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IJSRD - International Journal for Scientific Research & Development| Vol. 5, Issue 04, 2017 | ISSN (online): 2321-0613
All rights reserved by www.ijsrd.com 691
Design and Analysis of Stiffened Plate
Megharaj D S1 D C Patil2 1M.Tech student 2Assistant Professor
1,2Department of Mechanical Engineering 1,2KLE Dr MSSCET, Belagavi, Karnataka, India.
Abstract— Plates with stiffener are used in many fields of
engineering. These stiffened plates are used to strengthen
large structures, and these stiffened plate consists large
stiffeners like longitudinal stiffeners and transverse stiffeners
is to reduce buckling and bending and also to avoid damages
on plates. These structures avoid damage to dynamic load and
collision. Plates with stiffener are in the form curved
structures or flat structures. Flat structures are used in
automobile industries, ship industries and also used in aircraft
industries to make wings of an aircraft. Curved structures are
used in aircraft industries to build fuselage that is main body
of an aircraft. In plates to determine whether it is thick or thin
only if width to thickness ratio of plate is larger than 100 then
it is very thin, if ratio is with 20 to 100 than it is moderately
thin, if ratio is with 3 to 20 it is thick, if ratio is more than 3
then is very thick plate. Buckling stress is depend upon the
type of boundary condition which we used in the structure
while finding stress. Modal analysis is also done to determine
vibration characteristics such as natural frequency.
Key words: Stiffened Plate, Fuselage
I. INTRODUCTION
Types of failure in the structure namely material failure and
instability of structure is also known as buckling. Thin
structure or plates under applied compression load will
buckle very easily, where thick plates will sustain some
buckle. Therefore stiffeners are get attached to the plates, in
order to reduce buckling of plates. For failure of material we
need to consider yield stress for material which are ductile
and to consider ultimate strength for material which have
brittle. Most commonly used material in industries are
aluminium because it has high strength to weight ratio and it
is having good corrosion resistance to environmental
condition. In stiffened plates buckling is the main criteria to
know buckling behaviour on both stiffeners and plates. These
stiffened plates are able to withstand more load than the
applied load. If it is not able to with stand more load than the
applied load, the structure will fail. The load at point where
buckle take place are depend upon the stiffness of structure
or part.. This buckling behaviour will depend upon the
parameters of the structures like thickness, length of plate or
column and depend upon the material properties of material
used in the structure and also this buckling behaviour will
also depend upon distance between the stiffeners and type of
stiffeners used in structure. Stiffeners are mounted to the
plates by welding or rivets to avoid buckling of plate.
II. DESIGN OF STIFFENED PLATE
In this paper presents design of stiffened plates for different
stiffener shapes and for different materials. Material which I
have used are Aluminium 7075 and Glass Fibre. In aircraft
industries are using aluminium material for stiffened plate, so
I use composite material to replace aluminium material. In
order to design stiffened plate, first we want check design is
safe or not for a given model. Then design is done by
assuming thickness of plate stiffeners are equal. Taken
stiffened plate modal to determine buckling stress and natural
frequency is shown in figure 2.1.
Fig. 2.1: Modal of stiffened plate
A. Material properties:
1) Aluminium 7075
S No Parameters Value
1 Ultimate tensile strength (𝜎𝑢𝑡) 537 𝑀𝑃𝑎
2 Ultimate yield strength (𝜎𝑢𝑦) 489 𝑀𝑃𝑎
3 Young’s Modulus (E) 72 𝐺𝑃𝑎
4 Poisson’s ratio (𝜇) 0.34
5 Density (𝜌) 2795 𝐾𝑔 𝑚3⁄
Table 2.1: Material properties of aluminium 7075.
2) Glass Fibre:
S No Parameters Value
1 Ultimate tensile strength (𝜎𝑢𝑡) 550 𝑀𝑃𝑎
2 Young’s Modulus (E) 34 𝐺𝑃𝑎
3 Poisson’s ratio (𝜇) 0.22
4 Density (𝜌) 1799 𝐾𝑔 𝑚3⁄
Table 2.2: Material properties of glass fibre.
B. Checking design is safe or not:
Local buckling is considered satisfactory provided the
following proportions are not exceeded.
1) For web:
𝑑𝑤
𝑡𝑤
≤ 1.5 (√𝐸
𝜎𝑢𝑦
)
2) For flange:
𝑑𝑤
𝑡𝑤
≤ 0.5 (√𝐸
𝜎𝑢𝑦
)
Therefore design is not safe, because dimensions of
flange and web are larger than the required value. So design
is required.
Design and Analysis of Stiffened Plate
(IJSRD/Vol. 5/Issue 04/2017/174)
All rights reserved by www.ijsrd.com 692
C. Design procedure:
Design is done by assuming plate thickness and web, flange
thickness are equal by same compressive load 135 KN is as
shown in figure 2.2.
Fig. 2.2: Stiffened plate modal to design
By taking plate buckling stress formulae
𝜎 =𝑘𝑐𝜋2𝐸
12 (1 − 𝜇2)(
𝑡
𝑙)
2
Where
𝜎 =𝑃
𝐴
Therefore equation 3.3 can be written as
𝑃
𝐴=
𝑘𝑐𝜋2𝐸
12 (1 − 𝜇2)(
𝑡
𝑙)
2
𝑡 = 25.34 𝑚𝑚
Fig. 2.3: Designed stiffened plate modal
III. NUMERICAL SOLUTIONS FOR STIFFENED PLATE
A. Formulas for buckling stress:
Buckling stress formulae for plate with and without stiffeners
are different. Buckling stress formulae for plate without
stiffeners and plate with stiffeners for compressive load and
for all boundary condition is shown in the equation 4.1 and
equation 4.2. Boundary condition which is consider for my
project is two end fixed and two end free.
1) plate without stiffener:
Buckling stress for plate is given by
𝜎 =𝑘𝑐𝜋2𝐸
12(1−𝜇2) (
𝑡
𝑙)
2
... 𝑀𝑃𝑎
2) plate with stiffener T and J section:
Buckling stress for plate with stiffeners is given by
𝜎 =𝐼𝑒𝐸
𝐶𝐴𝑒𝑙2 .. 𝑀𝑃𝑎
3) Formulas for natural frequency:
Natural frequency formulae for plate with stiffener by
assuming self-weight of plate on beam is shown in equation
below.
𝛿 =𝑤𝑙2
384𝐸𝐼
𝑓𝑛 =0.571
√𝛿
IV. STIFFENED PLATE ANALYSIS IN ANSYS
A. Analysis of buckling stress in ANSYS:
The model of plate is modelled in ANSYS workbench 17 and
for this model selected materials and material properties are
shown in table 2.1 and table 2.2. The dimensions which I have
consider to do model for plate and plate with stiffener T and
J-section is shown in table 4.1, 4.2 and 4.3.
Parameter Dimensions (mm)
Length (l) 2500
Breadth (b) 1800
Thickness (t) 25.34, 20, and 30
Table 4.1: Dimensions of plate
Parameter Dimensions (mm)
Length (l) 2500
Breadth (b) 1800
Thickness (t) 25.34, 20, and 30
Web length 250
Flange length 120
Table 4.2: Stiffened plate with T-section
Parameter Dimensions (mm)
Length (l) 2500
Breadth (b) 1800
Thickness (t) 25.34, 20, and 30
Web length 250
Flange length 1 120
Flange length 2 72
Table 4.3: Stiffened plate with J-section
B. ANSYS Stiffened Plate Model with Thickness 25.34 Mm:
1) Aluminium 7075 material buckling stress
a) plate without stiffener
Fig. 4.1: Buckling stress for plate without stiffener
b) plate with stiffener T-section:
Fig. 4.2: Buckling stress for stiffened plate with T-section
Design and Analysis of Stiffened Plate
(IJSRD/Vol. 5/Issue 04/2017/174)
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c) Plate with stiffener J-section
Fig. 4.3: Buckling stress for stiffened plate with J-section
2) Glass fibre material buckling stress:
a) Plate Without Stiffeners:
Fig. 4.4: Buckling stress for plate without stiffener
b) Plate With Stiffener T-Section:
Fig. 4.5: Buckling stress for stiffened plate with T-section
c) Plate with Stiffener J-Section
Fig. 4.6: Buckling stress for stiffened plate with J-section
C. ANSYS stiffened plate model with thickness 20 mm:
1) Aluminium 7075 material buckling stress:
a) Plate without stiffeners
Fig. 4.7: Buckling stress for plate without stiffener
b) Plate with stiffener T-section:
Fig. 4.8: Buckling stress for stiffened plate with T-section
c) Plate with stiffener J-section:
Fig. 4.9: Buckling stress for stiffened plate with J-section
2) Glass fibre material buckling stress:
a) Plate without stiffener
Fig. 4.10: Buckling stress for plate without stiffener
Design and Analysis of Stiffened Plate
(IJSRD/Vol. 5/Issue 04/2017/174)
All rights reserved by www.ijsrd.com 694
b) Plate with stiffener T-section
Fig. 4.11: Buckling stress for stiffened plate with T-section
c) Plate with stiffener J-section
Fig. 4.12: Buckling stress for stiffened plate with J-section
D. ANSYS stiffened plate model with thickness 30 mm:
1) Aluminium 7075 material buckling stress:
a) Plate without stiffeners
Fig. 4.13: Buckling stress for plate without stiffener
b) Plate with Stiffener T-Section
Fig. 4.14: Buckling stress for stiffened plate with T-section
c) Plate with stiffener J-section
Fig. 4.15: Buckling stress for stiffened plate with J-section
2) Glass fibre material buckling stress:
a) Plate without stiffener
Fig. 4.16: Buckling stress for plate without stiffener
b) Plate with stiffener T-section:
Fig. 4.17: Buckling stress for stiffened plate with T-section
c) plate with stiffener J-section:
Fig. 4.18: Buckling stress for stiffened plate with J-section
V. MODAL ANALYSIS IN ANSYS APDL
The model of stiffened plate with T- section is modelled in
ANSYS APDL is as shown in figure 5.1 and for this model
Design and Analysis of Stiffened Plate
(IJSRD/Vol. 5/Issue 04/2017/174)
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selected materials and material properties are shown in table
2.1 and table 2.2. The dimensions which I have consider to
do model is shown in table 5.1 and table 5.2.
Parameter Dimensions (mm)
Length (l) 2500
Breadth (b) 1800
Thickness (t) 25.34, 20, and 30
Web length 250
Flange length 120
Table 5.1: Dimensions of stiffened plate with T-section
Fig. 5.1: Modal of stiffened plate with T-section
Parameter Dimensions (mm)
Length (l) 2500
Breadth (b) 1800
Thickness (t) 25.34, 20, and 30
Web length 250
Flange length 1 120
Flange length 2 72
Table 5.2: Dimensions of stiffened plate with J-section
Fig. 5.2: Modal of stiffened plate with J-section
A. ANSYS APDL Stiffened Plate Model With Thickness
25.34 Mm:
1) Natural frequency for aluminium 7075 material:
a) plate with stiffener T-Section:
Fig. 5.3: Natural frequency for stiffened plate with T-section
b) Plate with stiffener J-Section:
Fig. 5.4: Natural frequency for stiffened plate with J-section
2) Natural frequency for glass fibre material:
a) Plate with stiffener T-Section
Fig. 5.5: Natural frequency for stiffened plate with T-section
b) Plate with stiffener J-Section
Fig. 5.6: Natural frequency for stiffened plate with J-section
Design and Analysis of Stiffened Plate
(IJSRD/Vol. 5/Issue 04/2017/174)
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B. ANSYS APDL stiffened plate model with thickness 20
mm:
1) Natural frequency for aluminium 7075 material:
a) Plate with stiffener T-Section
Fig. 5.7: Natural frequency for stiffened plate with T-section
b) Plate with stiffener J-Section:
Fig. 5.8: Natural frequency for stiffened plate with J-section
2) Natural frequency for glass fibre material:
a) Plate with stiffener T-Section:
Fig. 5.9: Natural frequency for stiffened plate with T-section
b) Plate with stiffener J-Section:
Fig. 5.10: Natural frequency for stiffened plate with J-
section
C. ANSYS APDL stiffened plate model with thickness 30
mm:
1) Natural frequency for aluminium 7075 material:
a) Plate with stiffener T-Section:
Fig. 5.11: Natural frequency for stiffened plate with T-
section
b) Plate with stiffener J-Section
Fig. 5.12: Natural frequency for stiffened plate with J-
section
2) Natural frequency for glass fibre material:
a) Plate with stiffener T-Section
Fig. 5.44: Natural frequency for stiffened plate with T-
section
b) Plate with stiffener J-Section
Fig. 5.45: Natural frequency for stiffened plate with J-
section
Design and Analysis of Stiffened Plate
(IJSRD/Vol. 5/Issue 04/2017/174)
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VI. RESULTS AND DISCUSSIONS
A. Buckling stress results:
The buckling stress for plate without stiffener and plate with
stiffeners T and J-section with boundary condition two end
fixed and two end free with compressive load, results
obtained in analytical and in ANSYS workbench are
compared and have close agreement. Buckling stress
calculations done in three different thickness and table 6.1
shows validating results for thickness 25.34 mm with two end
fixed and two end free boundary condition at constant
compressive load 135 KN.
S.No Material Shape
Buckling Stresses
( MPa )
Analytical
Results
ANSYS
Results
1
Aluminium
7075
Plate
without
stiffener
2.95 2.70
Plate with
T-Section 5.62 5.16
Plate with
J-section 5.25 5.19
2
Glass Fibre
Plate
without
stiffener
1.29 1.13
Plate with
T- Section 2.67 3.06
Plate with
J-section 2.48 2.99
Table 6.1: Comparing results of buckling stress of thickness
25.34 mm
For 20 mm thickness buckling analytical results are
compared with buckling stress in ansys workbench and Table
6.2 shows validating results for thickness 20 mm with two
end fixed and two end free boundary condition at constant
compressive load 135 KN.
S.No Material Shape
Buckling Stresses
( MPa )
Analytical
Results
ANSYS
Results
1
Aluminium
7075
Plate
without
stiffener
1.84 2.14
Plate with
T-Section 3.53 3.58
Plate with
J-section 3.25 3.60
2
Glass Fibre
Plate
without
stiffener
0.80 0.90
Plate with
T-Section 1.66 1.80
Plate with
J-section 1.53 1.76
Table 6.2: Comparing results of buckling stress of thickness
20 mm
For 30 mm thickness buckling analytical results are
compared with buckling stress in ansys workbench and Table
6.3 shows validating results for thickness 30 mm with two
end fixed and two end free boundary condition at constant
compressive load 135 KN.
S.NO Material Shape
Buckling Stresses
( MPa )
Analytical
Results
ANSYS
Results
1
Aluminium
7075
Plate
without
stiffener
4.14 3.90
Plate with
T-Section 8.02 7.52
Plate with
J-section 7.36 7.54
2
Glass Fibre
Plate
without
stiffener
1.81 1.33
Plate with
T-Section 3.78 3.82
Plate with
J-section 3.47 3.79
Table 6.3: Comparing results of buckling stress of thickness
30 mm
B. Natural frequency results:
The natural frequency for plate without stiffener and plate
with stiffeners T and J-section with boundary condition two
end fixed and two end free, results obtained in analytical and
in ansys APDL are compared and have close agreement.
Natural frequency calculations done in three different
thickness and table 6.4 shows validating results for thickness
25.34 mm with two end fixed and two end free boundary
condition.
S.No Material Shape
Natural Frequency
( Hz )
Analytical
Results
Ansys
Results
1
Aluminium
7075
Plate With
T-Section 1.40 1.53
Plate With
J-Section 1.52 1.54
2
Glass Fibre
Plate With
T-Section 1.20 1.28
Plate With
J-Section 1.30 1.30
Table 6.4: Validating results for thickness 25.34 mm with
two end fixed and end free boundary condition
For 20 mm thickness analytical results are compared
with results in ansys APDL and Table 6.5 shows validating
results for thickness 20 mm with two end fixed and two end
free boundary condition.
S.No Material Shape
Natural Frequency
( Hz )
Analytical
Results
Ansys
Results
1
Aluminium
7075
Plate With
T-Section 1.38 1.20
Plate With
J-Section 1.51 1.22
2
Glass Fibre
Plate With
T-Section 1.18 1.02
Plate With
J-Section 1.29 1.03
Design and Analysis of Stiffened Plate
(IJSRD/Vol. 5/Issue 04/2017/174)
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Table 6.5: Validating results for thickness 20 mm with two
end fixed and end free boundary condition
For 30 mm thickness analytical results are compared
with results in ansys APDL and Table 6.6 shows validating
results for thickness 30 mm with two end fixed and two end
free boundary condition.
S.No Material Shape
Natural Frequency
( Hz )
Analytical
Results
Ansys
Results
1
Aluminium
7075
Plate With
T-Section 1.42 1.81
Plate With
J-Section 1.56 1.81
2
Glass Fibre
Plate With
T-Section 1.22 1.51
Plate With
J-Section 1.33 1.53
Table 6.6: Validating results for thickness 30 mm with two
end fixed and end free boundary condition
VII. CONCLUSION
In this report, general material used to construct aircraft
stiffened plate is aluminium 7075 but now in bigger aircraft
companies are researching to use glass fibre material instead
of aluminium 7075. So we tried to compare two materials that
is aluminium and glass fibre, through comparing analytical
and ANSYS results. In aircraft industries stiffened plate is
designed in such a way that, stiffened plate need to carry load
more than the applied load.
Firstly we check the design of stiffened plate model
is safe or not. After designing stiffened plate, we find
buckling stress for plate without stiffener and plate with
stiffener T and J-section. In this when we applied
compressive load on plate without stiffener and plate with
stiffener by considering boundary condition two end fixed
and two end free, we get buckling stress but we know that
buckling stress will not depended upon the load, its depended
upon the parameters and type of material we used. Buckling
stress obtained from glass fibre material is less than the
aluminium 7075 material but glass fibre can carry load more
than the applied load. So we can say that, we can use glass
fibre instead of aluminium 7075, because glass fibre have
good properties like low weight, high stiffness, high chemical
resistance, high temperature tolerance and low thermal
expansion.
Modal analysis is also done to determine the
vibration characteristics like natural frequency on designed
stiffened plate. Natural frequency for glass fibre is near
compared to aluminium 7075. So therefore we can use glass
fibre.
Therefore by comparing buckling stress and natural
frequency analytical results with ANSYS results, I found that
glass fibre is more robust than the aluminium 7075 material.
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Design and Analysis of Stiffened Plate
(IJSRD/Vol. 5/Issue 04/2017/174)
All rights reserved by www.ijsrd.com 699
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