Strength Analysis of Pressure Vessel by Using Finite Element Approach under the Pressure Loading Condition

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 10 Issue: 09 | Sep 2023 www.irjet.net p-ISSN: 2395-0072
© 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 316
Strength Analysis of Pressure Vessel by Using Finite Element Approach
under the Pressure Loading Condition
Ashifahmad Devalapur1, Samrat P Pingat2, Prof. Revanasiddappa H3, Dr. Anand C Mattikali4
1,2M.Tech Students, Dept. of Mechanical Engineering, Maratha Mandal Engineering College, Belgaum, Karnataka,
India
3Professor, Dept. of Mechanical Engineering, Maratha Mandal Engineering College, Belgaum, Karnataka, India
4H.O.D, Dept. of Mechanical Engineering, Maratha Mandal Engineering College, Belgaum, Karnataka, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract –The Pressure vesselsarecriticalcomponentsused
in various industries to contain liquids, gases, or vapors at
elevated pressures. Ensuring their structural integrity and
resistance to failure is of paramount importance to prevent
catastrophic incidents. The primary objective is to assess the
structural behavior of the pressure vessel and identify
potential weak points or areas of concern that may be prone
to failure. The study involves the utilization of advanced
computational tools, particularly finite element analysis
(FEA), to simulate the complex mechanical behavior of the
pressure vessel. The pressure loading conditions, which
simulate the operational environments, areappliedtotheFEA
model to evaluate stress distribution, deformations, and
potential failure modes. By employing the finite element
method, the study provides detailed insights into stress
distribution and deformation patterns within the pressure
vessel's components. The FEA results are analyzed to
determine the critical stress points and regions where
excessive deformations or stress concentrations occur. This
information is crucial for identifyingpotentialfailuresitesand
for making informed decisions on design modifications or
material selection.
The study's findings contribute to enhancing the safety and
reliability of pressure vessels by providing valuable insights
into their structural behavior under pressure loading
conditions. The finite element approach serves as a powerful
tool to predict potential failure modes, guide design
improvements, and optimize the overall performance of
pressure vessels. Ultimately, this research aids in ensuring the
robustness of pressure vessel designs, thereby mitigatingrisks
associated with potential structural failures and contributing
to safer industrial operations.
Key Words: Pressure Vessel, FiniteElementAnalysis,Ansys,
ASME, Stress, ASTM A357.
1. INTRODUCTION
Pressure vessels play a crucial role in various industries,
containing substances at significantly different pressures
than the surrounding environment. They're essential
components in industries such as petrochemicals, oil and
gas, chemicals, and food processing. Examples include
reactors, flash drums, separators, and heat exchangers.
Various standards and regulations govern pressure vessels,
ensuring their safety and performance. One of the most
widely recognized standards is the ASME Boiler and
Pressure Vessel Code (BPVC). This code encompasses the
design, construction, installation, testing, inspection, and
certification of boilers, pressure vessels, and nuclear power
plant components. Within the ASME BPVC, Section VIII
specifically addresses pressure vessels and is divided into
three divisions:
1. Division I:
• Covers pressure vessels designed to operate with
internal or external pressures exceeding 15 psig.
• Can include fired or unfired vessels, with pressure
derived from external sources or heating.
• Engineers use a design-by-rule approach based on
normal stress theory to ensure safety.
2. Division II: Addresses pressure vessels operatingat
pressures up to 10,000 psig, whether internal or external.
• Requirements for materials, design, and non-
destructive examination are more stringent compared to
Division I.
• Engineers employ more detailed calculations and a
design-by-analysis approach, allowing for higher stress
limits based on maximum distortion energy theory.
3. Division III:
• Pertains to pressurevesselsoperatingabove10,000
psig.
• Specifies mandatory requirementsandprohibitions
for vessels under these extreme pressure conditions.
The API 510 standard is another important guideline in the
realm of pressure vessels. The API 510 - Pressure Vessel
Inspection Code: In-Service Inspection, Rating, Repair, and
Alteration focuses on the ongoing maintenance, inspection,
repair, and alteration of pressure vessels that are already in
operation. Its primary objective is to ensure the safety,

reliability, and continued performance of pressure vessels
throughout their service life.
2. LITERATURE SURVEY
Niranjana.S. J and Smit Vishal Patel [1] developed a closed
container that adheres to ASME standards, determine the
necessary thickness of key components such as the shell,
head, nozzle, and leg support, and carry out thorough
analyses to ensurestructural integrityandsafety.Theproject
presents a holistic process for designing and analyzing a
vertical pressurevessel usingASME codes and finiteelement
analysis (FEA) techniques. Through the combination of
meticulous design, precise modelling, and rigorous analysis,
the project not only ensures structural soundness but also
highlights the effectiveness of employing FEA in modern
engineering practices.
E.S. Barboza Neto et al [2] conducted a study to focus on
investigating the performance of a pressure vessel liner
subjected to burst pressure testing. The liner was comprised
of a polymer blend consisting of 95 wt. % low linear density
polyethylene (LLDPE) and 5 wt. % high density polyethylene
(HDPE). Thisliner was intended to be an integral component
of a composite pressure vessel designed for containing
compressed natural gas (CNG), and it was manufactured
using a fiber winding process, with varying composite
thickness.Inconclusionresearchaddressedtheexperimental
and numerical analysis of a polymeric liner for a composite
pressure vessel. By conducting hydrostatic tests, utilizing
engineering analysis criteria, and employing FEA software,
the study aimed to characterize the liner's performance and
suitability for use in composite pressure vessels.
Jitendra Pandey and Prof A. K. Jain [3]carriedoutresearchon
the performance analysis of a pressure vessel using Finite
Element Analysis (FEA) with various stiffener designs. The
study aimed to enhance the understanding of the behaviour
and structural integrity of a transportation pressure vessel
that is commonly used for transporting liquid fuels. The
analysis was carried out using the ANSYS software package.
The study aimed to enhance the understanding of the
pressure vessel's behaviour and provide insights into its
structural integrity when used for transporting liquid fuels.
Brijesh KumarVishwakarmaandAmberGupta[4]workedon
the analysis of pressure vessels intended for storage
applications. The review sought to examine the design and
analysisaspectsofpressurevesselsusedforstoringmaterials
under varying pressure and temperature conditions, with a
particular emphasis on material selection. The review aimed
to provide valuable insights into the design considerations
that influence the behavior and performance of pressure
vessels used for storing various substances in industrial
settings.
Hazizi and ghalish [5] addressed the critical concernsrelated
to the design and manufacturing of pressure vessels,
specifically focusing on the safety aspectsassociatedwiththe
storage of hazardous liquids. The research particularly
emphasized the increasing global demand for liquefied
petroleum gas (LPG) and the need for safer pressure vessels
to accommodatethis demand. As the numberofLPGfacilities
grows, the requirement forsecurepressurevessels becomes
paramount to mitigate potential hazards such as explosions
and leakage.
3. PRESENT STUDY
The pressurevesselchosenforthisstudyisapressurevessel
used to hold liquefied petroleum gas (LPG). This pressure
vessel has elliptical heads and is designed to be used in a
fixed location on a leg support. The pressure vessel will have
an inner shell diameter of (d) mm and a shell length of (L)
mm, as shown in Fig -1. The overall ability of the tank is
driven by the design pressure for the required amount of
liquid to be stored. The requirement states 10,000 L of LPG,
not exceeding maximum pressure of 1.55 MPa.
Present study is concernedtocheckthestructuralintegrityof
the pressure vessel under pressure loads. Static analysis is
performed by taking different material and best material is
chosen based on the analysis results. The below is the CAD
model pressure vessel used for the study
Fig -1: CAD Model of Pressure Vessel
3.1 Material Selection
The study is carried out for three materials SS 304
steel, ASTM A357 steel and Aluminium 3003. The material
properties of all the chosen materials are given as shown in
the Table -1.
The analysis is performed for all the chosen materials under
the static loadingcondition. Stresses,deformationandFactor
of safety is evaluated for both the material and based on

safety margins, cost, reliability, availability and safety best
material is chosen for further study.
Table -1: Comparison of Material properties
4. RESULTS AND DISCUSSION
Fig -2: Equivalent stress- SS304 Material
The equivalent stress of 82.7 MPa is observedonthe
bottom of the pressure vessel for SS304 steel material due to
the application of internal pressureof 1.55 MPa.Thestresses
developed in the pressure vessel are lower than allowable
yield strength of the material.
Fig -3: Radial deformation – SS304 Material
The radial deformation of 0.298 mm is observed on the
centre of the pressure vessel in the SS 304 steel material due
to the application of 1.55 MPa internal pressure.
Fig -4: Equivalent stress- ASTM A357
bottom of the pressure vessel for ASTM A357 steel material
due to the application of internal pressure of 1.55 MPa. The
stresses developed in the pressure vessel are lower than
allowable yield strength of the material.
Parameters
SS 304
Steel
ASTM
A357
Aluminum
3003
Modulus of
Elasticity, GPa
193 200 68.9
Density, kg/m3 8000 7800 2730
Poison ratio 0.29 0.29 0.33
Yield strength,
MPa
215 310 185
Ultimate
Strength, MPa
505 585 200

Fig -5: Radial deformation –ASTM A357
centre of the pressurevessel in the ASTMA357steelmaterial
due to the application of 1.55 MPa internal pressure.
Fig -6: Equivalent stress- Aluminium 3003
bottom of the pressure vessel for Aluminium 3003 material
due to the application of internal pressure of 1.55 MPa. The
stresses developed in the pressure vessel are lower than
allowable yield strength of the material.
Fig -7: Radial deformation –Aluminium 3003
centre of the pressurevessel in theAluminium3003material
due to the application of 1.55 MPa internal pressure.
The analysis is performed for all three materials under the
static loading condition. Stresses, deformation and Factor of
safety is evaluated for all the material and based on factor of
safety and cost ASTM A357 material chosen.
Parameters
SS 304
Steel
ASTM
A357
Aluminum
3003
Modulus of
Elasticity, GPa
193 200 68.9
Density,
kg/m3
8000 7800 2730
Poison ratio 0.29 0.29 0.33
Yield
strength, MPa
215 310 185
Ultimate
Strength, MPa
505 585 200
Stress 82.7 82.7 81.6
Deformation 0.298 0.287 0.792
Cost Per Kg 125 75 260
Total Cost 196375 114877.5 139386
FOS for static 2.6 3.7 2.3
Table -2: Comparison of all three Material properties

4.1 Validation of FEA results by Analytical Method
The analytical calculations are carried out by using
strength of material approach to validate the results of
Simulation done from Ansys. Pressure vessel of thickness
18mm and internal diameter 1300mm is subjected to the
internal pressureof 1.55MPa. IfDiametertothicknessratiois
greater than20 the cylinder will fall in thin cylinder category.
For present case diametertothicknessratiois72whichcome
under thin cylinder category. Circumferential and
longitudinal stresses are calculated by using thin theory
approach as below
Circumferential Stress
The formula for circumferential stress can be written as
following.
σc= (PXd)/2Xt MPa………………………..Equation 1
Where:
σc = Circumferential/Hoop stress
P = Design pressure
d = Internal diameter
t = Wall thickness
Longitudinal Stress
The formula for longitudinal stress can be written as
following.
σL= (PXd)/4Xt MPa………………………..Equation 2
Where:
σL = Longitudinal stress
P = Design pressure
d = Internal diameter
t = Wall thickness
Table -3: Results of Analytical calculation of stress
Fig -8: Equivalent Stress Plot of pressure vessel
The equivalent stress of 56.2MPaisobservedonthecentreof
the pressurevessel under insideacting pressureof 1.55MPa.
The results from the simulation are very close to the stresses
from analytical approach.
Table -4: FEA and Analytical Results Comparison
Parameters Stress, MPa
FEA Results 56.2
Analytical approach Results 56
Difference in percentage 0.36
The stresses calculated from analytical calculation is 56MPa
are close to the stresses of 56.2 MPa observed from the
simulation. Hence it validates the simulation results are in
agreement with the analytical results.
5. CONCLUSIONS
Meticulous investigation was conducted to ensure the
robustness and efficiency of the pressure vessel design. The
process encompassed comprehensive material comparison
study was undertaken, assessing SS 304 steel, ASTM A357,
and Aluminium 3003. The subsequent analysis involved
evaluating all three materials under static loading
conditions, wherein stresses, deformations,andthefactor of
safety were rigorously examined. After a comprehensive
evaluation that considered both safety and cost factors,
ASTM A357 was chosen as the preferred material.
To assess the structural integrity of the pressure vessel,
simulations were conducted using ANSYS Workbench. The
static structural analysis revealed significant equivalentvon
Pressure, MPa 1.55
Diameter, mm 1300
Thickness, mm 18
Circumferential Stress, MPa 56
Longitudinal Stress, MPa 28

Mises stresses, maximum principal stresses, and maximum
shear stresses, all of which surpassed the yield strength of
the material. With the current design thickness yielding a
factor of safety of approximately 3.5, The thorough
evaluations conducted throughout thisstudyensurethatthe
pressure vessel design not only meets safety and
performance requirements but also undergoes meticulous
scrutiny to achieve optimal results in real-world
applications.
REFERENCES
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Design and Analysis of Vertical Pressure Vessel using
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[2] E.S. Barboza Neto , M. Chludzinski, P.B. Roese , J.S.O.
Fonseca , S.C. Amico , C.A. Ferreira, (2011),
“Experimental andnumerical analysisofa LLDPE/HDPE
linerfor a composite pressure vessel”, Polymer Testing
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“Performance Analysis of Pressure Vessel with various
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