Effect of multiple holes on dynamic buckling of stubby shells:
An experimental and numerical investigation
H. Ravi Sankar, Venkitanarayanan Parameswaran *
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, 208016, India
ARTICLE INFO
Article history:
Received 4 February 2016
Received in revised form 5 May 2016
Accepted 23 May 2016
Available online 26 May 2016
Keywords:
Dynamic buckling
Cylindrical shells
Collapse triggers
Split-Hopkinson pressure bar
Elastic waves
A B ST R AC T
Current study investigates the deformation behavior and energy absorption of thin walled cylinders having
multiple holes when subjected to dynamic compressive loading. A split-Hopkinson pressure bar (SHPB)
was utilized for obtaining short duration dynamic loading. A SIM02-16 high speed camera was em-
ployed to capture the real time images of the deformation process. Holes of different diameters were
arranged in different geometric configurations along the length of the cylinders. The effect of holes and
their arrangement on peak load reduction and energy absorption characteristics of the cylinders was in-
vestigated. From the experimental study, it was observed that the diameter of the holes, their spacing,
and pattern of arrangement, all have a strong influence on the peak load transmitted by the cylinders
and also on the deformation pattern. Larger number of smaller diameter holes resulted in higher peak
load reduction. Subsequently a numerical analysis was carried out using the commercially available finite
element package Abaqus Explicit 6.11. The results of the analysis revealed that both the level of stress
concentration induced by the holes and the interaction of stresses between adjacent holes have a role
to play in reducing the peak load through controlling the deformation.
© 2016 Elsevier Ltd. All rights reserved.
1. Introduction
Thin walled cylindrical shells are widely used for impact damage
mitigation [1]. A proper energy absorbing device should be capable
of absorbing maximum energy, but at the same time reduce the
maximum load transmitted. Reducing peak load ensures that minimal
load is transferred to inhabitants in case of a vehicle crash or to the
protected equipment in case of critical infrastructure. Further, energy
absorption has to be maximized and cannot be compromised during
peak load reduction. Energy absorption can be maximized if the ge-
ometric parameters and the loading conditions allow the shells to
buckle in the axisymmetric concertina mode rather than in the non-
axisymmetric diamond mode of buckling or global bending mode
[2–5]. So critical understanding of the deformation behavior at higher
strain rates, particularly the initial collapse of such shells, is im-
portant for their successful use as impact energy absorbers.
The dynamic deformation behavior of cylindrical shells has been
extensively studied before [2–12]. When cylindrical shells are sub-
jected to impact, energy absorption takes place mainly by formation
of consecutive lobes during deformation [1–11]. In previous re-
ported studies, the dynamic loading is mostly achieved either by a
moving mass impacting a stationary cylinder or by impacting the
moving cylinder against a stationary rigid mass. Abramowicz and
Jones [2–5] conducted a series of static and dynamic experiments
on circular and square steel tubes and developed a theoretical formula
for predicting the mean crushing force and the half fold length of
the buckle. Florence and Goodier [6] investigated dynamic plastic
buckling response of thick cylindrical shells made of aluminum im-
pacted by a mass moving at high velocities. Wang et al. [7] established
critical velocities of the impacting mass for which the shell will buckle
either in the axisymmetric mode or in the non-axisymmetric mode.
Langseth and Hopperstad [8] observed that the dynamic mean force
is much higher than the static mean force indicating the presence
of significant inertia effects in square tubes made of Al 6060 alloy.
Karagiozova et al. [9–12] carried out extensive numerical studies
on the effects of inertia of shell and striker, material properties, loading
technique and geometry of the shells on the dynamic buckling phe-
nomena of aluminum and steel tubes. They established a regime
for the loading parameters which cause different modes of buck-
ling [10] and confirmed that high velocity–low mass impacts produce
dynamic plastic buckling whereas low velocity–high mass impacts
produce dynamic progressive buckling. They observed that inertia
of the shell and striker has a decisive effect on the initial buckling
behavior of the shells [9,10]. Further studies affirmed that shells made
of strain rate insensitive materials deform either by dynamic plastic
or progressive buckling whereas those made of rate sensitive ma-
terials exhibit primarily dynamic progressive buckling [11]. The
geometric parameters, h/L and h/R (where h, R and L are respec-
tively the wall thickness, radius and length of the cylinder) and the
* Corresponding author. Department of Mechanical Engineering, Indian Institute of
Technology Kanpur, Kanpur, 208016, India. Tel.: +91 512 2597528; Fax: +91 512 2597408.
E-mail address: venkit@iitk.ac.in (V. Parameswaran).
http://dx.doi.org/10.1016/j.ijimpeng.2016.05.014
0734-743X/© 2016 Elsevier Ltd. All rights reserved.
International Journal of Impact Engineering 96 (2016) 129–145
Contents lists available at ScienceDirect
International Journal of Impact Engineering
journal homepage: www.elsevier.com/locate/ijimpeng