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point load. On the basis of the observed experimental deformed profiles it has been found that the shells deform
in axisymmetric mode of collapse. Load–compression curves of the deformed specimens are studied. A Finite
Element computational study of the development of this axisymmetricmode of collapse is also carried out using
FORGE2 [11] code to propose a computational model. Computational model has been verified by comparing
the experimental and computed results of the deformed shapes and their corresponding load–compression and
energy–compression curves. On the basis of the variations of the computed strains and stresses the mechanics
of the mode of collapse has been studied and discussed.
2 Experimental work
Aluminium hemispherical shells of R/t ranging between 25 and 43 were compressed between flat platen and
a hemispherical mandrel on a Universal testing INSTRON machine (see Table 1). A hemispherical nosedmandrel having 22mm diameter and 85mm length made up of hardened tool steel was used for applying con-
centrated load on the shell [8]. Commercially available aluminium sheets of standard thickness were obtained
and the spherical shell specimens used in the experiments were made by the process of spinning. Shells of
different radius and thickness were obtained. The shells were filled with emulsion of plaster of Paris and dried.
By holding these shells in lathe machine the edges were cut for accuracy with respect to the axis of shells.
The shells were tested in as-received condition. The shells were placed on the stationary flat platen and the
hemispherical mandrel fixed on the moving crosshead was moved in downward direction on its axis with a
speed of 2mm/min. Figure 1a shows the loading arrangement for the experimental work. Load versus cross-
head movement plot was obtained from the chart recorder of the machine. The experiments were interrupted at
regular intervals for studying the mode of collapse and for the measurements of radius of rolling plastic hinge
rp. Compression was continued up to 40–50mm movement of the mandrel in downward direction. The radius
of rolling plastic hinge rp was measured at selected number of sections at any typical stage of compression;
an average of the readings was obtained. For this measurement the radius gauges were used.3 Experimental results
All the shells were collapsed in an analogous mode of deformation throughout the compression process. Dur-
ing the compression of a typical spherical shell (see Fig. 1b), two stages of deformation were noticed. These
are designated as stage I and stage II. In the beginning of the compression process up to few milimeters of
compression all the spherical shells were deformed with formation of a small indent at the point of contact of
shell with the mandrel along with the local flattening of the adjoining area. This was designated as the stage I
deformation. It was observed that as the value of R/t increases the range of compression over which the stage
I deformation occurs decreases.With the progress of compression an axisymmetric inward dimple was formed
due to the development of a rolling plastic hinge; this is the stage II deformation. In the stage II deformation
with increase in compression (h) the axisymmetric inward dimple expands due to the radial outwardmovement
of the rolling plastic hinge.
It is already seen that over a large range of compression of spherical shells an inward dimple formation
takes place and with progress of compression this axisymmetric inward dimple expands due to the radial
outward movement of the rolling plastic hinge. As a result the radius of rolling plastic hinge rp decreases with
the progress of compression.
It was found that for all the shell specimens the load in the load–compression curve increased continuously
throughout the compression process (see Fig. 5a). The rate of increase in load decreased with increase in R/t