profound implications for efficient structural design.
This article is part of the theme issue ‘Probing and dynamics of shock sensitive shells’.
“…Among those, Hutchinson et al (1971) gave the analysis using asymptotic formula given by Amazigo and Budiansky (1972) (based on Koiter's general theory) for the compressive buckling strength of axially loaded cylindrical shells with an axisymmetric cosine dimple imperfections. The effect of multiple large diamond shaped dimples on the buckling behavior and load carrying capacity of cylindrical shells under axial compression was investigated experimentally by Krishnakumar and Forster (1991). Hambly and Calladine (1996) took specimens of drinks cans (R/t = 350) with dents.…”
It is well known that thin cylindrical shell structures have wide applications as one of the important structural elements in many engineering fields and its load carrying capacity is decided by its buckling strength which in turn predominantly depends on geometrical imperfections present in it. Geometrical imperfections can be classified as local and distributed geometrical imperfections. But in this work, only local geometrical imperfection namely dent is considered for analysis. The main aim of this study is to determine the more influential dimensional parameter out of two dent dimensional parameters, one is the extent of dent present over a surface area and the other is dent depth, which affect the buckling strength of the cylindrical shells drastically. To account for the parameter "extent of dent present over an area", the dent is considered as circular dent and its amplitude is considered as dent depth. For this purpose, finite element (FE) models of cylindrical shells with a circular dent at half the height of cylindrical shells having different dent sizes are generated. These FE models are analyzed using ANSYS nonlinear buckling analysis. It is concluded that extent of dent present over an area is more influential than dent depth. To verify this conclusion further, FE models of cylindrical shells with two circular dents at half the height of cylindrical shell placed at 180˚ apart having different dent sizes are generated and analyzed.
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