Buckling of thin-walled conical shells under uniform external pressure

supports. To ensure that the brink is properly tenable in the
groove it is covered by a grooved rubber and both the
groove of rubber and the rim is filled with silicone sealant.
Then connecting the vacuum pump to the rig the process of
air suction is conducted under the specimen. This trend is
performed in such a way that the loading is exerted
incrementally and in all stages every thing is under the very
control so that the specimen is not destroyed abruptly to
not let us study the process hesitantly and exhaustively.
3.2. Frusta testing system
The test rig of the frusta specimens is composed of two
parts (Fig. 3), which was invented by the authors. The first
part is designed to hold the test specimen at the desired place,
which is composed of two rigid circular grooved plates.
These grooves are entrenched in both sides of specimen.
Four threaded long bars are provided to adjust the plates for
the specimen height. The second part of the rig consisted of a
small platform to be used for installation of vacuum pump.
This pump is employed to generate uniform external pressure
over the shell surface. Careful measurements of the test
results were done by six circumferentially and meridionaly
mounted strain gauges, a manometer and four transducers.
All collected data were processed using a data logger and a
software named UCAM-20PC.
3.2.1. Setting up the frusta
The upper and lower brinks of the frusta were covered
by grooved rubber and then silicon glue was used over all
openings to prevent any possible air seepage during the
suction process. The frusta were placed on the lower
grooved rigid plate. For specimens SC1 and SC4, as the
slant of their inclined surfaces exceeded far more than
vertical position, they could luxate from the grooves; so a
special ring truncated on the edges equal to the slant of the
surfaces was employed to not let the frusta edges luxate
outwardly in case of higher loading and disarticulation.
For the top edges, as there is liability to luxate inwardly,
another specific round plate chamfered inwardly at the
edges is located to prop up this susceptible location
(Fig. 3). Using four threaded bars, the upper plate was
Supporting ring
Fig. 3. View of the frusta test rig and chamfered ring to support the lateral
luxating of edges.
ARTICLE IN PRESS
B.S. Golzan, H. Showkati / Thin-Walled Structures 46 (2008) 516–529 519
placed exactly over the top edge of the frusta in which the
simply supported boundary conditions were geared up at
both trimmings. The modification nuts could foil any axial
load to be applied to the specimens. On the top plate, three
holes were drilled for the purpose of air suction,
manometer installation and air release valve assembly to
control the rate of loading and unloading on shell
specimens. The produced pressure was measured by the
above-mentioned monometer. Fig. 3 shows a total view of
test provision.
3.3. Measurement of imperfections and deformations
Buckling of shells is generally known to be sensitive to
geometric imperfections; so precise surveys of initial
geometric imperfections are an essential step in any high
quality shell buckling experiments. In addition, it is also
desirable to have precise measurements of deformed shapes
of the shell during its loading so that the buckling/collapse
mode can be accurately determined and compared with
theoretical predictions. Many shell imperfection measurement
techniques have been developed [18]. LVDTs or other
contacting probes were usually used in most of the earlier
measurement systems [12,13]. For very thin shells with a
relatively low transverse stiffness, the small probe force
may induce distortions of the shell surface, so non-contact
probes are favored.
A simpler way has been applied in the present measurement
system for appraising both initial imperfections and
displacements. Seeing that the complete measurements of a
conical surface require a three-dimensional survey of the
radial, circumferential and meridional coordinates, manual
scanning was implemented as the measurement technique.
At first a number of meridians were drawn on the
expanded surfaces of the cones at specified degrees, and
then they were assembled, conducting their meridional
joints. After fabricating, circumferential segments were
segregated on the surface and then the cone was installed in
its place. Subsequently, at the contiguous of each meridian
a ruler was mounted and another ruler was employed to
measure the horizontally projected distance between nodes
of drawn meshes and the edge of the specimens identified
by the ruler rim. In each node of obtained mesh, three
coordinates of r, y and z are measured carefully in all
specimens. Therefore, a real geometry of shell is obtained
and then is used in finite element modeling of the structure
for further comparative analyses.
Despite the relatively stocky geometry of the specimens,
initial geometric imperfections were recorded on all specimens,
with the method and mesh outlined above. In order to
render these measurements functional for comparative
studies and numerical modeling, the unrefined imperfections
were subjected to some data processing techniques that
enable the identification of dominant modes and facilitate
comparisons of imperfections with observed buckling and
collapse modes. Fig. 4 shows typical imperfection layouts for
some of the models, (inward/outward) in two different views.