Buckling of thin-walled conical shells under uniform external pressure

the shells by naked eyes. These deformations continued to
grow with further loading, leading to obvious buckles of
non-similar wavelengths. The development of these buckling
lobes was associated with a reduction in the load
carrying capacity as it led to some deformations at the
radial base edge that caused seepage of the air. Explicitly,
the specimens indicated a stable postbuckling path.
Ultimate failure occurred by the formation of a plastic
collapse mechanism with nearly non-uniform plastic
deformations over a large part of the circumference that
resulted in failure of the supports to sustain the proper
function. Figs. 6 and 7 show the models after the failure.
Table 2
Buckling pressure and mode of the specimens
Specimens Buckling
load
obtained by
experiments
(KPa)
Buckling
load
obtained by
FEA (KPa)
Buckling
load
obtained by
Jawad
equation
(KPa)
ARTICLE IN PRESS
Mode
numbers by
experiments
SC1 25 28 35.4 7 (skirt mode)
SC2 20 25 32.3 7 (skirt mode)
SC3 14 22 24.68 6 (skirt mode)
SC4 20 27 24.1 6 (skirt mode)
SC5 25 40 31.35 6 (skirt mode)
SC6 21 35 27.27 6 (skirt mode)
SCC1 5.7 6.2 3.83 Sole-fish mode
SCC2 8 14.5 20.3 Sole-fish mode
SCC3 7.5 13 4.02 Sole-fish mode
SCC4 10 25 16.2 Sole-fish mode
Table 3
Layout of strain gauges and transducers on all specimens
These results show that most of the buckles on the
models were amplified from initial geometric imperfections
(Fig. 4). The buckling load can be defined as the pinnacle
load of a nonlinear load–displacement curve. Such a
buckling load incorporates the effect of imperfections.
For the in attendance models, the buckling load of the
corresponding perfect structure is believed to be a good
assess of its veracity, but the determination of buckling
load is not straightforward. A rough approach may be, to
take the load at which the strain readings started to
diverge, the same as the buckling load. This, on the other
hand, does not allocate a precise definition of the buckling
load as the strain readings had some differences right from
the beginning of loading due to the presence of initial
imperfections. Another drawback of using strain readings
is that due to the cost and installation considerations,
normally, merely part of the cone circumference is installed
with strain gauges. So the most sought-after locations of
strain measurements for buckling load determination may
have been disregarded. For these reasons, the use of
displacements of the cones, which are appraised around the
whole circumference in the current set-ups, is preferred for
attaining the buckling loads.
In Table 2, the buckling pressures and modes of six
frusta and four SCC specimens in diverse test stages are
tabulated. Before initial buckling the behavior of shell
is quite static with no pragmatic buckle lobe. As a
comparison three obtained buckling loads from different
approaches have been presented in this table. It is quite
apparent that the experimental outcomes are taking up the
lower range of load owing to the presence of initial
Strain gauges Transducers
SH1 horizontal
gauge
SV2 vertical
gauge
SH3 horizontal
gauge
SV4 vertical
gauge
SH5 horizontal
gauge
SV6 vertical
gauge
SC1 3061, 140 mm 2451, 110 mm 1501, 90 mm 1221, 60mm 541, 50mm 181, 80 mm 3121,
90 mm
SC2 771, 30mm 961, 350 mm 1341, 120 mm 1981, 220 mm 2581, 270 mm 3421, 170 mm 181,
150 mm
SC3 1901, 230 mm 2471, 385 mm 3071, 110 mm 81, 210 mm 691, 60 mm 1251, 310 mm 1501,
310 mm
SC4 1751, 120 mm 1751, 170 mm 1501, 70mm 481, 220 mm 3481, 50 mm 2641, 70 mm 2051,
70 mm
SC5 91, 120 mm 3511, 120 mm 2791, 30 mm 2421, 270 mm 1891, 120 mm 991, 320 mm 3421,
70 mm
SC6 8.51, 70mm 261, 170 mm 941, 270 mm 1631, 370 mm 2051, 95 mm 2911, 220 mm 3511,
120 mm
SCC1 3421, 30 mm 3061, 280 mm 2701, 120 mm 1621, 150 mm 1081, 30mm 541, 280 mm 3421,
120 mm
SCC2 3261, 80 mm 3401, 30 mm 1851, 130 mm 2751, 10mm 701, 20 mm 1231, 230 mm 3151,
80 mm
SCC3 511, 220 mm 2831, 220 mm 2311, 30 mm 2051, 120 mm 1771, 70mm 771, 120 mm 3471,
70 mm
SCC4 1081, 30 mm 1081, 288 mm 91, 120 mm 2971, 170 mm 2611, 285 mm 1891, 70 mm 1441,
30 mm
All distances are measured from the bigger base on the slant length.
B.S. Golzan, H. Showkati / Thin-Walled Structures 46 (2008) 516–529 521
T1 T2 T3 T4
1441,
190 mm
431,
100 mm
1501,
160 mm
601,
220 mm
2881,
220 mm
171,
170 mm
2341,
30 mm
2251,
20 mm
2571,
30 mm
721,
220 mm
841, 3481,
90 mm 90 mm
2311, 3021,
130 mm 50 mm
2701, 3451,
360 mm 210 mm
3481, 2641,
70 mm 120 mm
1981, 1261,
170 mm 120 mm
1201, 2491,
270 mm 220 mm
901, 1261,
70 mm 280 mm
1691, 301,
80 mm 230 mm
Apex 1031,
120 mm
3061, 1441,
285 mm 150 mm