REVIEW OF BUCKLING IN VARIOUS STRUCTURES LIKE PLATE & SHELLS

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IJRET: International Journal of Research in Engineering and Technology
eISSN: 2319-1163 | pISSN: 2321-7308
REVIEW OF BUCKLING IN VARIOUS STRUCTURES LIKE PLATE &
SHELLS
Amit Patil1, Amol Kolhe2, Abdul Sayeed AW Shaikh3
1Asst. Professor Department of Mechanical Engineering, Pad. DR D Y Patil Institute Engineering & Technology, Pimpri,
Pune Maharashtra, India
2Asst. Professor Department of Mechanical Engineering, Pad. DR D Y Patil Institute Engineering & Technology,
Pimpri, Pune Maharashtra, India
3Asst. Professor Department of Mechanical Engineering, P.R.Pote (Patil) College of Engineering & Management,
Amravati, Maharashtra India
Abstract
This paper represents discussion about the Buckling mechanism in the cylindrical vessels and plates as buckling is characterized by
sudden failure of structural member subjected to high compressive stress, where the actual compressive stress at the point of failure is
less than the ultimate compressive stresses that the material is able to withstand. Pressure vessels are the equipments which are used
for the storage of gases or liquids at specific temperature and pressure condition. The load carried by these pressure vessels also
imparts forces on its shell structure which are likely to be buckle
Keywords: buckling, cylinder, shell, FEA, Investigation
----------------------------------------------------------------------***----------------------------------------------------------------------
1. INTRODUCTION
conditions and for different cases such as shell with one end
pinned other free, shell with intermediate length, shell with
Basically buckling is the phenomenon associated with failure
open end. .G. Teng *, F. Chan 1 (2000) the study is all about
of column like structures which are having more length. In the
the elastic buckling strength of T-shaped ring beam used for
design of structures like pressure vessel, piping systems there
Tanks. The paper focuses on the new approximation by using
are mainly two concerns viz; 1.Abiliy to support specified
the effective section method to relate the loading on tank with
load without experiencing excessive stresses.2 Ability of the
circumferential
compressive
stresses.
The
interpolation
structure to support a specified load without undergoing
formula developed by Jumikis and Rotter for annular plate
unacceptable deformation. The failure of vessels depends
ring beams is found to be useful for T-shaped ring beams. S.
upon factors such as, type of vessel, Support conditions, Type
Kyriakides*, T.A. Netto (2000) the authors have presented
of load, and Materials used. If we consider shell of the
study on the dynamics of propagation of buckles in pipelines
pressure vessel, due to its size its axial displacement is going
under external pressure. The analytical study has been carried
to be small as compared to its lateral deflection it may be
out with Finite Element Model with ability to simulate
termed as buckling. The main objective of this review paper is
dynamics of buckle propagation and results are validated by
to discuss the work of various researchers on this buckling
experimental results. G. Michel *, A. Limam, J.F. Jullien
phenomenon with regards to all types of vessels, piping
(2000) the authors have presented study on the buckling of
systems, plates etc.
cylindrical shell with static & dynamic loadings due to seismic
activity. Finite Element Model simulation helped to know the
2. LITERATURE REVIEW
effect of vibration excitation which results into the large
W. Guggenberger a, R. Greiner a, J.M. Rotter b,* (2000) the
deformations and decrease in the stiffness of the shell. G.
authors have presented work on the buckling behavior of
Michel a, A. Combescureb, J.F. Jullien a,* (2000) the authors
cylindrical shells provided with discreet supports. This work
have presented research work on the dynamic buckling of the
has been carried out in the elastic-plastic range which results
cylinders under shear loading with the help of FEM based
in complications and suggests more work need to be. for
simulation. First part of study talks about the experimentation
defining buckling strength for the design of structures. The
and FEM codes being used. Second part of the study shows
nature of the study is linear & non - linear behavior of the
static tests and FEM calculations done. Third part is the
cylinders with discrete supports, for given loading conditions.
discussions of dynamic results. Hui-Shen Shen (2001) the
Rodney Pinna a,*, Beverley F. Ronalds b (2000) the study
authors have presented research work on post buckling
focuses on the buckling of shells subjected to hydrostatic
analysis of shear deformable cross-ply laminated cylindrical
loadings. The study is carried out with various boundary
shell under combined action of external pressure and axial
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Volume: 03 Issue: 04 | Apr-2014, Available @ http://www.ijret.org
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IJRET: International Journal of Research in Engineering and Technology
eISSN: 2319-1163 | pISSN: 2321-7308
compression. The study accounts for nonlinear pre buckling
obtained. Walter Wunderlich , Ursula Albertin (2002) the
deformations and initial geometric imperfections of the shell
authors have presented work on the buckling behavior of
along with boundary layer theory of shell buckling. With the
spherical shells subjected to external pressure with very
help of single perturbation method interactive buckling loads
limited information. The present study is carried out for
and post buckling equilibrium paths were determined. Mark
spherical shells for defining new design rules with relevant
W. Hilburger a,c,*, Vicki O. Britt b, Michael P. Nemeth c (2001)
details like boundary conditions, material properties and
the authors have presented research work on buckling
imperfections. Mark W. Hilburger , James H. Starnes Jr.
behavior of compression -loaded quasi-isotropic curved
(2002) the authors have presented work on analytical as well
panels with a centrally located circular cutout by analytical
as experimental study of effects of imperfections on the non-
and experimental method. Analytical results are generated
linear buckling behavior of thin walled compression loaded
with the help of Finite Element Method which consists of the
graphite-epoxy cylindrical shells. The research comprises of
effects of elastic circumferential edge restraints on the pre
traditional and non- traditional imperfections. Non-linear static
buckling and buckling response of a selected panel.Resuts
and non-linear transient analysis of shell is carried out. Seung-
shows that due to circumferential edge restraints there will be
Eock Kim , Chang-Sung Kim (2002) the objective of this
significant rise in buckling load. I.P. Pasqualino*, S.F. Estefen
research
work
is
to
evaluate
buckling
strength
of
(2001) this study is all about the non linear buckling
geometrically perfect and imperfect cylindrical shells and
propagation seen in deepwater piping system. The study
tanks subjected to axial compressive load. Numerical analysis
consists of thin shell theory, elastic-plastic behavior of
is carried out with sue considerations to modeling method,
materials. Finite difference method for solving equilibrium
element type and required number of elements. J. Bachut*
equations, at last all the experimental data & numerical results
(2002) the author has presented theoretical as well as
are correlated. Carl T.F. Ross, Andrew P.F., Little (2001) the
experimental study on buckling of barreled shells subjected to
authors have presented work on corrugated carbon fiber
external pressure. During the study sensitivity of buckling,
cylinder subjected to external pressure resulting into buckling.
geometric imperfections are also studied. C.A. Schenk, G.I.
For the purpose of theoretical study by using axisymmetric
Schueller (2003) the authors have presented study of buckling
thin-walled shell elements Finite element model is prepared.
analysis of thin-walled cylindrical shells with random
Experimental results are based on strain gauges. Comparison
geometric imperfections axial compressive load. Numerical
of both results shows that experimental results are good.
study is done by using direct Monte Carlo Simulation in
Jianghong Xue , Michelle S. Hoo Fatt* (2001) this study is all
context with finite element method. C.T.F. Ross a*, Bak Hock
about the buckling pressure propagation in the pipelines with
Huata, Tay Boon Chei a, Chai Min Chong a, M.D.A. Mackneyb
non-uniform thickness. However the results of this study are
(2003) the authors have presented study on the buckling of
forming basis for the buckling pressure propagation in the
GRP Hemi-ellipsoidal dome shells with different aspect ratio
corroded pipes which will fail either by shell buckling or the
under external hydrostatic pressure. Theoretical study is
local buckling. Gyeong-Hoi Koo*, Bong Yoo,
Jong -Bum
carried out by using finite element method in which both
Kim (2001) this paper is a study of finding out the buckling
material and geometry non-linearity taken into account. Cho-
strength and buckling mode shape of the reactor vessel of the
Chung Liang a*, Hung-Wen Chen b (2003) the authors have
Korea advanced liquid metal reactor (KALIMER) subjected to
presented study on the optimum design of fiber-reinforced
seismic loads. The study is carried out by means of numerical
composite cylindrical skirts used for rocket motor casing
simulation methods, Eigen value buckling analysis, non-linear
subjected to buckling. A skirt is a potential element for weight
buckling analysis with and without the effect of plasticity. X.
reduction in rocket motors as it leads to reduction of the total
H. Shi a,b *, Y. G. Gao a,b (2001) this paper shows that the
weight of solid rocket motor. Due to its significance for solid
concept of generalized new dimensionless number, response
rocket motors, the aim of this paper is to investigate the
number Rn(n) used for the study of elastic, plastic, dynamic
optimum design under aerodynamic torque and axial thrust.
elastic, dynamic plastic buckling problems of plates, columns
Classical lamination theory is used for the weight optimization
and shells. Michelle S. Hoo Fatt*, Jianghong Xue (2001) The
of rocket casing. M. Ozakca * , N. Taysi, F. Kolcu (2003) the
authors have presented research work on the buckling pressure
authors have presented buckling analysis of annular and
propagation in the corroded pipelines. The study is supported
circular plates with finite element approach. Through number
by deriving Rigid-plastic solutions for the steady-state, quasi-
of buckling analysis parameters like accuracy, efficiency and
static buckle propagation pressure in corroded pipelines and
convergence are explored. P.K. Das a,*, A. Thavalingam a, Y.
comparing with the finite element results (ABAQUS). X.
Bai b (2003) the main aim of this research work is to evaluate
Wanga; ,G.Lub,
D.G. Xiaoa (2002) this paper shows the
buckling and ultimate strength of ring stiffened shells
study carried out for non-linear thermal buckling behavior of
subjected to various modes of buckling due to axial
local delamination near the surface of fiber-reinforced
compressive load, radial pressure and combined loading.
laminated cylindrical shell. Young's modulus and coefficient
Parameters like bias and coefficient of variation are calculated
of thermal expansion are treated as function of temperature.
for reliability study. Azam Tafreshi a,*, Tobias Oswald b (2003)
With the help of energy principle critical temperatures,
this paper talks about the Finite element models developed for
different stacking pattern, and different radius of shell are
studying global, local and mixed mode buckling behavior of
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Volume: 03 Issue: 04 | Apr-2014, Available @ http://www.ijret.org
397

IJRET: International Journal of Research in Engineering and Technology
eISSN: 2319-1163 | pISSN: 2321-7308
composite
plates
with
embedded
delaminations
under
axisymmetric deformation mode to asymmetric one. Henrique
compression. The global modelling results were compared
Santos a , Cristo vao M. Mota Soares a,*, Carlos A. Mota
with corresponding experimental results. It is shown that the
Soares a , J.N. Reddyb (2005) this paper talks about the
numerical results for embedded delaminations agree very well
general semi-analytical finite element model
developed for
with the experimental results. In the course of global buckling,
bending, free vibration and buckling analysis of shells made of
a parametric study was carried out to identify the influence of
laminated orthotropic elastic material. The 3D elasticity theory
the delamination size, shape and alignment of a series of
is used and the equations of motion are obtained by expanding
composite plates. G.H. Nie* (2003) the author has presented
the displacement field. J. Mark F.G. Holst*, J. Michael Rotter
work on non-linear analysis of elastically restrained imperfect
(2005) this paper talks about the study
of initiation and
shallow spherical shells on pasternak foundation. By adopting
development
of
imperfections
due to local differential
the
asymptotic
iteration
method
(AIM),
an
analytical
settlement
at
the supported base and their effect
on the
expression concerning the external load and the central
elastic buckling of a thin cylindrical shell under axial
deflection of the shell is derived in a non-dimensional form.
compression. M. Barski a , J. Kruzelecki b,* (2005) the authors
Various parameters like geometrical imperfection, extensional
have presented work on, A thin- walled shell is loaded, by an
and shear moduli of foundation and edge-restraint coefficients
external pressure and lateral forces causing overall bending
as well as structural geometry are also considered which are
moment and the appropriate shearing force. As the equality
useful for buckling analysis of the structure. L. Grunitz* (2003)
constraints, the volume of material and the capacity of a shell
the author has presented his research work on the effect of
are considered. D. Redekop* (2005) the author has presented
welding on the buckling behavior of a spherical cap used in
method developed for predicting the buckling properties of an
tank closures, roofs and marine structures. This paper aims to
orthotropic shell subjected to a normal pressure. The solution
determine the buckling strength of clamped and hinged
is given within the context of the linearized Sanders-
spherical caps under uniform pressure with a circumferential
Budiansky shell buckling theory and applies the differential
weld depression by using the finite element method.
N.
quadrature method. Numerical results for buckling pressures
Ganesan , V. Pradeep (2005) the authors have presented
and mode shapes are given for complete toroidal shells J.C.
research work on the buckling & vibration of cylindrical shell
Virella a ,L.A.Godoy a,b, L.E.Suarez a (2006) the authors have
using FEA. Free vibration analysis carried out by considering
presented investigation of dynamic buckling
above ground
initial stress effect and added mass effect due to hot liquid.
steel tanks with conical roofs and anchored to the foundation,
Z.G. Wei a,b, J.L. Yu a,*, R.C. Batra b (2005) the authors have
subjected to horizontal parts of real earthquake records. The
presented
research work on the Dynamic buckling of thin
study attempts to estimate the critical horizontal peak ground
cylindrical shells under axial impact by analytical and
acceleration (Critical PGA), which induces elastic buckling at
numerical
method.
Analytical
study
is
based
on
the
the
top
of
the
cylindrical
shell,
for
the
impulsive
assumption
of the stressed/deformed state of a shell. The
hydrodynamic response of the tank-liquid system. B.A.
finite element method is used to analyze the collapse of an
Samsam Shariat, M.R. Eslami *(2006) this paper talks about
imperfect circular cylindrical tube with axial impact B.
the thermal buckling analysis of rectangular functionally
Skalleruda*a, K. Holthe a, B. Haugen b (2005) the main aim of
graded plates (FGPs) with geometrical imperfections. The
this research work is to evaluate Thin shell and surface crack
equilibrium, stability, and compatibility equations graded plate
finite elements for simulation of combined failure mode
are derived using the classical plate theory. Azam Tafreshi *
analysis. It consists of combination of a rectangular assumed
(2006) The author has presented his work on delaminated
natural deviatoric strain thin shell finite element and an
composite cylindrical shells subject to combined axial
improved linespring finite element. Roberto Brighenti* (2005)
compression and pressure are carried out varying the
the main aim of this research work is to study the buckling
delamination thickness and length, material properties and
behavior of cracked rectangular elastic thin plates under
stacking
sequence.
Based
on
the
FEA
results,
the
tension or compression, by considering the effects of various
characteristics of the buckling and postbuckling behaviour of
geometrical, mechanical and boundary conditions of the
delaminated composite cylindrical shells are evaluated. W.
problem. With the help of finite element method several
Szyc a,*, Z. Laszczyk a , K. Magnucki b (2006) the authors have
numerical parametric analyses are performed, in order to
presented work on
elastic buckling of an open sandwich
determine the critical load multiplier, in compression or in
cylindrical
thin-walled
panel
with three
edges
simply
tension, by varying some of the problem's geometrical and
supported and one edge free under axial compression. On the
mechanical parameters. B.P. Patel a,*, K.K. Shukla b, Y. Nath c
basis of force and moment equilibrium conditions for the shell
(2005) the authors have presented work on , thermoelastic
element, a set of the fundamental equations are derived. Omer
postbuckling behavior of cross-ply laminated composite
Civalek (2007) the author has presented his work on the study
conical shells under uniform temperature distribution The
of numerical solution of three-dimensional analysis of thick
finite deflection analysis is carried out to find out the
rectangular plates. The analysis uses discrete singular
relationship between the maximum deflection and the
convolution (DSC) method to know Free vibration, bending
temperature rise, and to evaluate the minimum temperature
and buckling of rectangular plates. Anton Hubner* , Matthias
parameter
that
causes
the
shell
deformation
from
Albiez, Dietmar Kohler, Helmut Saal. (2007) this paper aims
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Volume: 03 Issue: 04 | Apr-2014, Available @ http://www.ijret.org
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IJRET: International Journal of Research in Engineering and Technology
eISSN: 2319-1163 | pISSN: 2321-7308
to mark the discrepancies found in design codes for very long
and (2 ) both internal pressure and external bending moment,
externally pressurized cylindrical shells subjected to uniform
in order to determine the plastic collapse load by applying the
external pressure: although the failure is similar to the column
twice-elastic slope (TES) as recommended by the ASME and
buckling subjected to an external compressive load, design
to determine the buckling load. A.H. Sofiyev (2010) the
codes provide far smaller design values of the buckling load
author has presented work on buckling analysis of functionally
for the cylindrical shell in comparison to the ring. Based on
graded material (FGM) circular truncated conical and
the Euro code 3 (EN 1993-1-6) on shell buckling this study is
cylindrical shells subjected to combined axial loads and
directed and validated by numerical studies. X. Wang *, K.
hydrostatic pressure. Zhi-Min Li a,*, Zhong-Qin Lin a,b (2010)
Dong (2007) this research work comparises of an energy
the authors have presented work on Non-linear buckling and
method applied for studying
hygrothermal effects on local
postbuckling of a thick anisotropic laminated cylindrical shell
buckling for different delaminated shapes near the surface of
of finite length subjected to lateral pressure, hydrostatic
cylindrical laminated shells. The delaminated region is
pressure and external fluid pressure. F. Meng, H. Wang, X.
monolayer or multilayer. The effect of non-linear buckling for
Wang *,Z.Li (2010) this research paper aims about the local
local delamination of cylindrical laminated shells is obtained
buckling for the delimitation of an elliptic shape near the
by considering transverse displacements of sub-laminate
surface of piezoelectric laminated shells,
where local
shells. Hsuan-Teh Hu *, Jiing-Sen Yang (2007) this paper
delaminated sub-shells which are either
monolayer and
talks about the buckling resistance of fiber-reinforced
multiplayer,
and
the
geometrical
axes
of
elliptically
laminated cylindrical panels subjected to uniaxial compressive
delaminated sub-shells are not in line with the geometrical
force. The influences of panel thicknesses, curvatures, aspect
main axes of piezoelectric laminated base-shells. M. Shariati ,
ratios, cutouts and end conditions on the optimal fiber
H.R. Allahbakhsh (2010) the authors have presented work on
orientations and the associated optimal buckling loads of
buckling and post-buckling of steel thin-walled semi-spherical
laminated cylindrical panels have been studied. H. Sofiyev a,* ,
shells under different loadings, both experimentally and
Z. Zerin b, A. Korkmaz a(2008) the authors have presented
numerically. Various vertical compression loadings are
work on the stability of thin three-layered truncated conical
applied to specimens using methods such as a rigid flat plate
shells with functionally graded (FG) layer subjected to non-
and some rigid bars with circular, square and spherical cross
uniform lateral pressure varying with the longitudinal
sections, a rigid tube, a plate with a hole, and an indented tube.
coordinate. The material properties of the functionally graded
J.H. Wang* , A. Koizumi (2010) the authors have presented
layer are assumed to vary continuously through the thickness
work on the bucking of cylindrical shells with longitudinal
of the shell. Seong-Hwa Hur, Hee-Jin Son, Jin-Hwe Kweon *,
joint with experimental and numerical analysis. It was stated
Jin-Ho Choi (2008) the present research work focuses on the
that
the
buckling behavior
of cylindrical
shells
with
postbuckling behavior and failure of composite cylinders
longitudinal joints under lateral external pressure is not only
subjected to external hydrostatic pressure.The theoretical
related to its dimension, but also longitudinal joint and an
study consists of finite element method and experiment. A
imperfection.
Tohid
Ghanbari
Ghazijahani
a, Hossein
nonlinear finite element program, ACOSwin, is used for
Showkati b,*(2011) the authors have studied buckling behavior
postbuckling failure analysis of composite cylinders. E.
of conical shell reducers under uniform peripheral pressure
Magnucka-Blandzi (2008) the author has presented work on
and evaluated by experimentation. Along with this FEA
axi-symmetrical deflection and buckling of circular porous-
simulations as well as theoretical predictions were taken into
cellular plate. A critical load and a deflection are determined.
account to compare buckling load and modes of deformation.
The results obtained for porous plates are compared with
S.K. Panda a , B.N. Singh b,* (2011) the authors have studied
homogeneous circular plates. T. Hong a, J.G. Teng b,* (2008)
nonlinear free vibration behavior of single/doubly curved shell
this paper talks about an efficient semi-analytical finite
panel is addressed within the post-buckled state.
Thermal
element method for the nonlinear analysis of imperfect shells
post-buckling of shell panel is accounted for a uniform
subject to nonsymmetric loads. Both the applied loads and the
temperature.
A mathematical model is developed l by
initial geometric imperfections may take any form and
introducing the geometric nonlinearity based on higher order
approximated by Fourier series. P. Malekzadeh a,b *, A. Ouji c,d
shear deformation theory. Izzet U. Cagdas a,*,1, Sarp Adali b
(2008) the author has presented work on Axisymmetric
(2011) the authors have studied Buckling phenomenon of
buckling analysis of laterally restrained thick annular plates
cross-ply cylinders under hydrostatic pressure with a semi-
using a hybrid numerical method. R. Lo Frano* , G. Forasassi
analytical finite element analysis based on a first order shear
(2009) the authors have done investigation on the instabilities
deformable shell theory. After solving numerous problems the
of long homogeneous and isotropic thin elastic tubes, with
numerical results are compared with the analytical results
geometric imperfections like eccentricity or ovality, on the
available in the literature. F. Albermani , H. Khalilpasha, H.
buckling behaviour in conditions for which, at present, a
Karampour
(2011)
the
authors
have
studied
buckle
complete theoretical analysis was not found in literature. N.
propagation in deep sub-sea pipelines. Experimental results
Mukaimachia a,, S. Konosu b (2009)
the authors have
are presented using ring squash tests and hyperbaric chamber
presented work on FEAs for large diameter vessels with an
tests, and are compared with a modified analytical solution
external flaw subjected to (1) pure external bending moment,
and with numerical results using finite element analysis. The
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IJRET: International Journal of Research in Engineering and Technology
eISSN: 2319-1163 | pISSN: 2321-7308
experimental investigation was conducted using commercial
[10]
Carl T.F. Ross, Andrew P.F. Little, The buckling of a
aluminum pipes Preliminary analysis of these pipelines shows
corrugated carbon fibre cylinder under external
that a substantial increase in buckling capacity.
hydrostatic pressure, Ocean Engineering, 28(10), 2001,
1247-1264.
3. CONCLUSIONS
[11]
Jianghong
Xue,
Michelle
S.
Hoo
Fatt,
Buckle
propagation in pipelines with non-uniform thickness,
Since buckling can be simply defined as the instability of any
Ocean Engineering, 28 (10), 2001, 1383-1382.
structure. The present paper summarizes study of buckling
[12]
Gyeong-Hoi Koo , Bong Yoo, Jong Bum Kim,
phenomenon in structures like thin -thick shell and plates by
Buckling limit
evaluation
for
reactor
vessel
of
authors from different background. All the authors have
KALIMER liquid metal under lateral seismic loads,
presented research work in terms of mathematical study
International Journal of Pressure Vessel & Piping , 8 (
supported by Finite Element method as well as in some cases
5), 2001, 321-330.
conducting experimental test to compare the results. The study
[13]
X. H. Shi , Y. G. Gao, Generalization of response
shows different types of buckling such as plastic, dynamic,
number
for
dynamic
plastic
response
of
shells
buckling of cylindrical shells with axial load, and external
subjected to impulsive loading, International Journal of
pressure there causes & effects on the structural members.
Pressure Vessel & Piping, 78 (6), 2001, 453-460.
Some of the authors have presented new set of design rules for
[14]
Michelle S. Hoo Fatt, Jianghong Xue,
Propagating
critical cases of buckling such as spherical shell etc.
buckles in corroded pipelines, Marine Structures, 14 (
6), 2001, 571-592.
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Mark W. Hilburger , James H. Starnes Jr., Effects of
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the
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response
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random
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BIOGRAPHIES
Amit M. Patil is currently working as Asst.
Professor in Department of Mechanical
Engineering, at Pad. DR D Y Patil Institute
Engineering & Technology, Pimpri, Pune.
He
has
completed
M.E
(Design
Engineering).
Amol M. Kolhe is currently working as
Asst. Professor in Department of Mechanical
Engineering, at Pad. DR D Y Patil Institute
Engineering & Technology, Pimpri, Pune.
He has completed M.E (CAD/CAM)
Abdul Sayeed AW Shaikh is currently
working as Asst. Professor in Department
of Mechanical Engineering, at P.R. Pote
(Patil)
College
of
Engineering
&
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