Design and Analysis of Stiffened Plate · In stiffened plates buckling is the main criteria to know buckling behaviour on both stiffeners and plates. These stiffened plates are able

IJSRD - International Journal for Scientific Research & Development| Vol. 5, Issue 04, 2017 | ISSN (online): 2321-0613

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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.


(IJSRD/Vol. 5/Issue 04/2017/174)


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


Length (l) 2500

Breadth (b) 1800


Web length 250

Flange length 120

Table 4.2: Stiffened plate with T-section


Length (l) 2500

Breadth (b) 1800


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




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:


b) Plate With Stiffener T-Section:


c) Plate with Stiffener J-Section


C. ANSYS stiffened plate model with thickness 20 mm:

1) Aluminium 7075 material buckling stress:

a) Plate without stiffeners


b) Plate with stiffener T-section:


c) Plate with stiffener J-section:



a) Plate without stiffener





b) Plate with stiffener T-section




D. ANSYS stiffened plate model with thickness 30 mm:

1) Aluminium 7075 material buckling stress:

a) Plate without stiffeners


b) Plate with Stiffener T-Section





a) Plate without stiffener


b) Plate with stiffener T-section:


c) plate with stiffener 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




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.


Length (l) 2500

Breadth (b) 1800


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


Length (l) 2500

Breadth (b) 1800


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


b) Plate with stiffener J-Section





B. ANSYS APDL stiffened plate model with thickness 20

mm:







a) Plate with stiffener T-Section:



Fig. 5.10: Natural frequency for stiffened plate with J-

section

C. ANSYS APDL stiffened plate model with thickness 30

mm:


a) Plate with stiffener T-Section:

Fig. 5.11: Natural frequency for stiffened plate with T-

section



section



Fig. 5.44: Natural frequency for stiffened plate with T-

section



section




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


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


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


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


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




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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Documents

Design and Analysis of Stiffened Plate · In stiffened plates buckling is the main criteria to know buckling behaviour on both stiffeners and plates. These stiffened plates are able