Buckling of thin-walled conical shells under uniform external pressure

p cr p
125
120
115
110
105
By various substitutions [19], it can be shown that Eq. (1)
can be transferred to the form
0:92Eðte=RÞ 25
pcr ¼ , (2)
Le=R
where te is the effective thickness of cone t cos a; t the
thickness of cone; and Le the effective length of cone L/2
(1+r/R). Thus, conical shells subjected to external
pressure may be analyzed as cylindrical shells with an
effective thickness and length.
6.1. Sole-fish buckling mode
Fig. 8. Parametric considerations.
100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1-r/R
Fig. 9. Cone function.
An important parameter in buckling analysis of axisymmetrically
loaded shells, for instance, the models thrashed
out herein, is the number of circumferential waves in the
buckling mode layout. Notionally speaking, the buckling
mode is in the form of a single harmonic mode around the
circumference, but in a test, owing to the incidence of
imperfections, miscellaneous modes may be implicated. A
well-established way of construing geometric imperfection
and deformation measurements to decipher the dominant
harmonic modes and their relationship is to carry out
ARTICLE IN PRESS
B.S. Golzan, H. Showkati / Thin-Walled Structures 46 (2008) 516–529 525
Fourier decompositions. Such decompositions were not
carried out for the imperfection or deformation measurements
on these models, since the form of buckling that was
developed all over the cones was drastically outlying from a
well-ordered wave configuration. On such specimens there
was an overall buckling predisposed by position of weld
lines and efficiency of the supports and formation of the
initial leakage point. So as to set forth a better depiction of
this buckling, principally based on empirical remarks and
for the first time we coined the name ‘‘sole-fish buckling
mode’’ on this phenomenon. The spine of this animal can
better illustrate the weld line and its impact on the other
parts of the shell. The appearance of non-periodical waves
can be easily spotted from this plot.
7. Observations and milestones
7.1. Frusta specimens
In Figs. 10 and 11 a contrast is carried out between
initial and ultimate geometry of specimen SC5 in which the
maximum deformation is located roughly at the height
of 1
3 h.
In all shells of this study the loading was continued to
farther than the range of postbuckling behavior. It is
observed that a ‘‘V’’ shape yield line is developed in the
region close to the restrained boundaries of the frusta,
before failure takes place. The same phenomenon was
reported by Showkati [21]. InFig. 6 a typical behavior is
represented for specimen SC5 and SC6.
By escalating the external pressure, the failure mode
was gradually approached. In most specimens, incidence
of a very large displacement in one edge caused an
288
270
252
306
234
324
216
342
198
300
280
260
240
220
200
180
160
140
120
100
80
60
40
20
0
0
180
18
162
36
144
54
126
Fig. 10. Polar plot of final geometry measured on specimen SC5.
72
90
108