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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
90
DESIGN AND OPTIMIZATION OF ELECTROSTATIC PRECIPITATOR
USING FINITE ELEMENT ANALYSIS TOOL
Mr. Abhijeet Rane, Gajendra V. Patil, Gajanan Thokal, Vinayak Khatwate
1
(Mechanical Engineering, Pillai’s institute of Information and Technology, Mumbai University,
New Panvel, India)
2, 3, 4
(Assistant Professor, Mechanical Engineering, Pillai’s institute of Information and Technology,
Mumbai University, New Panvel, India)
ABSTRACT
An electrostatic precipitator is designed to trap and remove dust particles from the exhaust
gas. The computer aided design and finite element analysis of electrostatic precipitator cone structure
has been carried out. For static structure analysis two models (Model A and Model B) is being
considered having horizontal and vertical stiffener arrangement. As per ISO (IS 808: 1989, Edition
4.1) standard for stiffeners, the various sizes of stiffeners are analyzed for electrostatic precipitator
cone structure. The deformation of Model A cone structure and Model B cone structure is analyzed
with various stiffener arrangements with allowable deformation 39mm. From analysis it is observed
that deformation goes on decrease as weight of electrostatic precipitator cone structure increase. Also
it is interestingly noted that maximum deflection region in each case of model is at centre of face
having maximum surface area.
Keywords: Electrostatic Precipitator, Finite Element Analysis, Stiffener, Cone Structure.
1. INTRODUCTION
1.1 Electrostatic precipitator
An electrostatic precipitator is an emission-control unit which is designed to trap and remove
dust particles from the exhaust gas stream from boiler. The cone structure is air tight conduit to
transport air or flue gases under positive or negative pressure. In order to accommodate the
expansion due to the temperature, expansions joints are introduced along the duct length. This
creates independent pieces of ducts with own floating supports. Figure 2 illustrates the cone structure
with expansion joints [1].
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 5, Issue 1, January (2014), pp. 90-97
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2013): 5.7731 (Calculated by GISI)
www.jifactor.com
IJMET
© I A E M E
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
91
Fig.2. Block diagram of electrostatic precipitator Fig.3. Cone structure with expansion joints
The cone system is designed to resist the loads such as internal suction pressure, weight of
the cone structure, thermal expansion. The internal pressure load consists of two components;
operating pressure, which is the expected pressure continuously acting on the wall, and transient
pressure, which is the very high pressure for relatively very short period of time during an abnormal
event. The cone side panels are often joined longitudinally with angles or bent plates at the corner of
the duct. Corner angles provide air tight seal in addition to strength and stiffness. The stiffener and
the plate act as one composite section to jointly resist the loads. In order to be a complete composite
section, the attachment between the stiffener and the plate must have adequate strength.
The effect of stiffener location on the overall deformation and overall weight of the cone
structure is analysed. The proposed results can be used to develop an improved design for
electrostatic precipitator cone structure along with best suited stiffener arrangement. There is need to
control the deformation of electrostatic precipitator cone structure within considerable limit i.e.
maximum deformation should not exceed more than 39mm. So to make the cone stiffer various
arrangements of stiffeners are analyzed.
The structural failure of electrostatic precipitator cone which is suspended in a cantilever
arrangement is analyzed using Finite Element Analysis tool (ANSYS 12.0) to analyze the
deformation and to reduce the weight so as to make it economical. Comparative study of non-linear
analysis [2] on cone structure of electrostatic precipitator with Model A and Model B which have
horizontal and vertical stiffener arrangement respectively has been done. Various arrangements of
stiffeners are analyzed so as to reduce the deformation and weight of structure. Maximum
deformation should not exceed 39mm. Model B gives minimum deflection as compare to other
models.
2. PROBLEM FORMULATION AND METHODOLOGY
Finite element analysis software ANSYS 12.0 (Workbench) has been used for static
structural analysis of electrostatic precipitator cone structure. In this investigation, the nonlinearity
comes from the material properties and buckling behaviour of stiffened panels.
2.1. MODELING OF THE ELECTROSTATIC PRECIPITATOR CONE
The three dimensional computer aided design model of electrostatic precipitator cone
structure is created as Model A and Model B. Model A consists of cone structure with arrangement
of stiffeners crossing the axis of cone (gas flow). Model B model having stiffeners are arranged in
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
92
the direction of gas flow. The channel section dimensions i.e. its web height and flange width gets
varied as per ISO standards to reduce deformation of the electrostatic precipitator cone structure and
make it safer. The different model of electrostatic cone structure with channel sizes 150×75mm,
250×80mm, 300×90mm and 400×100mm is developed in ANSYS12.0. Total height of cone is
13900mm and length is 4530mm respectively as shown in fig below.
Fig. 4. Two dimensional view of electrostatic precipitator cone
Fig.5. Model A: Horizontal Stiffener Fig.6. ModelB: Vertical Stiffener
Applying Material Properties
• Material : Structural Steel
• Young’s Modulus (E) : 200 e9 MPa
• Poisson’s Ratio (µ) : 0.3
• Density : 7850 kg/mm3
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
93
2.2. MESHING
Meshing is done using shell181 element.
Fig.7. Element Shell 181
2.2.1. AUTOMATIC METHOD
• Scoping method :Geometry selection
• Geometry : 77 Bodies
• Method : Quadrilateral dominant
• Element midside node : Use global setting
• Free face mesh Type : Quad/Tri
2.2.2. BODY SIZING
• Scoping method : Geometry selection
• Geometry : 77 Bodies
• Suppressed : No
• Element size : 50mm
• Behaviour : Soft
2.3. MODAL ANALYSIS
Contact between two bodies of electrostatic precipitator cone structure is checked in modal
analysis. Bigger side of inlet is fixed because bigger end is connected to main body and smaller end
is connected to expansion joint to facilitate the expansion due to thermal loads. Maximum modes to
find are kept as six so the analysis will take place in six steps. Total deformation has been checked to
confirm the contact between two connecting bodies.
Table 1 Modal analysis of electrostatic precipitator cone structure.
Mode Frequency [Hz]
1 15.448
2 18.526
3 21.577
4 21.985
5 23.21
6 25.144
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
94
2.4. STATIC STRUCTURAL ANALYSIS
Bigger end having six edges and twenty faces is considered as fixed support 1, fixed support2
is connected to main body. Smaller end is connected to expansion joint to facilitate the expansion
due to thermal loads. All edges and faces at bigger end of cone structure which is connected to main
body are fixed and pressure of 0.05 MPa is applied normal to each cone surface. The nonlinearity [3]
comes from the material properties and buckling behaviour of stiffened panels, the nonlinear finite
element method was done using ANSYS.
2.5. SOLUTION
The static structural analysis of Model A and Model B having channel sizes used are
150×75mm, 250×80mm, 300×90mm and 400×100mm, analysed the results as follows:
Total deformation of model A and model B electrostatic precipitator cone structure.
Overall weight of electrostatic precipitator cone structure.
3. RESULTS AND DISCUSSION
All edges and faces at bigger end of cone structure which is connected to main body are kept
fixed and pressure of 0.05 MPa is applied on each cone surface, as bigger end is connected to main
body and smaller end is connected to expansion joint to facilitate the expansion due to thermal loads.
It is need to control the deformation of Electrostatic precipitator cone structure within considerable
limit i.e. maximum deformation should not exceed than 39mm. The cone structure with different
arrangements of stiffeners is analyzed.
Fig. 8.Deformation of model A with stiffener size 400×100mm
Table 2. Results with model A
Stiffener size in mm Deformation in mm Weight in kg
150×75 244.11 36132
250×80 172.79 37132
300×90 123.13 38029
400×100 88.114 39360
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
95
Fig.8. Graph of deformation vs weight for model B
Table 3. Results with model B
Stiffener size Deformation in mm Weight in kg
150×75 167.34 36025
250×80 85.347 37159
300×90 60.137 37973
400×100 36.781 39277
0
50
100
150
200
250
300
36132 37132 38029 39360
Deformationinmm
Weight in kg
Results with model A
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
96
Fig.9. Graph of deformation vs weight for model B
4. CONCLUSION
Comparative study of nonlinear analysis has been done for two different arrangements of
stiffeners (horizontal and vertical) on the cone structure of Electrostatic Precipitator. Deflections &
weights for all two models are as listed in table.
Table 4. Deflections & weights for model A and Model B
Model with
400×100 mm
stiffener
Weight in kg
Maximum
deformation
in mm
Allowable
Deformation
in mm
Model A 39277 88.114 39
Model B 39360 36.781 39
After observing above results some conclusions can be made that Model B having stiffener
size 400x100mm and with vertical arrangement gives minimum deflection as compare to other
models. So thinking toward safety perspective model B is safer as compare to models A whereas
weight of model B is more as compare to model A. So model B will require more material and it will
cause increase in cost. Also it is interestingly noted that maximum deflection region in each case of
model is at centre of face having maximum surface area. The reason behind this is extended portion
on this face which kept fixed as per boundary condition requirements and deflection distribution in
all cases is nearly symmetric.
0
20
40
60
80
100
120
140
160
180
36025 37159 37973 39277
Deformationinmm
Weight in kg
Results with model B
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME
97
REFERENCES
[1] Je-Hoon Kim1, Jin-Ho Kim1*, Sang-Hyun Jeong2, and Bang-Woo Han2, “Design and
Experiment of an Electromagnetic Vibration Exciter for the Rapping of an Electrostatic
Precipitator”, International Scientific Journal published by Journal of Magnetics volume 17,
MARCH 2012, page 61-67.
[2] Cook, R. D., Malkus, D. S. and Plesha, M. E., “Concepts and Applications of Finite Element
Analysis”, 4th Edition, John Wiley & Sons, New York, 2002, pp 530-587.
[3] Crisfield, M. A., “Non-linear Finite Element Analysis of Solids and Structures”, John Wiley
& Sons, Chichester, 1991, Volume 1, pp 77-80,131-132, 211-220.
[4] Mukund Kavekar, Vinayak H.Khatawate and Gajendra V. Patil, “Weight Reduction of
Pressure Vessel using FRP Composite Material”, International Journal of Mechanical
Engineering & Technology (IJMET), Volume 4, Issue 4, 2013, pp. 300 - 310, ISSN Print:
0976 – 6340, ISSN Online: 0976 – 6359.
[5] Sanjay Paliwal and H.Chandra, “Investigation of Particulate Control in Thermal Power Plant
using Electrostatic Precipitator”, International Journal of Mechanical Engineering &
Technology (IJMET), Volume 4, Issue 3, 2013, pp. 149 - 154, ISSN Print: 0976 – 6340,
ISSN Online: 0976 – 6359.
[6] I.M.Jamadar, S.M.Patil, S.S.Chavan, G.B.Pawar and G.N.Rakate, “Thickness Optimization
of Inclined Pressure Vessel Using Non Linear Finite Element Analysis using Design by
Analysis Approach”, International Journal of Mechanical Engineering & Technology
(IJMET), Volume 3, Issue 3, 2012, pp. 682 - 689, ISSN Print: 0976 – 6340, ISSN Online:
0976 – 6359.

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DESIGN AND OPTIMIZATION OF ELECTROSTATIC PRECIPITATOR USING FINITE ELEMENT ANALYSIS TOOL

  • 1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME 90 DESIGN AND OPTIMIZATION OF ELECTROSTATIC PRECIPITATOR USING FINITE ELEMENT ANALYSIS TOOL Mr. Abhijeet Rane, Gajendra V. Patil, Gajanan Thokal, Vinayak Khatwate 1 (Mechanical Engineering, Pillai’s institute of Information and Technology, Mumbai University, New Panvel, India) 2, 3, 4 (Assistant Professor, Mechanical Engineering, Pillai’s institute of Information and Technology, Mumbai University, New Panvel, India) ABSTRACT An electrostatic precipitator is designed to trap and remove dust particles from the exhaust gas. The computer aided design and finite element analysis of electrostatic precipitator cone structure has been carried out. For static structure analysis two models (Model A and Model B) is being considered having horizontal and vertical stiffener arrangement. As per ISO (IS 808: 1989, Edition 4.1) standard for stiffeners, the various sizes of stiffeners are analyzed for electrostatic precipitator cone structure. The deformation of Model A cone structure and Model B cone structure is analyzed with various stiffener arrangements with allowable deformation 39mm. From analysis it is observed that deformation goes on decrease as weight of electrostatic precipitator cone structure increase. Also it is interestingly noted that maximum deflection region in each case of model is at centre of face having maximum surface area. Keywords: Electrostatic Precipitator, Finite Element Analysis, Stiffener, Cone Structure. 1. INTRODUCTION 1.1 Electrostatic precipitator An electrostatic precipitator is an emission-control unit which is designed to trap and remove dust particles from the exhaust gas stream from boiler. The cone structure is air tight conduit to transport air or flue gases under positive or negative pressure. In order to accommodate the expansion due to the temperature, expansions joints are introduced along the duct length. This creates independent pieces of ducts with own floating supports. Figure 2 illustrates the cone structure with expansion joints [1]. INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 5, Issue 1, January (2014), pp. 90-97 © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) www.jifactor.com IJMET © I A E M E
  • 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME 91 Fig.2. Block diagram of electrostatic precipitator Fig.3. Cone structure with expansion joints The cone system is designed to resist the loads such as internal suction pressure, weight of the cone structure, thermal expansion. The internal pressure load consists of two components; operating pressure, which is the expected pressure continuously acting on the wall, and transient pressure, which is the very high pressure for relatively very short period of time during an abnormal event. The cone side panels are often joined longitudinally with angles or bent plates at the corner of the duct. Corner angles provide air tight seal in addition to strength and stiffness. The stiffener and the plate act as one composite section to jointly resist the loads. In order to be a complete composite section, the attachment between the stiffener and the plate must have adequate strength. The effect of stiffener location on the overall deformation and overall weight of the cone structure is analysed. The proposed results can be used to develop an improved design for electrostatic precipitator cone structure along with best suited stiffener arrangement. There is need to control the deformation of electrostatic precipitator cone structure within considerable limit i.e. maximum deformation should not exceed more than 39mm. So to make the cone stiffer various arrangements of stiffeners are analyzed. The structural failure of electrostatic precipitator cone which is suspended in a cantilever arrangement is analyzed using Finite Element Analysis tool (ANSYS 12.0) to analyze the deformation and to reduce the weight so as to make it economical. Comparative study of non-linear analysis [2] on cone structure of electrostatic precipitator with Model A and Model B which have horizontal and vertical stiffener arrangement respectively has been done. Various arrangements of stiffeners are analyzed so as to reduce the deformation and weight of structure. Maximum deformation should not exceed 39mm. Model B gives minimum deflection as compare to other models. 2. PROBLEM FORMULATION AND METHODOLOGY Finite element analysis software ANSYS 12.0 (Workbench) has been used for static structural analysis of electrostatic precipitator cone structure. In this investigation, the nonlinearity comes from the material properties and buckling behaviour of stiffened panels. 2.1. MODELING OF THE ELECTROSTATIC PRECIPITATOR CONE The three dimensional computer aided design model of electrostatic precipitator cone structure is created as Model A and Model B. Model A consists of cone structure with arrangement of stiffeners crossing the axis of cone (gas flow). Model B model having stiffeners are arranged in
  • 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME 92 the direction of gas flow. The channel section dimensions i.e. its web height and flange width gets varied as per ISO standards to reduce deformation of the electrostatic precipitator cone structure and make it safer. The different model of electrostatic cone structure with channel sizes 150×75mm, 250×80mm, 300×90mm and 400×100mm is developed in ANSYS12.0. Total height of cone is 13900mm and length is 4530mm respectively as shown in fig below. Fig. 4. Two dimensional view of electrostatic precipitator cone Fig.5. Model A: Horizontal Stiffener Fig.6. ModelB: Vertical Stiffener Applying Material Properties • Material : Structural Steel • Young’s Modulus (E) : 200 e9 MPa • Poisson’s Ratio (µ) : 0.3 • Density : 7850 kg/mm3
  • 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME 93 2.2. MESHING Meshing is done using shell181 element. Fig.7. Element Shell 181 2.2.1. AUTOMATIC METHOD • Scoping method :Geometry selection • Geometry : 77 Bodies • Method : Quadrilateral dominant • Element midside node : Use global setting • Free face mesh Type : Quad/Tri 2.2.2. BODY SIZING • Scoping method : Geometry selection • Geometry : 77 Bodies • Suppressed : No • Element size : 50mm • Behaviour : Soft 2.3. MODAL ANALYSIS Contact between two bodies of electrostatic precipitator cone structure is checked in modal analysis. Bigger side of inlet is fixed because bigger end is connected to main body and smaller end is connected to expansion joint to facilitate the expansion due to thermal loads. Maximum modes to find are kept as six so the analysis will take place in six steps. Total deformation has been checked to confirm the contact between two connecting bodies. Table 1 Modal analysis of electrostatic precipitator cone structure. Mode Frequency [Hz] 1 15.448 2 18.526 3 21.577 4 21.985 5 23.21 6 25.144
  • 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME 94 2.4. STATIC STRUCTURAL ANALYSIS Bigger end having six edges and twenty faces is considered as fixed support 1, fixed support2 is connected to main body. Smaller end is connected to expansion joint to facilitate the expansion due to thermal loads. All edges and faces at bigger end of cone structure which is connected to main body are fixed and pressure of 0.05 MPa is applied normal to each cone surface. The nonlinearity [3] comes from the material properties and buckling behaviour of stiffened panels, the nonlinear finite element method was done using ANSYS. 2.5. SOLUTION The static structural analysis of Model A and Model B having channel sizes used are 150×75mm, 250×80mm, 300×90mm and 400×100mm, analysed the results as follows: Total deformation of model A and model B electrostatic precipitator cone structure. Overall weight of electrostatic precipitator cone structure. 3. RESULTS AND DISCUSSION All edges and faces at bigger end of cone structure which is connected to main body are kept fixed and pressure of 0.05 MPa is applied on each cone surface, as bigger end is connected to main body and smaller end is connected to expansion joint to facilitate the expansion due to thermal loads. It is need to control the deformation of Electrostatic precipitator cone structure within considerable limit i.e. maximum deformation should not exceed than 39mm. The cone structure with different arrangements of stiffeners is analyzed. Fig. 8.Deformation of model A with stiffener size 400×100mm Table 2. Results with model A Stiffener size in mm Deformation in mm Weight in kg 150×75 244.11 36132 250×80 172.79 37132 300×90 123.13 38029 400×100 88.114 39360
  • 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME 95 Fig.8. Graph of deformation vs weight for model B Table 3. Results with model B Stiffener size Deformation in mm Weight in kg 150×75 167.34 36025 250×80 85.347 37159 300×90 60.137 37973 400×100 36.781 39277 0 50 100 150 200 250 300 36132 37132 38029 39360 Deformationinmm Weight in kg Results with model A
  • 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME 96 Fig.9. Graph of deformation vs weight for model B 4. CONCLUSION Comparative study of nonlinear analysis has been done for two different arrangements of stiffeners (horizontal and vertical) on the cone structure of Electrostatic Precipitator. Deflections & weights for all two models are as listed in table. Table 4. Deflections & weights for model A and Model B Model with 400×100 mm stiffener Weight in kg Maximum deformation in mm Allowable Deformation in mm Model A 39277 88.114 39 Model B 39360 36.781 39 After observing above results some conclusions can be made that Model B having stiffener size 400x100mm and with vertical arrangement gives minimum deflection as compare to other models. So thinking toward safety perspective model B is safer as compare to models A whereas weight of model B is more as compare to model A. So model B will require more material and it will cause increase in cost. Also it is interestingly noted that maximum deflection region in each case of model is at centre of face having maximum surface area. The reason behind this is extended portion on this face which kept fixed as per boundary condition requirements and deflection distribution in all cases is nearly symmetric. 0 20 40 60 80 100 120 140 160 180 36025 37159 37973 39277 Deformationinmm Weight in kg Results with model B
  • 8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 1, January (2014), © IAEME 97 REFERENCES [1] Je-Hoon Kim1, Jin-Ho Kim1*, Sang-Hyun Jeong2, and Bang-Woo Han2, “Design and Experiment of an Electromagnetic Vibration Exciter for the Rapping of an Electrostatic Precipitator”, International Scientific Journal published by Journal of Magnetics volume 17, MARCH 2012, page 61-67. [2] Cook, R. D., Malkus, D. S. and Plesha, M. E., “Concepts and Applications of Finite Element Analysis”, 4th Edition, John Wiley & Sons, New York, 2002, pp 530-587. [3] Crisfield, M. A., “Non-linear Finite Element Analysis of Solids and Structures”, John Wiley & Sons, Chichester, 1991, Volume 1, pp 77-80,131-132, 211-220. [4] Mukund Kavekar, Vinayak H.Khatawate and Gajendra V. Patil, “Weight Reduction of Pressure Vessel using FRP Composite Material”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 4, Issue 4, 2013, pp. 300 - 310, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359. [5] Sanjay Paliwal and H.Chandra, “Investigation of Particulate Control in Thermal Power Plant using Electrostatic Precipitator”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 4, Issue 3, 2013, pp. 149 - 154, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359. [6] I.M.Jamadar, S.M.Patil, S.S.Chavan, G.B.Pawar and G.N.Rakate, “Thickness Optimization of Inclined Pressure Vessel Using Non Linear Finite Element Analysis using Design by Analysis Approach”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue 3, 2012, pp. 682 - 689, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359.