Experimental Study and Numerical Analysis of Steel Cylindrical Panel Buckling Features

This article focuses on the experimental and numerical research conducted on cylindrical panels to determine the bulking load and evaluate the post-bulking features of the panels.

Cylindrical shells 1
EXPERIMENTAL STUDY AND NUMERICAL ANALYSIS OF STEEL CYLINDRICAL
PANEL BUCKLING FEATURES
By (Student’s Name)
Professor Name
University
City
Date

Cylindrical shells 2
Abstract
The impact of the sector angle length and varying conditions of the boundary on post-buckling
and buckling load features of the cylindrical panel has been studied using the numerical and
experimental approach. Abaqus finite element tests have been conducted for numerical analysis
whereas the servo-hydraulic machine has been used in conducting the experimental tests. The
results for numerical analysis are similar to the experimental.
Keywords: Mechanical testing, buckling analysis, and plastic and elastic features

Cylindrical shells 3
Introduction
Cylindrical shells are commonly applied in a number of constructions. They are exposed to many
loading combinations. Axial compression is the most complex load that poses a threat on the thin
shell's stability. The failure modes that are so common in thin shell constructions are buckling
(Jawad, 2017). Over 60 years many studies have focused on the challenges of the axial
compression. The theory of linear shell was the first presented based on classic elasticity whereas
the second presentation was based on the approximation theory. The eighth order differential
equation was developed for determining the cylinder's critical strength with edges for support
under torsion. It was observed that the real edge support's first deviations and imperfections from
the theoretical state of the supports were the cause of the discrepancies between theoretical
buckling and experimental stress figures. A simple approach for analyzing the thin cylindrical
shell's elastic stability. The linear theory was also developed as a guide and created empirical
curves with the information of various earlier researchers. These tests showed a decrease in
critical stress compared to theoretical values. They observed that the buckle pattern revealed is
different from the theory based predictions. A huge deflection theory was employed to determine
the buckling feature of the long cylinders. It was revealed that long cylinders are able to be at
equilibrium in buckling conditions under minimal stress as compared to the linear theory's
critical stress. The buckle pattern present in the initial stages of buckling was also accounted for
successfully.
Many experiments were done on different long and short cylinders under axial compression.
Design curves were employed for the buckling coefficient against Batdorf parameter from 100 –
2000 and over 2000 for r/t ratios. The theoretical justification was presented for the influence of
the first geometrical discrepancies of the shell buckling load. NASA employed a monograph in

Cylindrical shells 4
which the analysis and design criteria are covered for both unstiffened and stiffened circular thin
walled shells under many loading states. Experimentation based design charts and empirical
formulae were provided too. Charts and practical design equations were developed to
approximate the buckling strength of both the imperfect and perfect tanks and cylindrical shells
under loads axially compressed based on parametric research using ABAQUS. The nonlinear in
thin-wall members were studied and the impacts of the first imperfections as a result of the
residual and geometry stress. Tests conducted on the imperfect shells exposed to transverse load
and the nonlinear FE model imperfection was modelled using ABAQUS. Two models were
created whereby in the first, the actual imperfections were imposed at every node. In the second
FE model, the imposition of the imperfections was by renormalization of the eigenmode where
the maximum imperfection measured was applied. Circular- compressed shell cylinders with
geometric imperfections were analyzed for the dynamic and static environment. The Sanders
shell theory and Donnel’s theory of nonlinear shallow-shell were applied for the analysis.
Shell structures are commonly used in marine structures, shell roofs, pipelines, cooling towers,
aerospace and liquid-retaining structures. One of the major challenges in designing such
structures is buckling. Researchers initially focused on determining the buckling load exposed to
linear elastic zone however these were experimental research. It was revealed that the buckling
capacity of thin cylindrical shells is very low as compared to that quantity found in the classical
theory. Thin cylindrical panels can be used in many structures. Where the stress distribution in
these structures is compressive, such structures may collapse in most cases before the buckling
phenomena reveal its capacity of loading or yielding because of the huge radius values to the
thickness ration. The subject was conducted using the numerical approach based on the
analytical method and finite element (FE) inside the elastic area. The actual solution for

Cylindrical shells 5
anisotropic and isotropic panels was determined. The simply supported panel's stability exposed
to distributed external pressure was studied. The Donnel’s equation for Buckling of three-edged
panels simply supported was solved and one-edged free under an axial load using the Galerkin
approach (Hui-shen, 2017). Experimental and numerical tests on cylindrical panels axially
loaded for postbuckling were conducted with simply supported edges and curved clamped edges.
The Australian standards in regards to designing steel structures are different from other
international standards as it does not involve a particular publication concerning the design of
structural fire. Instead, policies for designing structures related to fire are found in every steel-
related principal standards of designs. They include:
 AS/NZS 5100.6 Bridge Design – composite and steel construction
 AS 4100 steel structures
 AS/NZS 4600 - structures with cold-formed steel
 AS/NZS 2327composite structures – buildings constructed with composite steel-concrete
Different standards can be at varying stages of performance-based implementation methods for
engineering fire designs.
Experimental studies of cold-formed tube columns of stainless steel filled with concrete and high
strengths exposed to distributed axial compression were presented. The impact of plate thickness,
tube shapes and strength of concrete were also studied. The results of the test were compared to
the Australian and American standards. The strength and failure modes of aluminium alloy with
and with no transverse weld axially compressed between fixed edges. Among the failure modes

Cylindrical shells 6
observed include buckling and yielding for various lengths. The results of the test were
compared to other aluminium standards for structures (Matsagar, 2014).
An experimental approach for hollow cold-formed squared stainless steel sections exposed to
axially pure compression was described. The conclusion was that the Australian design policies
are very reliable as compared to the European and American specifications for studies
conducted. Numerical and experimental studies on the efficiency of thin-skinned repaired
composite panels with stiffened blades inside the post-buckling range have been performed. The
results revealed that the panel's strength can be satisfactorily restored under the present repair
plan. Additionally, the repair plan was observed to have the ability to recover the load's general
path in panels and the general post-buckling feature.
This article focuses on the experimental and numerical research conducted on cylindrical panels
to determine the bulking load and evaluate the post-bulking features of the panels. The Abaqus
(FE) element has been applied for the numerical analysis to determine the impact of the sector
angle, thickness, length and different boundary states (Zamani, 2017). For the experimental
study, tests on the panels were conducted using the servo-hydraulic machine. The experimental
results are similar to the numerical ones. Based on this study, the panel's buckling load can be
approximated which relies on the mechanical and geometrical features of it. The experimented
panels that have been clamped and constrained between simple supports contain two boundary
states. Thus the average buckling coefficient of the two boundaries can be applied to get a
correlation.

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Analysis: Circular Cylindrical Panel Buckling from Axial Compression
Finite Element Method
This is the computational approach applied to get the estimate solutions of limit value
challenges. These boundary value challenges are also known as field difficulties. The areas of
focus are the field challenges which usually represent the actual structures. The field difficulties
are outlined using the differential equation discretization contained in the element method. These
elements provide approximated strains and stresses experienced by complete structures. Based
on the structure's complexity, type of every element and the number of finite elements, the FEM
estimate solutions will be varied. Nodes are zones at which the mesh elements are linked. The
mesh is the structure in which all elements are connected whereby the mesh is either crude or
fine based on the size of a finite element. Developing a very fine field grading mesh can cause
unwanted computational power hence resulting in convergence analysis. The commercial
Abaqus software is the most suitable in developing a 3D model which forms an FE model with
3D modelling (Rao, 2017).
Abaqus model
This part describes the Abaqus model and the method of placing up the model. There are the
required procedural steps for running the model as well as setting up it up.
 Shell Element
The initial modelling procedure of the shell’s structure is by defining the areas which form the
complete structure whereby only a single element is needed. This element is formed as a shell
element that can be perceived as an amalgamation of disc and plate elements. Disc features are
used to evaluate structures predisposed to in-plane forces with two translation of in-plane

Cylindrical shells 8
degrees of freedom. The plate features contain a single out of a plane’s degree of freedom and
two out of the rotational plane degrees of freedom (Rao, 2017). An additional sixth degree of
freedom with a degree of freedom rotational features known as the drilling degree of freedom is
added to the five degrees of freedom that are resulted from a disc and plate. The dimensions,
geometry and material elements of a shell element can be obtained later. The below figure shows
the structure of a shell (Matsagar, 2014):
Fig 15: structure of a shell with its material features
The thickness of a shell consists of offsets that start from half its thickness and the middle area
extending inside while the other half extends outside the offsets. The radius value is obtained
from the centre of the thickness which is applied in calculations.
 Defining surfaces and sets
Before applying the limit conditions, the surfaces and sets are determined. The sets stand for the
cylinder edges where loads or supports or both are used. The creation of cylinders in a 3D –space
is by default when a Cartesian coordinate system is applied. In cases of loads with shear-edged
shells, it can be very feasible if it is converted into the cylindrical coordinate system. This will
result in coordination if a load is applied using (r,θ,z).

Cylindrical shells 9
 Boundary states
The model’s limit conditions include the supports that define loads and restrictions used on
structures.
Supports
The structure of the shell is presumed to be clamped at the bottom region. This means that the
rotations and all directions are fixed while the top region is pinned to enable it to rotate and move
along the length of the axis. This axis is called the z-axis whereas the rest of the directions are
clamped. These limit conditions can be applied in all load circumstances. The figure below
shows the bottom limit state:
Fig 16: the shell structure’s bottom limit condition
Loads
The structure of the shell is subjected to four various load cases namely; circumferential
compression, meridional compression, an amalgamation of all of them and shear stress (Rao,
2017). The loads vary of each other. The Abaqus does not apply units thus an individual must
have such information when creating the combination of loads. The loads have a value of 1.0
input reference and therefore the eigenvalue (λ) output can be applied in creating combined
loads. Loads are used in axial directions in meridional compression scenarios using the z-axis.

Cylindrical shells 10
Therefore, it will be irrelevant whether loads are applied inside the cylindrical coordinate system
or Cartesian. It is very important to apply the cylindrical coordinate system for the shear stress
case than for the Cartesian due to the shear load being applied towards θ- directions. This angle
is the cylinder’s circumference.
Fig 17: Shell structure respectively showing meridional, circumferential compressions and shear
stress.
 Mesh
The quadrilateral or triangular properties make up the shell element. A convergence analysis is
conducted so as to obtain the most suitable type of element. Every node contains some quantity
of degrees of freedom that determine displacements in various rotations or directions. The
triangular feature does not have the θw, drilling degree of freedom, hence consists of five
degrees of freedom for every node. The quadrilateral feature consists of six degrees of freedom
for each node which implies three rotational and three displacement degrees of freedom. This
renders it the most suitable for addressing three-dimensional challenges. The figure below
illustrates a quadrilateral shaped shell element:

Cylindrical shells 11
Fig 18: quadrilateral shell feature
The quadrilateral feature consists of either quadratic features having eight nodes or linear
features having four nodes. The linear features are not absolutely correct to be applied in
modelling curved structures such as cylinders. This is due to each side of elements being linear
while the quadratic element sides will curve because of the additional quantity of nodes for each
element. Therefore, to obtain results that are very correct with minimal computational powers,
meshing is done using the quadratic quadrilateral features. The figure below shows a shell
structure mesh:
Fig 19: A shell structure’s mesh containing 975 elements
A loaded curved plate will buckle when acted upon by axial compression identically as cylinders
with large plate curvature. Smaller plate curvature cylinders would, however, buckle similarly to
flat plates. Taking note of the two limits, one type of behaviour transitions to another. Applying a

Cylindrical shells 12
load to a plate drives the plate to critical loading, afterwards, the load drops. On additional axial
deformation, the load rises once more and reaching the failure load having a greater value than
the buckling load, during elastic situations. In case the plate has a plastic buckling, failure and
buckling occur coincidentally.
Considering a simple restrained cylindrical panel with thickness t, length L and central angle w,
uniformly applying an axial compression force shown in figure 1 below is being governed by the
differential equations shown below.
In the differential equations above, w, v and u are radial displacements, tangential displacement
and longitudinal displacement respectively. However, the one gets the differential functions by

Cylindrical shells 13
Figure 1 above shows compressive forces acting on a cylindrical panel
In equations 4, 5 and 6, Bmn, Amn, Cmn are unidentified buckling amplitudes. Through the
substitution of equation 4 to equation 6 into equations 1 to equation 3, the result becomes
That denotes b ¼ mL pR, therefore, the buckling load acting on cylindrical panels during
uniform axial compressive force can be derived using the equation 8
Instances that involve a smaller w angle indicate that the buckling characteristic of such
cylindrical panels will approach those of longitudinally rectangular plate compression.
Panel Features
Using the mechanical steel alloy panel properties, in this experiment, standard test samples will
be prepared using original tubes a specified by the ASTM E8 specifications while the tensile
tests were conducted using the INSTRON 8802 test machine’s accuracy. Figure 2 identifies the
stress-strain graph for a sample. Its Poisson's ratios were taken as 0.33. Table 1 shows the
mechanical and geometrical properties of the experimental panels (Jawad, 2017).

Cylindrical shells 14
Boundary Conditions
For the application of the boundary conditions on cylindrical panels’ edges, 2 rigid plates were
chosen and mounted to the cylindrical panel ends. Additionally, to enable buckling analysis due
to axial loading, 15 mm spacing was centrally placed on the upper plate. This placement led to
compressive load distribution on the cylindrical panel edges. Within the experimental result
section, there will be a description of the used fulcrum in the tests. The fulcrum had an 18.1 mm
height as shown in figure 3. Hence, during the numerical simulation, the shell edges will be
restricted to this elevation apart from the cylinder axis direction.
Figure 2 above shows the stress-strain graph.
Table 1 below shows the geometrical and mechanical panels’ properties.
Thickness t=0.9mm
Diameter D=60mm
Length L=150, 100, 250mm
Sector angle θ=1200, 900, 355o, 1800, complete
Elasticity modulus E= 150GPa
Yield Stress Σy=240 MPa

Cylindrical shells 15
Figure 3 above shows the experimental tests fixtures for simply support as well as clamped
respectively.
Numerical method
During numerical analysis, the Abaqus FE software was used. In this type of analysis, S8R5
which is the nonlinear element has eight nodes with 6 degrees of freedom in every node
(Öchsner & Öchsner, 2017). This is suitable for thin shells analysis as well as the S4R linear
element with four nodes used. A section of the meshed specimen is displayed in figure 4. Both
nonlinear and linear elements are being used in analyzing the shells, eventually, the results will
be put analyzed against one another.
The boundary conditions are set to be clamped or having free straight edges and simple arc
edges. There is a buckling load overestimation when using the Eigenvalue analysis since in the
process of analyzing, the material's elastic properties are not being used or considered. In
buckling analysis, analysis through Eigenvalue method has to be performed at first for all
samples to determine their corresponding Eigenvalues and mode shapes. Smaller Eigenvalues
correspond with primary nodes and buckling will also occur in the primary nodes. The software
used the ‘buckle’ step method in analyzing the Eigenvalues (Isaac, 2017). Three initial
corresponding displacements and mode shapes of the specimen under study were determined.
The impact of the determined mode shapes to play when they are considered during the analysis

Cylindrical shells 16
of nonlinear buckling. Otherwise, an arbitrarily selected buckling mode would be conducted by
the software, leading into unrealistic results within the nonlinear analysis. The ‘buckle’ step
experiment was undertaken using the software’s subspace solver technique. However, it is
important noting that the existence of the contact constraints between the shells and the rigid
plates when using the Lanczos solver technique is not applicable for the specimens in these
experiments. As displayed in figure 5, there are three primary mode shapes in the L100-u908
specimen. Once the buckling analysis is through, there was a nonlinear analysis done to draw the
load-displacement curve. The highest value within this graph is identified as the buckling load.
Figure 4 shown above displays a panel mesh pattern.
Figure 5 above shows the shapes during buckling mode for sample θ=900 L=100mm for the first,
second and third modes respectively.
This techniques used in getting the buckling load is the ‘Static Riks’ method that makes use of
the arc length procedure in the post-buckling analysis. During this analysis, one has to take into

Cylindrical shells 17
consideration the nonlinearity of the geometry and material properties. Static Rik's technique has
been performed on various panels listed in table 1 by simple and clamped boundary conditions
and in every case, there is a derivation of the load-displacement graph.
Experimental Method
A portion of specimens enlisted in table 1 was availed and taken through the compression test
using the servo-hydraulic machine (Brown, 2017).
Figure 6 above shows the load-displacement graphs for three identical panels having θ=1200,
L=100mm

Cylindrical shells 18
Figure 7 above shows the setup for conducting the experiments.
To begin with, the reliability of the system had to be tested. Similar panels having specifications
u ¼ 120 L ¼100mm were put to test. Looking at figure 6, there is a load-displacement graph
gotten from the test of the panels. This graph shows the good reliability of the system by the
existence of similar results from repetitive tests of the panels.
Additionally, there were various boundary conditions being investigated. On applying the axial
load on the panels, the load-axial displacements were drawn. Every test was performed using
free straight edges and simply supported or clamped arc edges. Other appropriate fixtures had to
be designed to come up with simple and clamped boundary as a shown test set up in figure 7.
Results Discussion
The experimental and numerical load displacement diagrams for different length panels are
shown in figure 8. The buckling load is described as the peak values in all the diagrams. It is
evident that through the increase of length, there is a decrease in the buckling load (negative
covariance between length and buckling load). In shorter lengths, this covariance becomes more.
In longer lengths, the load-displacement graph produced using the smallest sector angle for
example u ¼180 and u ¼90 (figure 10 and figure 9) is inclined to Euler mode of buckling.
Figures 10 and 9 display the load-displacement graphs for u ¼180, 90. Figure 11 displays that
through increasing a sector angle, there is an increase in buckling load. In cases of an existing
narrow cut of about u ¼355, there is a noticeable decrease in the buckling load. The varying
buckling load due to the effect from the sector angle has been displayed in figure 12. The
variation is semi-linear and has a very large change when a cylinder is used. Figure 13 displays
the deformed shape of one panel having a narrow cut (Jawad, 2017). The first buckling modes

Cylindrical shells 19
and their load-displacement graphs for various panels are listed in table 2. These are similar
buckling modes with a good relationship between the various load-displacement graphs.
Figure 8 shown above displays the load-displacement graphs for various lengths (simply
supported θ=120)
Figure 9 shown above displays the load-displacement graphs for various lengths (simply
supported θ=90)

Cylindrical shells 20
Figure 10 shown above displays the load-displacement graphs for various lengths (simply
supported θ=180)
Figure 11 shown above displays the length buckling load taken from various sector angles.

Cylindrical shells 21
Figure 12 shown above displays the buckling load as a sector angle from various simply
supported sector angles.
Figure 13 above displays the deformed panel shape for the experimental and the numerical
methods respectively (L=100, θ=355, simply supported)
The main differences occurring between the diagrams exist in the post-buckling region while the
FE value results becoming bigger than the test values. This observation may be existing due to
the defined approximation in the plasticity section of the stress-strain graph as well as not
considering the defects of the FE model specimens. The analysis of the FE stress indicates that
some instances Von-Mises panel stress is higher compared to the yield stress or there lacks
elasticity in the panel during buckling load. Figure 14 displays Von-Mises panel stresses during
buckling loading, an effect coming from the boundary condition (Shih, 2017).
Boundary Condition effects
Investigating how various boundary conditions have influence requires performing some tests on
panels with simple supports while others are clamped. Table 3 gives a load-displacement graph

Cylindrical shells 22
for the simply supported and clamped boundary conditions. The results show that the capacity of
buckling loading can increase when the panels are in clamped boundary conditions since
clamping the boundaries restricts the degrees of freedom (Rao, 2017).
Table 2 shown below displays the experimental and numerical load displacement graphs and
buckling modes for various sector angles and lengths.

Cylindrical shells 23

Cylindrical shells 24
Figure 14 shown above displays the Von-Mises panel stress distribution for various simply
supported loads within the post-buckling region and elastic region load application (Öchsner &
Öchsner, 2017).
The Euler mode of buckling was seen for u ¼ 908 and L ¼ 250 mm experimental and numerical
results. The buckling loads values required in these boundaries are noted in table 4.

Cylindrical shells 25
Effect of Nonlinear and Linear Element
Once through comparing the graphs in figure 15, it is true to state that when comparing nonlinear
elements to linear elements brings out the better prediction qualities of the linear elements in
instances of post-buckling when the mild steel alloy is concerned in elliptically cutout cylindrical
shells. During pre-buckling phases, both nonlinear and linear elements produce alike results.
It is visible that the load vs. end-shortening curves slope is higher in the results coming from the
numerical analysis than in the experimental before buckling begins. Such discrepancy comes
from the existence of internal defects in the material that decrease the specimen stiffness when
being experimented on while during the numerical analyses procedure assumes the material to be
ideal (Isaac, 2017).
The experimental results are put in comparison with numerical results in table 5. Evidently, there
are negligible differences between the numerical and experimental results. For instance, the
profound discrepancy between the two analyses exists in the nonlinear element 6.7% S8R5 and
liner element S4R. Moreover, one can note the important greatest difference existing in short
experiments. This can be accounted for by the fact that the shells. Bending theory is better suited
for lesser t/L ratios with this theory best applicable in calculations by the software.

Cylindrical shells 26
Model
designation
Buckling Load
S8R5
element
S4R
element
Experimental S8R5 element S4R element
L100-θ90 7.41 7.54 7.06 4.8 6.8
L100-θ120 12.49 12.74 11.81 5.8 7.9
L100-θ180 16.03 16.12 15.02 6.7 7.3
L100-θ355 34.82 35.21 32.98 5.6 6.8
L100-Perfect 43.04 43.24 40.93 5.1 5.6
L150-θ90 7.04 7.20 6.61 6.5 8.8
L150-θ120 11.26 11.46 11.04 2.0 3.7
L150-θ180 14.30 14.60 13.63 4.9 7.1
L150-θ355 31.02 32.25 29.65 4.6 8.7
L150-Perfect 40.10 40.99 37.69 6.4 8.7
L150- θ90 4.80 4.91 4.66 3.1 5.4
L250-θ120 9.49 9.58 8.94 6.2 7.1
L250-θ180 13.34 13.37 12.60 5.9 6.2
L250-θ355 29.87 30.01 28.59 4.5 5.0
L250-Perfect 37.44 38.01 36.22 3.4 4.9
Correlation of Theoretical data with Experimental Data
When a curved plate is axially loaded with compressive buckling force in a similar manner as the
cylindrical shell, the plate’s curvature is large. Instances that involve small plate curvature, the
buckling is similar to a flat plate. Using the two plate limits, there exists a transition from one
behaviour type to the other (Matsagar, 2014). Applying a load to a plate makes it reach the
critical loading point, after which loading suddenly drops. When further axial deformation is
continued, the loading rises and get to a failure load point that is higher than the buckling load,
during an elastic process. In case the plate has a plastic buckling, failure and buckling

Cylindrical shells 27
coincidentally occur. Some data tests involving the L ¼ 150 mm partitioned into three sector
angles (u ¼1208, 908, 1808) exist as displayed in figure 16 in Zb and Kc terms where:
B in equations 9 and 10 above represents the cylindrical panel. The tested boundary conditions of
the panels were between clamped and simple supports. Hence, the two limit cases have an
average buckling coefficient of Kpl = 5.7 that was identified for correlation purposes. Ultimately,
the results from the theoretical part were good in supporting the conclusion from the
experimental tests.
Table 3 shown below displays the load-displacement graphs for the simply supported and
clamped boundary conditions.

Cylindrical shells 28
Table 4 shown below identifies the buckling load for the various boundary conditions
θ=900 L = 150mm L = 100mm L = 250mm
Experiment Numeric Experiment Numeric Experiment Numeric
Clamped 6.99 7.67 7.92 8.45 5.05 5.19
Simply
Supported
6.61 7.04 7.06 8.40 4.66 4.80

Cylindrical shells 29
Conclusion
The numerical analysis and experimental tests conducted on the panels revealed the following:
1. When the sector angle is increased, there will be a semilinear increase of the buckling
load causing significant changes for cylinders.
2. An increase in the length reduces the buckling load. The impact is very significant for
very short panels.
3. This justifies the suitability of the shells bending theory in lower t/L ratios. The theory
can be applied in calculations using the software.
4. The clamped states of the limit will increase the panel’s capability to withstand loads or
an increase in the buckling load.
5. The presence of narrower slots leads to a noticeable reduction of the buckling load.
6. The simple supports limit conditions cause the buckling load to be delayed due to the
simple supports allowing addition rotation of the axial displacement whereas structures at
the clamped limit states are highly restricted as compared to the initial case.
7. In many of the conducted analysis, there have been similar results between the
experimental tests and numerical analysis results.
8. Results have revealed that the post-buckling area is more predictable by the curves
resulted from the linear elements compared to the nonlinear elements. The nonlinear
elements, however, are the most suitable for indicating the buckling loads.
9. An increase in the length slightly reduces the buckling load as shown in figure 6. The
reduction impact is very high in lengths that are shorter. There is an increase in the

Cylindrical shells 30
buckling when the panel’s sector angle is increased. The buckling load can simply be
approximated as:
Whereby the constants are n, m, K that relies on the mechanical and geometrical features
of the panels?
Limitations found in this research are that the experimental procedure will differ when compared
to the numerical analysis as numerical analysis will use ideal conditions. Moreover, bending
theory is better suited for lesser t/L ratios with this theory best applicable in calculations by the
software and not through experiments.

Cylindrical shells 31
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