|
Civil-Comp Proceedings ISSN 1759-3433
CCP: 81 PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 54 Buckling of Axially Compressed Cylinders with Imperfect Length
J. Blachut Mechanical Engineering, The University of Liverpool, United Kingdom
Full Bibliographic Reference for this paper
J. Blachut, "Buckling of Axially Compressed Cylinders with Imperfect Length", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 54, 2005. doi:10.4203/ccp.81.54
Keywords: bifurcation buckling, collapse, non-uniform length, cylindrical shell, non-uniform compression, contact.
Summary
In many real life situations one needs to connect several cylindrical segments
to form a prime load bearing structure. When loading is an axial compression - the
interaction between two neighbouring cylindrical segments becomes critical.
Possibility of buckling of either one, or both segments further complicates
segment-to-segment interaction. This is not a new problem but it is far from being
satisfactorily understood or solved. The type of instability induced by
cylinder-cylinder interaction is relevant to many industries, i.e. aerospace, civil, and
mechanical.
The prime objective of this paper is to examine buckling which can occur due
to uneven contact between two cylindrical segments when subjected to axial
compression. This is an entirely numerical study. Contact stresses at
segment-to-segment interface are limited to one end of a single cylindrical shell. It is assumed
that a single cylinder has a non-uniform and 'wavy' axial length at one end. The
assembly stresses are induced by clamping the cylinder at one end, and by
compressing it by a rigid plate, moving axially, at the other end. The non-uniform
axial length has a sinusoidal shape along the compressed edge. The number of
waves, , is varied between two and six. Also, the amplitude, , is taken as a
variable. The ratio of axial amplitude, , to the wall thickness, , i.e. is varied
between
. The length-to-shell radius, , is kept constant throughout and
equal to whilst the radius-to-thickness ratio, , varies from 165 to 1000.
Results are provided for mild steel cylinders with typical material properties (i.e.
with the Young's modulus, GPa, Poisson's ratio,
, and with the
yield point
MPa). The initial contact between the rigid surface and
deformable cylinder occurs at -points. As the rigid plate moves further down the
contact area between the plate and the cylinder changes. As a result of axial
compression the load carrying capacity of the cylinder can be limited either by
collapse or by bifurcation buckling. A set of four different boundary conditions
applied at 'the sinusoidal edge' of axially compressed cylinder has been used to
examine the load carrying capacity. Modelling of contact problem is based on a
standard 'slave-master' algorithm with no friction between the rigid surface and
deformable cylinder.
This numerical study of static stability of cylinders with variable axial length and
subjected to axial compression by a rigid plate has revealed a complicated nature of
contact between the rigid plate and deformable shell.
For thicker shells, i.e. with , the magnitude of bifurcation buckling load
and its position on the load deflection curve depends on the -ratio. For smaller
values of the -ratio the failure is controlled by collapse, and bifurcation mode
occurs on the-post-collapse-path, and hence it remains irrelevant from a practical
point of view. For larger magnitudes of the -ratio, on the other hand, bifurcation
can appear well below the collapse load on the initial, primary path of the load
deflection curve. This can be dangerous if not accounted for during the design stage.
Equally interesting is the size of contact between imperfect cylinder and rigid plate
which triggers buckling. Generally larger the amplitude less contact is needed to
trigger bifurcation buckling.
For thinner shells, e.g., , asymmetric bifurcation buckling ends the load
carrying capacity but only for smaller values of the -ratio. For larger -ratios
collapse remains the controlling mode of failure.
Within the investigated range of , i.e.
, and the
buckling load is being grossly reduced for all cylinders with sinusoidal imperfection
of axial length. The thinner shells suffer the largest reduction of the load carrying
capacity especially for small magnitudes of the imperfection.
Some background information on buckling and/or collapse of cylindrical shell with
non-uniform axial length can be found in references [1,2,3,4].
References
- 1
- Albus, J., Gomez-Garcia, J., Ory, H., "Control of assembly induced stresses and deformations due to waviness of the interface flanges of the ESC-A upper stage", in "Proceedings of 52nd Intl Astronautical Congress", Toulouse, 1-9, 2001.
- 2
- Guggenberger, W., Greiner, R., Rotter, J.M., "The behaviour of locally-supported cylindrical shells: unstiffened shells", J. Constructional Steel, 56, 175-197, 2000. doi:10.1016/S0143-974X(99)00102-9
- 3
- Galletly, G.D., Blachut, J., "Axially compressed cylindrical shells - a comparison of experiment and theory", in "Inelastic Solids and Structures", Kleiber, M., and König, J.A., (Editors), Pineridge Press, Swansea, 257-276, ISBN 0-906674-67-0, 1990.
- 4
- Blachut, J., "Pressure vessel components: some recent developments in strength and buckling", Progress in Structural Engineering and Materials, 1, 415-421, 1998. doi:10.1002/pse.2260010410
purchase the full-text of this paper (price £20)
go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)
|