Buckling of thin-walled conical shells under uniform external pressure

finite length which were subjected to combined axial and
external pressure. They showed that this behavior is
dependant on geometry, loading and initial imperfections.
Also Yamaki [8] has studied the nonlinear behavior of
externally pressurized cylindrical shells and effects of
geometrical imperfections. Further, other authors have
studied stability of the shells that are outlined in the
perspective to come.
Performing test on manufactured specimens is the most
steadfast method in engineering researches. In this paper,
six frusta and four shallow conical cap (SCC) specimens
have been manufactured and tested under the effect of
uniform external pressure. The material consisted of mild
steel with yield stress of 277 MPa [9]. Boundary conditions
are all simply supported in which only a radial constraint is
provided at the edges. A loading of uniform external
pressure is produced by gauged vacuum pump using
suction process. The stages of prebuckling, initial buckling,
overall buckling and collapse have been observed and
evaluated and nonlinear response of these conical shells has
been studied.
2. Experimental syllabus
2.1. Model size
In deciding on the model size for testing, a number of
issues were considered. Firstly, the models should not be
too large, to avoid any undesirable inconveniences
associated with laboratory testing. Secondly, the models
should not be too small, so as to cause difficulties in their
fabrication. Thirdly, the radius-to-thickness ratios (R/t) of
the models should be analogous to those used in realistic
structures, since the effect of interaction between yielding
and buckling needs to be appropriately captured in the
tests. Typical real values for the R/t ratio are within the
range of 300–1000. As thin steel sheets of 0.5 mm and
above can be easily obtained, welded or soldered effortlessly
to produce high quality models with special welding
machine or soldering apparatus, it was decided that the
models ought to be of 600 mm in diameter. Consequently,
Table 1
Dimensions and aspect ratios of the specimens
Specimen code Thickness t
(mm)
ARTICLE IN PRESS
B.S. Golzan, H. Showkati / Thin-Walled Structures 46 (2008) 516–529 517
Top radius
(mm)
Bottom radius
(mm)
proper (R/t) ratios can be achieved with different steel
sheet thicknesses.
2.2. Test specimens
In this paper, six different frusta specimens were used,
namely SC1, SC2, SC3, SC4, SC5, SC6 along with four
SCC specimens represented by SCC1, SCC2, SCC3,
and SCC4. . The properties of all models are outlined in
Table 1. The thickness of specimens is totally constant. The
frusta specimens have the same lower base diameter of
600 mm whereas the top base of the first three measures
200 mm in diameter and in the second three it is 100 mm.
The SCC specimens have the same lower base diameter of
600 mm except for SCC3 with a base diameter equal to
500 mm. For the detailed geometry and slenderness ratios
of specimens refer to Table 1. Edge conditions are all
simply supported, in which only radial restraint was
provided.
Three tensile coupon tests were performed identically to
obtain the properties of material. The yield and failure
stresses of this mild steel are 277 and 373 Mpa, correspondingly.
The Young modulus acquired, equals 210 GPa.
Each specimen was assembled by cord-oriented welding
over the rolled sheet fragment edges, as is shown in Fig. 1.
A loading of uniform external pressure is produced by
gauged vacuum pump using suction process.
2.3. Fabrication modus operandi
An important issue in shell buckling experiments is the
fabrication of good quality specimens, including the choice
of material and fabrication method. Many fabrication
techniques have been developed [10,11], among which are
electroforming (making duplicates by electroplating metal
onto a mold of an object, then removing the mold in which
the intricate surface details are precisely reproduced by this
process), thermal forming of plastics (PVC, polyethylene,
Lexan, or other materials) and cold working of metal
(spinning, explosive forming, or hydroforming). Most of
these are specialized laboratory techniques for fabricating
nearly perfect model shells. Where tests are intended to
Height h
(mm)
Semi-vertex
angle (a)
R/t R/r L/R L ¼ slant
length
SC1 0.6 100 300 223.6 41.81 500 3 1
SC2 0.6 100 300 403.2 26.36 500 3 1.5
SC3 0.6 100 300 565.7 19.47 500 3 2
SC4 0.6 50 300 165.8 56.44 500 6 1
SC5 0.6 50 300 374.2 33.75 500 6 1.5
SC6 0.6 50 300 545.4 24.62 500 6 2
SCC1 0.5 – 300 60 78.69 600 – 1.02
SCC2 0.8 – 300 60 78.69 375 – 1.02
SCC3 0.5 – 250 62.5 75.96 500 – 1.03
SCC4 0.8 – 300 75 75.96 375 – 1.03