Numerical Simulation of Buckling of Thin Cylindrical Shells
1. Numerical Simulation of Buckling of
Thin Cylindrical Shells
Master of Technology
(M.Tech)
in
Structural Engineering
By
Khaja misba uddin
oct 1st, 2013
Department of Civil Engineering
JNTUH College of Engineering, Kukatpally, Hyderabad
2. Outline of the Presentation
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Introduction
Importance
Literature Review
Lacuna in the field
Present work
Numerical modeling and analysis
Results
Conclusions
Scope for future work
References
Acknowledgement
3. Introduction
It is well known that thin walled cylinders are
proven efficient structures with a variety of
applications in
- construction
- chemical
&
- aero-space industry.
4.
The strength of these structures is limited to
their buckling strength when subjected to axial
compressive loads and external pressures.
Failure of these thin cylindrical shells under
buckling loads is a matter of concern for
engineers, while predicting the reliability of these
structures.
5.
Definition -Thin Shells
If the wall thickness of the shell is less that 10%
of the diameter of the shell then it can be treated a
thin shell.
When the shell is subjected to internal Pressure
the stresses developed are assumed to be uniform
throughout the wall thickness.
6. Importance
Knowledge of
- Stress distribution
- Vibration Pattern
- Buckling Behaviour
is very important in the design of thin cylindrical
shells.
8. Literature Review
There are several research papers and technical
reports published in this field.
Euler’s research in 18th century gave birth to
classical theory of buckling.
Successful applications of a variety of the structures
is well documented in Theory of Elastic Stability by
Timoshenko and Gere.
9.
A very pertinent literature survey has been
conducted in this field.
Certain gaps are identified in the open published
literature.
Some of these gaps are detailed hereunder.
10.
According to the classical theory of buckling, for
axially-loaded thin cylindrical shells, buckling
stress is directly proportional to the wall thickness
‘t’, other things being equal.
t
σ cr =
2
3(1 − υ ) R
E
Where, “σ” is critical compressive stress, “E” is
Young’s modulus, “υ” is Poisson ratio of isotropic material, “t” is the uniform thickness and
“R” is the radius of the shell.
11.
However, from the experimental investigations
of the several researchers the empirical data
show clearly that the buckling stress is actually
proportional to t1.5, other things being equal.
1.5
σ mean
t
= 5
E
R
12. Lacuna in the Field
It is well known that there is wide scatter in the
buckling-stress data, ranging from one half to twice
the mean value.
Current theories of shell buckling attribute both
the scatter and the low buckling stress – in
comparison with the classical – to “imperfectionsensitive”, non-linear structural behaviour.
All those theories considered classical shell theory
as their ideal reference and treated as perfect.
13. Present Work
The present work deals with the investigation of
1. The stress distribution – Static Analysis
2. Buckling Behaviour
using FEM when thin cylindrical shells are
subjected to axial compressive loads and
external pressures.
14. NUMERICAL MODELING AND
ANALYSIS
A complete ABAQUS analysis flow chart usually
consists of three distinct stages:
1) Preprocessing,
2) Simulation,
3) Post-Processing.
These three stages are linked together by the
corresponding files.
30. Shell subjected to axial compression of 100 N
and varying the thickness of the shell the
buckling load is calculated.
Length
in
mm
Thickness
mm
Radius
mm
Eigen value
for
Mode 1
Buckling
Load in
N
6000
0.1
500
31.592
3159.2
6000
0.3
500
237.24
23724
6000
0.5
500
618.9
61890
31. CONCLUSIONS
The following are the important conclusions drawn from
the present study on numerical simulation of buckling of
thin cylindrical shells.
During buckling, half sine waves will be formed along the
generator and along the circumference.
The number of half sine waves formed along the generator
and along the circumference are independent of the length
of the cylindrical shell.
The number of half sine waves formed along the generator
and along the circumference are dependent on the radius
and thickness of the shell.
32. SCOPE FOR FUTURE WORK
As an extension to the present work:
A number of variations of the problem
specifications can be tried with the available soft
wares in estimating the critical buckling loads.
There is always a need for the experimental data to
be generated to validate the numerical results.
In these endeavors an experimental test facility can
be built with data acquisition and recording systems.
33. There is a wide scope to further investigate the
effect of geometric nonlinearity and material
nonlinearity on the critical buckling loads.
Buckling of thin shells, made of functionally
graded materials, subjected to internal/
external loads.
Vibration behaviour and impact resistance of
thin cylindrical shells.
34. References
1.
2.
3.
4.
Euler, L., 1744. Methodus inveniend lincas curves maxim:
minimive proprietate gaudentes (Appendix, de curvis
elastics). Marcum Michaelem Bousquet, Lausanne and
Geneva.
Timoshenko SP, Gerri JM. Theory of elastic stability, 2nd
ed. New York: McGraw-Hill, 1961
Von Karman, T., Dunn, L.G., Tsien, H., 1940. The
influence of curvature on the buckling characteristics of
structures. Journal of the Aeronautical Sciences 7, 276289..
Koiter WT. On the stability of elastic equilibrium (in
Dutch with English summary). Ph.D. thesis, Delft, H.J.
Paris, Amsterdam, 1945. Air Force Dynamics Laboratory,
Technical Report, AFFDL-TR-70-25, Ohio, February
1970(English translation)
35. 5.
6.
7.
8.
9.
Arbocz., J., 1974. The effect of initial imperfections on
shell stability. In: Fung, Y.C., Sechler, E.E. (Eds), thin
shell structures.
Abramovich H, Singer J, Weller T. The influence of
initial imperfections on the buckling of stiffened
cylindrical shells under combined loading. In: Jullian JF,
editor. Buckling of shell structures on land, in the sea,
and on the air. London: Elsevier Applied Science,
1991.p. 205-45.
Yamaki, N., 1984. Elastic Stability of Circular Cylindrical
Shells. North – Holland, Amsterdam.
Heyman J. Equilibrium of shell structures. Oxford:
Clarendon Press, 1977
Lancaster, E.R., Calladine, C.R., Palmer S.C., 1998.
Experimental observations on the buckling of a thin
cylindrical shell subjected to axial compression.
International Journal of Mechanical Sciences.
36. 10.
11.
12.
13.
T.D. Park and S.Kyriakides, “On the collapse of dented
cylinders under external pressure”, Int.J.Mech.Sci. v.38,
No.5, pp. 557-558 (1996)
Y. Bai, R.T.Igland, T.Moan, “Tube Collapse Under
Combined External Pressure, Tension and Bending”,
Marine Structures, v.10, 389-410 (1997)
G.Forasassi, R.Lo Frano., “Buckling of imperfect thin
cylindrical shells under lateral pressure”, Journal of
Achievements in Materials and Manufacturing
Engineering, pp287-290, Vol.18, Issue 1-2, September –
October 2006.
R.Lo Frano and G.Forasassi,., “Buckling of imperfect
thin cylindrical shells under lateral pressure”, Journal of
Achievements in Materials and Manufacturing
Engineering, pp1-8, Vol.20, 2008.
37. ACKNOWLEDGEMENT
I profusely thank Dr. N. V. Ramana Rao,
PRINCIPAL & PROFESSOR, JNTUH College of
Engineering, Kukatpally, Hyderabad, for his valuable
guidance and constant inspiration at every stage of
this dissertation. I sincerely thank for supporting my
work.
I am indebted to Dr. M.V. Seshagiri Rao, the Head
of the Department of Civil Engineering for his
valuable suggestions and co-operation during the
entire period of work, without whom, this project
could not have been completed.
38.
I would like to express my gratitude to the then
Head of the Department of Civil Engineering Dr.
G. K. Viswanadh, for his support in a number of
ways to M.Tech Program in the department during
the entire period of my course.
I sincerely express my thanks to all the faculty
members of Civil Engineering Department who
all helped me at different stages of my M.Tech
course work and project work.
39.
I would like to sincerely thank all my
classmates who made my stay in JNTUH
College of Engineering, really a memorable
one.
V.L.S. BANU
