Upload
others
View
11
Download
0
Embed Size (px)
Citation preview
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 100
DESIGN & ANALYSIS OF INDUSTRIAL SPHERICAL
PRESSURE VESSEL USING FEA
G.Nagendra1, G Bhemanna2 and Dr P Sampath Rao3 1PG Student,Mechanical Engineering, Vijay Rural Engineering College, Nizamabad, Telangana, India
2Associate Professor, Department of Mechanical Engineering, Vijay Rural Engineering College,
Nizamabad, Telangana, India 3Professor Department of Mechanical Engineering, Vijay Rural Engineering College
Nizamabad, Telangana, India
Abstract—A pressure vessel is a type of container which
is used to store liquids or gases under a pressure different
from the ambient pressure. Different shapes of pressure
vessels exist but most generally cylindrical and spherical
shapes are used. Spherical vessels are theoretically 2
times stronger than cylindrical ones but due to the
manufacturing difficulties, cylindrical ones are generally
preferred in the industry. Mostly the pressure vessels are
thin walled but here we are generating multi layered
wall.
In this project we are designing spherical pressure vessel
by using pro-e and the analysis is done by using ansys.
Here two models are generated one is solid walled which
is regularly used and another one is multi layered
pressure vessel. And the analysis is done on the two
models by changing the actual material with the
composite material. The results are compared actual
solid model with the multi layered pressure vessel and
the comparison further extended to find the better
material for that the actual material results of the model
is compared with the composite material results. By the
comparison we may find better design and the design
proposed to the company.
Index Terms—Friction stir weld, TiAlN Coated tool, Un
– coated welding tool, welding parameters.
I. INTRODUCTION
The main objective of this project is to design a
pressure vessel which is subjected to internal fluid
pressures. This pressure vessel is used to test the
components, which are used in submarine
applications.
The following are determined in design process, The
thickness of the shell wall (t),The diameter of bolt and
number of bolts required for flange and pressure
chamber assembly, The thickness of flange for the
pressure chamber and hemispherical cover plate,
Thicknesses of the end cover plates and The thickness
of the gasket in between the flange and cylindrical
chamber are determined in order to sustain the internal
fluid pressure.
The pressure chambers, when empty are subjected to
atmospheric pressure internally as well as externally.
So the resultant pressure on the walls of chamber is nil.
The component placed in the pressure vessel may fail
in service when subjected to an excessively high
internal fluid pressure.
About pressure vessels
A pressure vessel is a container used to contain things
at more than 15 psi.this means that they can withstand
greater than normal amounts of pressure without
bursting. Pressure vessels are used to contain a
multitude of things, including air, water, chemicals,
nitrogen, and fuel. They are used in paper and pulp,
energy, food and beverage, and chemical industries.
Pressure vessels also frequently control for
temperature as well as for pressure. This is especially
important when they hold more volatile substances.
Gauges on the outside can be read that will show what
the internal pressure and temperature is. If the
substance inside is potentially dangerous, alarms,
pressure releases, and other safety-measures should be
built-in to the pressure vessel.
The fluids being stored may undergo a change of state
inside the pressure vessel as in case of steam boilers or
it may combine with other reagents as in a chemical
plant. The pressure vessels are designed with great
care because rupture of a pressure vessel means an
expression which may cause loss of life and property.
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 101
Classifications of pressure vessels
According to the dimensions
1. Thin shell: If the thickness of shell is less
than 1/20th of the diameter of the shell, then the shell
is said to be thin shell.Thin pressure vessels can
withstand only internal fluid pressure, but they cannot
withstand external fluid pressure.
2.Thick shell: If the thickness of the shell is
greater than 1/20th of the diameter the shell, then the
shell is said to be thick shell.
Thick pressure vessels can withstand both internal as
well as external fluid pressure.
According to the internal fluid pressure
1.Thin shell: If the internal fluid pressure (p)
is less than 1/6 of allowable stress (σt), then the shell
is said to be thin shell.
2.Thick shell: If the internal fluid pressure (p)
is greater than 1/6 of the allowable stress (σt), then
the shell is said to be thick shell.
Material selection
The material of pressure vessel may be brittle or
ductile.
1.Brittle material: These materials are weak
in tension, but strong in compression. These materials
fail along a 450 inclined plane.
E.g.: cast iron.
2.Ductile material: These materials are
weak in shear, but strong in tension.
These materials fail by crack formation
along a plane normal to the applied load.
E.g.: Mild steel, copper, brass etc..
a.For boiler tubes, the carbon % used is 0.08
to 0.18.
b.Nickel steel is an alloy of steel, 2% nickel
makes steel more suitable for boilerplates as nickel
increases tensile strength; yield strength, elasticity,
heat resistance and decreases corrosion without
lowering the ultimate strain.
Welded joints
A welded joint is a permanent joint which is obtained
by the fusion of the edges of the two parts to be joined
together, with or without the applications of pressure
and a filler material. The heat required for the fusion
of the material may be obtained by burning of gas (in
case of gas welding) or by an electric arc (in case of
electric arc welding). The latter method is extensively
used because of greater speed of welding.
Welding is extensively used in fabrication as an
alternative method for casting or forging and as a
replacement for bolted and riveted joints.
Welded joint efficiency: Welded joints are not as
strong as the parent plate unless welds are thoroughly
inspected and, if flawed, repaired during manufacture
- all of which is expensive. This strength reduction is
characterized by the weld or joint efficiency, η = joint
strength / parent strength - which varies from 100% for
a perfect weld (i.e. virtually seamless) through 75-85%
for a tolerably good weld. Generally longitudinal or
butt joint is used for getting the required diameter of
pressure vessel.
Longitudinal joint (or) Butt joint
1) Diameter of the rivet: The diameter of rivet
hole is calculated by the empirical relation, d = 6√t.
Where t = thickness of the pressure vessel.
2) Pitch of the rivets: The maximum pitch of
the rivets is given by the empirical relation =
Ct+41.28mm.
Where t = thickness of the shell plate in mm = 8mm.
Assuming two rivets per pitch length,
C = constant=3.06.
3) Distance between rows of rivets:
Assuming riveting to be chain riveting, the distance
between the rows of rivet = 2d
(Where d = diameter of the rivet)
4) Thickness of the butt strap or cover plate
(t1):
t1 = 1.125t (for chain riveting and single
strap butt joint)
Where t = thickness of the shell plate.
5) Margin or marginal pitch (m): Margin or
marginal pitch is the distance between the centers of
the rivet hole to the nearest edge of the plate. Margin
is given by
m = 1.5d
Where d = diameter of the riveted hole.
Rivet materials
Rivets are made of wrought iron or soft steel for most
uses, but where corrosive resistance or light weight is
a requirement, rivets or copper or aluminum alloy are
used. Rivet materials must be strong and highly
ductile, I.S.1960-1962 gives the specifications for
steel rivets and stay bars for boilers. Rivets are used in
such manner that they resist shearing action. However
if the tensile loading is un avoidable the safe tension
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 102
value of a rivet may be taken as one half the safe single
shear value.
The materials to be joined and the material used for the
rivet should be carefully considered from the stand
point of electrolytic corrosion in the presence of
moisture. If desired by the purchaser, the rivet shall be
painted with one coat of boiled linseed oil or suitable
preventive material to be agreed mutually between the
supplier and purchaser.
Caulking and Fullering
Joints in pressure vessels like steam boilers, spheres,
air receivers and tanks etc. are made fluid tight by
caulking. A narrow blunt chisel like tool (m) called a
caulking tool, about 5mm. Thick and 38mm in
breadth, the edge ground to an angle of 800. It is
moved after each blow along the edge of the plate,
which is planed to a bevel of 800 to facilitate the
forcing down of edge. It can be noted that the tool
burns down the plate at C forming a metal to metal
joint, care being taken not to damage the plate below
the tool or spring the joint open. Generally both edges
B and C are caulked and the rivet head also as at A.
A more satisfactory way of making the joint staunch
and tight is known as fullering which has largely
superseded caulking. The fullering tool having a
thickness at the end equal to that of the plate, is used
in such a way that the greatest pressure due to the
blows occurs at near the joint giving a clean finish,
with less risk of damaging the plate.
Bolted joints
Initial stresses due to screwing up forces
The following stresses are induced in a bolt, screw or
stud when it is screwed up tightly.
Tensile stress due to stretching of bolt. Since none of
the above mentioned stresses are accurately
determined, therefore bolts are designed on the basis
of direct tensile stress with a large factor of safety in
order to account for the indeterminate stresses. The
initial tension in a bolt, based on experiments, may be
found by the relation
Pi=2840d N
Where,
Pi=initial tension in a bolt, in mm.
d=nominal diameter of bolt, in mm.
The above relation is used for making a joint fluid tight
like steam engine cylinder cover joints etc. when the
joint fluid is not required as tight as fluid tight joint,
then the initial tension in a bolt may be reduced to half
of the above value. In such cases Pi=1420d N.
The small diameter bolts may fail during tightening;
therefore bolts of smaller diameter (less than M16 or
M18) are not permitted in making fluid tight joints.
If the bolt is not initially stressed, then the maximum
safe axial load which may be applied to it, is given by
P= permissible stress*cross sectional area at
bottom of the thread
The stress area may be obtained by stress
area =π/4(dp+dc/2)2
Where,
dp=pitch diameter, and
dc=core or minor diameter.
Stress due to combined forces
The resultant axial load on a bolt depends upon the
following factors
The initial tension due to tightening of the bolt,
The external load, and
The relative elastic yielding (springiness) of the
bolt and the connected members.
When the connected members are very yielding as
compared with the bolt, which is a soft gasket, then the
resultant load on the bolt is approximately equal to the
sum of the initial tension and the external load. On the
other hand, if the bolt is very yielding as compared
with the connected members, then the resultant load
will be either the initial tension or the external load,
whichever load, whichever is greater. The actual
conditions usually lie between the two extremes. In
order to determine the resultant axial load (P) on the
bolt, the following equation may be used
P=P1+(a/1+a)*P2=P1+K.P2
P1=Initial tension due to tightening of
the bolt,
P2=External load on the bolt, and
a=Ratio of elasticity of connected
parts to the elasticity of bolt.
For soft gaskets and large bolts, the value of ‘a’ is high
and the value of a/a+1 is approximately equal to unity,
so that the resultant load is equal to the sum of the
initial tension and the external load.
For hard gaskets or metal to metal contact surfaces and
with small bolts, the value for the resultant load. The
designer thus has control over the influence on the
resultant load on a bolt by proportioning the sizes of
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 103
the connected parts and bolts and by specifying initial
tension in the bolt.
The value for soft copper gasket with long through
bolts ranges from 0.50 to 0.75.
Circular flat plates
1. Plates with uniformly distributed load: The
thickness ‘tc’ of the plates of diameter‘d’ supported at
the circumference and subjected to a pressure ‘p’
uniformly distributed over the area is given as :
tc = k1d√(p/ft)
Where ft=allowable design stress
k1 is a coefficient, whose values are
given below. It depends upon the material and method
of holding the edges.
C.I: freely supported, k1=0.54, the maximum stress
occurs at the centre of head.
Fixed k1=0.44, the maximum stress occurs at the edge.
M.S: freely supported, k1=0.42 the maximum stress
occurs at the centre of head.
Fixed k1=0.35 the maximum stress occurs at the edge.
The following equations are used to find the thickness
of the circular plates
tc=√[3F(3+1/m)/8π ft] for plates with edges
freely supported,and tc=√3F/4πft for plates with edges
rigidly fixed,
Where F= total load on the plates=pπr2
1/m =Poisson's ratio.
Hemispherical cover (integral or welded)
tc =p. d/4 ftη.
Flange and bolt (or) stud arrangement
Cover with studs
Thickness of flange, tf = (1.1 to 1.25)*t
= (1.25 to 1.5)*db
The distance, l=t+ db+5
=t+0.5db+5, when nut is spot
faced, so as to keep the arm of the bending moment ‘l’
small.
Design of cylinder covers
The cylinder covers may be secured by means of bolts
or studs, but studs are preferred. The bolts or studs,
cylinders cover plate and cylinder flange may be
designed as discussed below.
In order to find the size and number of bolts or studs,
the following procedure may be adopted.
Let D=Diameter of the cylinder,
p=pressure in the cylinder,
dc=Core diameter of the bolts or studs,
n=Number of bolts or studs, and
σtb=Permissible tensile stress for the
bolt or stud material.
We know that upward force acting on the cylinder
cover,
P=π/4(D)2p
This force is resisted by n number of bolts or studs
provided on the cover.
Therefore resisting force offered by n numbers of bolts
or studs,
P=π/4(dc)2σtb*n
From the above equations we have
π/4(D)2p=π/4(dc)2σtb*n
From this equation the number of bolts or studs may
be obtained, if the size of the bolt or stud is known and
vice-versa. Usually the size of the bolt is assumed. If
the value of n as obtained from the above relation is
odd or a fraction, then next higher even number is
adopted.
The bolts or studs are screwed up tightly, along with
metal gasket or asbestos packing, in order to provide a
leak proof joint. We have already discussed that due to
the tightening of bolts, sufficient tensile stress is
produced in the bolts or studs. This may break the bolts
or studs, even before any load due to internal pressure
acts upon them. Therefore a bolt or a stud less than
16mm diameter should never be used.
The tightness of the joint also depends upon the
circumferential pitch of the bolts or studs. The
circumferential pitch should be between 20√d1 and
30√d1, where d1, is the diameter of the hole in mm for
bolt or stud. The pitch circle diameter is usually taken
as D+2t+3d1 and outside diameter of the cover is kept
as.
Do=Dp+3d1=D+2t+6d1
Where t=thickness of the cylinder wall.
Gasket
A gasket is a relatively elastic or plastic device which
is used to create and maintain a barrier against the flow
of fluids across mating surface of a mechanical
assembly, when the surfaces do not have a relative
motion with respect to each other. The common
example of the gasket is the member placed between
the cylinder block of an engine to make the joint tight.
When the gasket is used, the mating surfaces need not
be accurately machined as in the case of metal joint.
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 104
A gasket effects a seal by deforming and filling surface
irregularities of the members between which it is
placed and is, therefore, made of relatively soft
material compared to flange mating surfaces.
Although a seal can be obtained without the use of
gasket, it provides the following extra advantages:
It promotes the efficient initial seal.
It prolongs the useful life of an assembly.
It acts as a calking compound in compensating for
errors and irregularities in joined rigid members
of an assembly.
The joint should be designed and constructed to make
the best use of the properties of the gasket. Hence Joint
and gasket design must be considered together. The
forces acting on the gasket are quite complex and
variable. Some of these may be summarized as: bolt
squeeze on gasket, fluid pressure, due to
environmental conditions. Also misalignment, gravity
and thermal movement try to separate faces.
The two basic types of joints are
a) Basic flange joints
b) Metal to metal joints
The flange joint are suitable for all kinds of flat
gaskets. simple flange joint, is suitable for pressures
up to 1.5N/mm2. For higher fluid pressures, the
reduced section joint, and tongue and groove joint, are
preferred.
In reduced section joint, the gasket wall section has
been reduced to give a high gasket stress without
change in bolt stress. The tongue and groove joint is
used for applying extremely high stress to gasket, and
for holding extremely high pressures.
Metal to metal joints are suitable for compressible
material such as cork and rubber. These are useful for
limiting the amount of stress on the gasket and are
particularly good where it is essential to maintain
accurate internal clearances or alignments.
The choice of gasket material for any application
depends upon:
(1) Operating conditions
(2) Mechanical features of the flange
assembly
(3) Gasket characteristics.
The gasket material must meet the following
requirements
(a) Impermeability
(b) Ability to flow into joint imperfections
when compressed
(c) Maintain seal inspite of age, and
variations in temperature and pressure.
(d)Resistance to environmental deterioration.
Depending upon the materials, the gaskets may be
grouped as below
(1) Metallic gaskets.
(2) Non-metallic gaskets.
Non-metallic gaskets are used for low pressures
whereas for high pressures and under severe condition,
metallic or combination gaskets are used. A rough
guide as to whether a metallic or non metallic gasket
should be used for given condition is: If (operating
pressure in N/mm2 *operating temperature in oc is
>900 only metallic gaskets should be used.
Generally, a non-metallic gasket should not be used
for pressures in excess of about 8.7 N/mm2 and
temperatures above 450oc and below -18oc.
The most common composites for non-metallic
gaskets can be written as below
Asbestos products can work efficiently up to a
temperature of about 260oc. these gaskets are tough
and durable and dimensionally stable. These are used
for heavy duty bolted and threaded joints as in water
and steam pipe fitting, manifold connections, etc.
Cork is lightweight, non-capillary, does not deteriorate
with age, practically inert, and has a high coefficient
of friction. It has excellent oil and solvent resistance
but poor resistance to alkalies and corrosive acids.
These gaskets are used for mating rough or irregular
parts, such as glass, light stamping, unfinished casting;
etc. Temperature limit about 70oc Metallic gaskets
may be made of the following metals lead, brasses,
copper, aluminum, soft iron, low carbon steel,
stainless steel, titanium, silver, nickels, Monel and
Inconel.
Metallic gaskets fall into several basic groups:
1. Corrugated or embossed, thin metal.
2. Metal jacketed, soft metal.
3. Spiral wound.
4. Plain or machined flat metal.
5. Round cross section, solid metal.
6. Special, heavy cross-section, solid metal.
7. Pressure actuated, light cross section.
Gasket joints: In bolted assembly of cylinder, cylinder
head and gasket initially the bolt is tightened by a
spanner to induce a preload Pl.. The stiffness or spring
constant k of a machine element is the load required to
produce unit deflection. It is given by the ratio of the
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 105
load to the deflection produced by that load. When a
machine member is loaded in tension or compression,
δ=P/k (or)
k=P/ δ= AE/l
The stiffness of the bolt is given by
kb=(πd2/4)E/l
Where
kb= stiffness of the bolt (N/mm)
d=nominal diameter of the bolt (mm)
l=total thickness of the parts held
together by the bolt (mm)
E=modulus of elasticity of bolt
material (N/mm2)
There are three members in the grip of the bolt –
cylinder cover, cylinder flange and gasket. They act as
three compression springs in series. Their combined
stiffness kc is given by
1/kc= 1/k1 +1/k2 + 1/kg
Where k1 and k2 are the stiffness of the cylinder cover
and the cylinder flange respectively and kg is the
stiffness of the gasket. It is difficult to predict the area
of flanges compressed by the bolt. It is assumed that a
hollow circular area of 3d and d as outer and inner
diameters respectively is under the grip of the bolt.
A= π/4[(3d)2-d2]=2πd2 and
k=AE/l= 2πd2E/t
k= 2πd2E/t
Where t is thickness of the member under
compression.
When the gasket is very soft relative to the flanges, it
is the gasket which is compressed during the
tightening of bolt. In such cases, the flanges are
neglected and the stiffness of the gasket is considered
to be kc.
Danger of pressure vessels
Because they are containing substances at greater than
normal pressures, upkeep and maintenance of the
vessels is very important. If they were to rupture, not
only would the vessel be damaged (and would
probably be unsalvageable) but injury could result due
to shrapnel and dangerous chemicals. It is important to
buy pressure vessels that have been approved by the
ASME as safe. These have been inspected and
conform to industry-wide standards of strength.
Corrosion
In design, corrosion which occurs over the life of a
vessel is catered for by a corrosion allowance, whose
design value depends upon the vessel duty and
contents' corrosiveness - for example 1 mm is typical
for air receivers in which condensation of air moisture
is normally inevitable. It is important to realize that
when dimensions in any formula refer to a corrodible
surface, then the dimensions inserted into the formula
are those at the end of the vessel's life, when all the
corrosion allowance has been eaten away. So, if a plate
is of nominal thickness T now, and is subject to
corrosion on one side, then (T - c ) must be substituted
whenever nominal thickness appears in an equation.
Similarly a tube of current bore Di which corrodes will
have a bore of (Di + 2c) at the end of its life.
Failures of pressure vessel
Fig.1.1 Failure of a cylindrical shell along the
longitudinal section
The above figure 1.1 shows the failure along the
longitudinally section(i.e. circumferentially) splitting
the cylinder into two troughs i.e. it might fail by
bursting along a path following the circumference of
the cylinder, under normal circumstance it fails by
bursting along a path parallel to the axis. This indicates
that hoop stress is significantly higher than axial stress
Fig.1.2 Failure of cylindrical shell along the transverse
section
The failure across the transverse section (i.e.
longitudinally) splitting the cylinder into two
cylindrical shells as shown in fig 1.2.
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 106
Literature review
The main theme of the presented work is to design a
pressure vessel which is subjected to internal fluid
pressure .This pressure vessel is used to test the
components, which are used in submarine
applications. The some of the researches are worked
on the pressure vessels and related areas and few them
discussed below.
II. BRIEF OVERVIEW OF RELATED
RESEARCH
David Heckman1 et.al (1998) Finite element analysis
is an extremely powerful tool for pressure vessel
analysis when used correctly. Tested models were run
with errors ranging from seven to nearly zero percent
error and could be run in a relatively short time.
However, even with such results the operator still is
required to be knowledgeable of not just how to run
the finite element analysis, but also how to read the
results. Data must be verified with hand calculations
to confirm that solutions are relatively accurate.
Where results are questionable, such as in the final
contact element model, one must understand just what
the finite element model is modeling and how well this
approximates the actual subject. For this pressure
vessel, the model had a sharp corner, where in the
actual pressure vessel there is a small radius which
reduces the stress. For pressure vessels finite element
analysis provides an additional tool for use in analysis.
However, it must be compared to other available data,
not taken as being correct just because it looks right.
Used with this understanding, finite element analysis
offers great insight into the complex interactions found
in pressure vessel design
Farhad Nabhani2 et.al Three main factors are seen to
contribute extensively to the development of stresses
in pressure vessels. These are thickness, nozzle
positions and the joints of the enclosure heads. From
the model design cases used in this research, it could
be seen that as the thickness of pressure vessel
increases, the stresses decreases, however this is not a
viable solution due to cost. Nozzles though are safety
relief devices and important component of pressure
vessels comes with its own disadvantages of
increasing weak areas and stress concentration.
However, this was mitigated by use of high alloy
reinforcement pads as applied in the design case two
and three of this work. The high strength
reinforcement pad used has a chemical composition of
titanium 0.4 to 1.20%; hollow disc shaped with
rectangular section can also reduce the stresses
concentration around the nozzle. Finally, the joints of
enclosure heads either welded or bolted were
identified as areas with the highest concentration of
stresses i.e. with peak stress. Addition of 254 mm skirt
length at the end of enclosure heads provide more
room for the stresses to develop slowly in the wall of
the head regions, thus making the pressure vessels
more resistant to the loadings.
Siva Krishna Raparla13 et.al The theoretical values
and ANSYS values are compared for both solid wall
and multilayer pressure vessels. There is a percentage
saving in material of 26.02% by using multilayered
vessels in the place of solid walled vessel. This
decreases not only the overall weight of the
component but also the cost of the material required to
manufacture the pressure vessel. This is one of the
main aspects of designer to keep the weight and cost
as low as possible. The Stress variation from inner side
to outer side of the multilayered pressure vessel is
around 12.5%, where as to that of solid wall vessel is
17.35%. This means that the stress distribution is
uniform when compared to that of solid wall vessel.
Minimization of stress concentration is another most
important aspect of the designer. It also shows that the
material is utilized most effectively in the fabrication
of shell. Theoretical calculated values by using
different formulas are very close to that of the values
obtained from ANSYS analysis. This indicates that
ANSYS analysis is suitable for multilayer pressure
vessels.Owing to the advantages of the multi layered
pressure vessels over the conventional mono block
pressure vessels, it is concluded that multi layered
pressure vessels are superior for high pressures and
high temperature operating conditions.
Shaik Abdul Lathuef4 et.al In the past several years
there have been significant changes to the American
Society of Mechanical Engineers (ASME)Boiler and
Pressure Vessel (B&PV) Code and the use of
international pressure vessel codes such as EN13445.
This paper discusses some of the potential unintended
consequences related to Governing Thickness of shell
as per ASME. Here have a scope to change the code
values by take the minimum governing thickness of
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 107
pressure vessel shell to the desired requirements and
also relocate of nozzle location to minimize the
stresses in the shell. A low value of the factor of safety
results in economy of material this will lead to thinner
and more flexible and economical vessels. Here we
evaluated the stress in the vessel by Zick analysis
approach.A numerical design study was performed to
examination structural failure of pressure vessels
exposed to internal pressure by varying the shell
thickness and nozzle location. By inspecting these
plots it apparent that the minimum thickness 8mm will
taken safe for design conditions.
Bandarupalli Praneeth5 et.al The main objective of this
paper is finite element analysis of pressure vessel and
piping design. Features of multilayered high pressure
vessels, their advantages over mono block vessel are
discussed. Various parameters of Solid Pressure
Vessel are designed and checked according to the
principles specified in American Society of
Mechanical Engineers (A.S.M.E)Sec VIII Division 1.
Various parameters of Multilayer Pressure vessels are
designed and checked according to the principles
specified in American Society of Mechanical
Engineers (A.S.M.E)Sec VIII Division 1.The stresses
developed in Solid wall pressure vessel and Multilayer
pressure vessel is analyzed by using ANSYS, a
versatile Finite Element Package. The theoretical
values and ANSYS values are compared for both solid
wall and multilayer pressure vessels
III. OBJECTIVE OF THE WORK
The main objective of this project is to design a
pressure vessel using Ansys. This pressure vessel has
to withstand an internal fluid pressure of 75 bar.
Design the thickness of plate material and also
thickness of the hemispherical cover plate.
Finally the Von-Mises stresses are found in the
pressure vessel. The design should be safe for the
applied load.
IV. METHODOLOGY
To achieve the above objective the following
methodology has been adopted in the present work.
A pressure vessel which will withstand a pressure
of 75bar has been theoretically designed.
Modeling of the pressure vessel is done using pro-
E
The model is imported to Ansys and analysis is
preformed as follows.
Shell element is chosen & a real constant of 3mm
is added which is the thickness of the shell.
Material properties are added.
Meshing is done, finally the boundary conditions
are applied & it is solved.
After solution the results are viewed in general
postprocessor.
Then the results from the analytical method & the
Ansys are compared.
The shear stress induced in the plate is less than
allowable stress in the plate material. Hence the
design is safe.
V. DESIGN OF PRESSURE VESSEL
Thin cylindrical pressure vessel
The analysis of stresses in the thin cylindrical shell is
made on the following assumptions.
1. The normal stress (tensile or compressive) is
uniformly distributed over the thickness of wall.
2. The stress along the radial direction will be small
and negligible.
3. Thickness is small compared to radius.
4. There are no discontinuities in curves.
5. Bending of the wall of the shell is neglected.
6. Shear stress across a cross section is negligible.
Stresses
1. Hoop stress or circumferential stress (σh).
2. Longitudinal stress (σl).
3. Radial stress is zero.
Strains
1. Hoop Strain (Єh).
2. Longitudinal Strain (Єl).
Hoop strain (єh): Єh= (σh/E)-(σl/mE)
Therefore Єh= (pd/2tE) (1-1/2m)
Longitudinal strain (єl): Єl=(σl/E)-(σh/mE)
Therefore Єl=pd/2tE {(1/2)-(1/m)}
Volumetricstrain(єv):δv/v=Єv=(δl/l)+2(δd/d)orЄv=Є+2
Єh
Єv=pd/2tE{(5/2-2/m)}.
Thick cylindrical pressure vessel
The analysis is made on the following Lame’s
assumptions:
1. The material is homogeneous and isotropic.
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 108
2. Plane sections of the cylinder perpendicular to the
longitudinal axis remain plane under the pressure i.e..,
longitudinal strain independent of radius.
3. Longitudinal stress is assumed to be zero.
Stresses in Thick vessels:
1. Hoop/tangential stress (σh).
2. Radial stress (σr).
Design equations for thick vessels:
Lame’s equation:
Hoop stress, σh =a+b/x2
Radial stress,σr = a-b/x2
For internal fluid pressure, σh is tensile and σr is
compressive.
Special cases:
Internal pressure =p; external pressure =0
Hoop stress σh= p (ri)2/(ro)2-(ri)2[1+ (ro)2/x2]
Radial stress σr=p (ri)2/(ro)2-(ri)2[1+ (ro)2/x2]
Birnie’s equation:
According to maximum strain theory, the failure
occurs when the strain reaches a limiting value.
Birnie’s equation for the wall thick of the cylinder is
t=ri [√ (σt+ (1-μ)p)/ (σt - (1+μ) p)-1]
The above equation is applicable to open ended
cylinders (such as gun barrels, rams, pump cylinders)
Clavarino’s equations:
This equation is also based on the maximum strain
theory of failure. According to this equation the
thickness of a cylinder is
t=ri [√(σt+(1-2μ)p)/ (σt -(1+μ)p)-1]
Barlow’s equations:
This equation is generally used for high pressure oil
and gas pipes. According to this equation the thickness
of a cylinder is
t=pro/σt
According to maximum shear stress theory:
τmax = [σt(max) - σt(min) ]/2 from which the thickness
of the cylinder is
t=ri[√ (ז/ז-p)-1]
Where τ = σt/2
t=ri [√(σt/σt-2p)-1]
Longitudinal strain:
єl = (σi –νσh-νσr)= constant
Where ν = Poisson’s ratio.
Hoop strain: It is used to determine the change in the
diameter of the pressurevessel which is subjected to
internal pressure.From the above strains we calculate
the volumetric change in the pressure vessel єv =
2(δd/d)+ δl/l.
Problem Description:
Material = mild steel
Height of the cylinder = 400 mm
Young’s modulus (Ε) = 207Gpa =207000N/mm2
Poisson’s ratio (μ) = 0.3 ;Yield strength (σy) =400Mpa
Hemispherical Cover Plate
Flange
Fig.Thickness of hemispherical cover plate
The above figure 3.3 shows the Hemispherical cover
plate, the thickness of the cover plate obtained by
analytical calculation is 3.75mm. But, it is
approximated to 4mm, as this is the standard thickness
available.
Longitudinal joint or Butt joint
Longitudinal joint or butt joint is used to get the
required diameter of the pressure vessel. For this
purpose riveted joints are used along with caulking
and fullering in order to make the joints leak proof.
1) Diameter of the rivet:
The diameter of rivet hole is calculated by the
empirical relation, d = 6√t.
Where t = thickness of the pressure vessel =
8mm
Therefore, d = 6√8 = 17mm.
But the next available diameter of the rivet, d = 18mm
The corresponding diameter of the rivet hole = 19mm
2) Pitch of the rivets:
The maximum pitch of the rivets is given by the
empirical relation,
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 109
P = Ct+41.28mm
Where t = thickness of the shell plate in
mm = 8mm.
Assuming two rivets per pitch length, C =
constant=3.06
Therefore pitch, P = 3.06*8+41.28 = 65.76mm
= 66mm (approx).
3) Distance between rows of rivets:
Assuming riveting to be chain riveting, the distance
between the rows of rive = 2d
(Where d = diameter of the rivet)
= 2*18= 36mm
4) Thickness of the butt strap or cover plate (t1):
t1 = 1.125t (for chain riveting and single strap butt
joint) Where t = thickness of the shell plate.
t1 = 1.125*8 = 9mm.
5) Margin or marginal pitch (m):
Margin or marginal pitch is the distance between the
centers of the rivet hole to the nearest edge of the plate.
Margin is given by
m = 1.5d
Where d = diameter of the riveted hole = 18mm
m = 1.5*18 = 27mm.
Design of gasket
Assuming ‘Silicone’ as a gasket material because it
has high performance against high temperature and
low temperature applications.
There are three members in the grip of the bolt. They
are cylinder cover, cylinder flange and gasket. They
act as three compression springs in series. Their
combined stiffness ‘kc’ is given by
1/kc = 1/k1+1/k2+1/kg
Where ‘k1’ and ‘k2’ are the stiffness of the cylinder
cover and the cylinder flange respectively and kg is the
stiffness of the gasket.
k1 = k2 = 2πd2Ef/tf
kg = 2πd2Eg/tg
Where ‘tf’ and ‘tg’ are the thicknesses of cylinder
flange and gasket respectively and d is the diameter of
the bolt.
tf = 10mm
d = 18mm.
tg is to be calculated.
Young’s modulus of
1) Bolt Eb = 207GPa = 207000MPa
2) Gasket Eg = 1200*103 lb/in2
=1200*6.8947Mpa(1000lb/in2=6.8947MPa)
= 8273.64MPa
Stiffness of the bolt, kb = (π/4)d2*Eb/l
Where Eb = Young’s modulus of bolt material
= 207000MPa
L = combined thickness of the three members in series
= 10+tg+10 = 20+tg
Therefore kb = (π/4)*182 *207000/(20+tg)
= 52675084.02/(20+tg)
kg=2πd2Eg/tg=2π*182*8273.64/tg=16843079.
5/tgN/mm
k1 = k2 = 2πd2Ef/tf = 2π*182*207000/10
= 42140067202N/mm
but K = 0.75 = kc/(kc+kb)
Therefore kc/kb = 3
Kc = 3kb = 3*52675084.02/(20+tg)
= (158.025*106)/(20+tg)
Therefore, 1/kc = 1/k1+1/k2+1/kg
(20+tg)/(158.025*106) = {(1/421.4)+(tg/16.843)}/(106)
20+tg = 0.75+9.3822tg
19.25 = 8.3822tg
tg = 2.29mm
= 3mm (approx)
Therefore the thickness of the gasket is found to be tg
= 3mm
VI. MODELLING AND ANALYSYS OF
PRESSURE VESSEL
Modelling software
There are different software’s available for modelling.
Some of them are
Solid works
1. Pro-E
2. Ideas
3. Inventor
4. Mechanical Desktop
5. Unigraphics
6. Catia
Pro-E is used as the modelling tool in this project
which is discussed as follows.
Introduction of PRO-E
The Pro-E provides the power of parametric design.
With parametrics, we define the model according to
the size, shape and positional relationship of its parts.
Part modeling
Many mechanical designs consist of complex
assemblies made from angular shaped parts. This type
of design work can be made easier by part and
assembly modeling capabilities that are well
integrated. The Pro-E is a 3D parametric solid modeler
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 110
with both part and assembly modeling abilities. You
can use the Pro-E to model piece parts and then
combine them into more complex assemblies.
With Pro-E, you design a part by sketching its
component shapes and defining their size, shape, and
inter-relationships. By successively creating these
shapes, called features, you construct the part in a
building block fashion.
Because the Pro-E has parametric features, you can
change one feature and all related features are
automatically updated to reflect the change and its
effects throughout the part.
The Pro-E can be used to create angular shaped parts,
to which you can apply 3D surfaces to create hybrid
parts consisting of a mixture of angular and curved
shapes. The Pro-E provides the ability to create mode
designs with shapes of varying types.
You can apply surfaces to Pro-E parts and use them to
cut material from a solid to create the hybrid shapes
that your design requires.
Follow the same general modeling process for each
Part :
Plan the part
Create the base feature
Create the remaining features
Analyze the part
Modify the features as necessary
Assembly Modeling
You create assemblies from parts, either combined
individually or grouped in subassemblies. The Pro-E
builds these individual parts and subassemblies into an
assembly in a hierarchical manner according to
relationships defined by constrains.
As in part modeling, the parametric relationship
allows you to quickly update an entire assembly based
on a change in one of its parts.
We can also use the Pro-E to create subassembly and
assembly models from previously made parts. You can
build 3D solid assembly models from two or more
parts or subassemblies. Like part features, parts and
subassemblies act as building blocks.
The general process used to build assemblies and
subassemblies is similar to that for building parts :
Lay out the assembly
Create the base part
Create and attach the remaining parts
Analyze the assembly
Modify the assembly as necessary.
Fundamental
Pro-E employs two operating modes for part
modeling, Model mode for modeling 3D parametric
parts and Drawing mode for creating 2D drawings of
them. These modes operate independently but share
the same design data. You can switch back and forth
between modes at any time. Part modeling requires
you to begin your design work in Model mode where
you immediately build a model of the part. You then
use Drawing mode at any point to document the
design.
In traditional computer-aided design, you began by
creating a 2D drawing and then building a 3D model
to analyze, verify and refine the initial concept. With
Pro-E, you are not limited to using 2D drawings to
stimulate thinking about 3D design concepts. Pro-E
recognizes and supports the creation of models and
drawings in their natural order.
Design process
The process to build a Pro-E part is same for all as
described below.
Layout the part
Creating the base feature
Creating the remaining part features
Modify the features as necessary
Half of the sketch of the model is generated and it is
revolved to get the solid model. It is converted into a
iges file and is imported into Ansys.
The drawing views are to be identified and the Pro-E
software automatically removes the hidden lines and
also places the dimensions on the drawing. Changes
made to the part update the drawing also.
A sketch plane is a planar surface or workplace on the
active part, in a 3D space. New features are sketched
on this plane. All the profiles must lie on the active
sketch plane.
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 111
The solid modelling of pressure vessel, which is done
pro_e modeling software as shown in fig4.1.
Finite element method
The finite element is a mathematical method for
solving ordinary and partial differentials equations.
Because it is a numerical method, it has the ability to
solve complex problems that can be represented in
differential equation form. As these types of equations
occur naturally in virtually all fields of the physical
sciences, the applications of the finite element method
are limitless as regards the solution of practical design
problems.
Due to high cost of computing power of years gone by,
FEA has history of being used to solve complex and
cost critical problems. Classical methods alone usually
cannot provide adequate information to determine the
safe working limits of a major civil engineering
construction or an automobile or an aircraft. If a tall
building, a large suspension bridge or an automobile
or a nuclear reactor failed catastrophically, the
economic and social cost would be unacceptably high.
In recent years, FEA has been used almost universally
to solve structural engineering problems. One
discipline that has relied heavily on this technology is
the automotive and aerospace industry. Due to the
need to meet the extreme demands for faster, stronger,
efficient and light weight automobiles and aircrafts,
manufacturers have to rely on the technique to stay
competitive. But more importantly, due to safety, high
manufacturing costs of components and the high
media coverage that the industry is exposed to,
automotive and aircraft companies need to ensure that
none of their components fail, that is to cease
providing the services that the design intended.
FEA has been used routinely in high volume
production and manufacturing industries for many
years, as to get a product design wrong would be
detrimental. For example, if a large manufacturer had
to recall one model alone due to a piston design fault,
they would end up having to replace up to 10 million
pistons. Similarly, if an oil platform had to shut down
due to one of the major components failing (platform
frames, turrets, etc), the cost of lost revenue is far
greater than the cost of fixing or replacing the
components, not to mention the huge environmental
and safety costs that such an incident could incur.
The finite element is a very important tool for those
involved in engineering design; it is now used
routinely to solve problems in the following areas:
Structural strength design
Structural interaction with fluids flows
Analysis of shock (underwater and in materials)
Acoustics
Thermal analysis
Vibrations
Crash simulations
Fluid flows
Electrical analysis
Mass diffusion
Buckling problems
Dynamic analysis
Electromagnetic evaluations
Metal forming
Coupled analysis
Nowadays, even the most simple of products rely on
the finite element for design evaluation. This is
because contemporary design problems usually cannot
be solved as accurately and cheaply using any other
method that is currently available. Physical testing was
the norm in years gone by, but now it is simply too
expensive and time consuming.
More about FEA
Finite element analysis was first developed for use in
the aerospace and nuclear industries where the safety
of structures is critical. Today, the growth in usage of
the method is directly attributable to the rapid
advances in Computer technology in recent years. As
a result, commercial finite element packages exist that
are capable of solving the most sophisticated
problems, not just in structural analysis, but for a wide
range of phenomena such as steady state and dynamic
temperature distributions, fluid flow and
manufacturing process such as Injection moulding and
metal forming.
FEA consists of a computer model of a material or
design that is loaded and analyzed for specific results.
It is used in used in new product design, and existing
product refinement. A Design Engineer shall be able
to verify a proposed design, which is intended to meet
the customer specifications prior to manufacturing or
Construction.
Things such as, modifying the design of an existing
product or structure in order to qualify the product or
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 112
structure for a new service condition. Can also be
accomplished in case of structural failure. FEA may be
used to help determine the design modifications to
meet the new condition.
The basic steps involved in ‘FEA’
Mathematically, the structure to be analyzed is
subdivided into a mesh of finite sized elements of
simple shape. Within each element, the variation of
displacement is assumed to be determined by simple
polynomial shape functions and nodal displacements.
Equations for the strains and stresses are developed in
terms of the unknown nodal displacements. From this,
the equations of equilibrium are assembled in a matrix
from which can be easily be programmed and solved
on a computer. After applying the appropriate
boundary conditions, the nodal displacements are
found by solving the matrix stiffness equation. Once
the nodal displacements are known, element stresses
and strains can be calculated.
Within each of these modeling schemes, the Engineer
can insert numerous algorithms (functions) which may
make the system behave linearly or non linearly.
Linear systems are far less complex and generally
ignore many subtleties of model loading and behavior.
Non linear systems can account for more realistic
behavior such as plastic deformation, changing loads
etc. and is capable of testing a component all the way
to failure.
The following are the five basic steps involved in an
FEA analysis:
1. Discretization of the domain
2. Applications of field/boundary conditions
3. Assembling the system equations
4. Solution for the system equations
5. Review of results
Let us understand the above five steps one by one
sequentially and see what it really means to an
Engineer.
Discretization of the domain
Here the task would be to divide the continuum under
study into a number of subdivisions called elements.
Based upon the geometry, the continuum or the system
under study can be divided into a numbers of elements
.FEA permits us to do so!
• If the continuum is a single point it can discretized
using point elements.
• If the continuum is 1D it can be discretized using line
elements.
• If the continuum is 2D it can be discretized using
area elements.
• If the continuum is 3D it can be discretized using
volume elements.
Once the discretization is done, we shall include
the known field/boundary conditions which shall
serve as references and help us in solving for the
unknowns.
Once the reference or known conditions are
imposed, we shall define sets of equations which
are suitable to define the behavior of system. This
involves formulation of respective characteristic
(stiffness in case of structural ) equation matrices.
Once the equations are set up we shall solve the
same to know the unknowns and get insight into
system behavior. That is basically the system of
matrices which are nothing but a set of
simultaneous equations are solved.
Upon the completion of solution, we shall review
the results.
When we use CAE software either developed in house
of commercially available, the first three steps are
called as pre- processing phase, the fourth phase is
called solution phase and the fifth phase is called post-
processing phase. Since FEA involves matrix
operations, it was referred to as Matrix methods for
structural analysis, in the initial days where it was used
only for structural behavior simulations.
Despite the proliferation and power of commercial
software packages available, it is essential to have an
understanding of the technique and physical processes
involved in the analysis. Only then can an appropriate
and accurate analysis model be selected, correctly
defined and subsequently interpreted.
Before proceeding further to learn more, we shall
familiarize our selves with the following:
What is an element?
Element is an entity, into which a system under study
can be divided into. Nodes can specify an element
definition. The shape (area, length and volume)
element depends upon the nodes with which it is made
up of.
What are nodes?
Nodes are the corner point of an element. Nodes are
independent entities in space. These are similar to
points in geometry. By moving a node in space an
element shape can be changed.
Procedure for finite element analysis
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 113
ANSYS is a general purpose finite element modeling
package for numerically solving a wide variety of
mechanical problems. These problems include:
static/dynamic structural analysis(both linear and non-
linear), heat transfer and fluid problems, as well as
acoustic and electro-magnetic problems. Basically
there are four stages which are to be executed while
solving any simulation problem by using ANSYS.
They are as follows
Preferences:
In this stage, the option structural is selected out of
structural, thermal, Ansys fluid because the problem to
be solved belongs to structural category.
Preprocessor:
In this stage, the following steps are executed.
1) Initially, geometry of required size and shape is
build or imported from other CAD files.
2) Depending upon the geometry, element shape is
selected i.e.., for the current problem ‘SHELL-93’
is selected.
3) Inputting the real constants such as thickness of
the shell (t=8mm), thickness of the circular flat
plate (=34mm), thickness of the flange (=10mm),
thickness of the hemispherical cover plate
(=4mm).
4) Defining the element material and its properties.
E.g. Either isotropic or composite material, etc.
For the present problem Isotropic material (Mild steel)
is selected whose material properties are Poisson’s
ratio (μ=0.3), Young’s modulus (E=207GPa).
5) Finite Element Modeling.
Solution:
In this stage the type of analysis is selected. Again in
which either ‘STATIC’ or ‘DYNAMIC’ option is
selected.
For E.g. Structural, Thermal, etc.
For the current problem the option structural along
with static is selected because the pressure vessel is
designed for static pressure load.
A pressure of 7.5bar is applied on the inner walls of
the pressure vessel and degrees of freedom are arrested
wherever required. Finally the option ‘solve current
LS’ is executed.
General postprocessor:
In this stage, results are viewed and plotted.
Time history postprocessor:
By executing this option, graphs are plotted.
For e.g. Displacement vs time, etc are plotted.
2.1 Structural Analysis of spherical pressure vessel
with hydrostatic pressure.
Fig 1.Vector sum displacement Fig 2. Von-misses
stresses
Structural Analysis of spherical pressure vessel with
burst pressure
Fig 3.Vector sum displacement Fig 4. Von-misses
stresses
Structural Analysis of dished end of the multi layer
pressure vessel with hydrostatic pressure 27.3 N/mm2
Fig 5.Vector sum displacement Fig 6. Von-misses
stresses
Structural Analysis of dished end of the multi layer
pressure vessel with burst pressure 64.52 N/mm2
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 114
Fig 7.Vector sum displacement Fig 8.Von-misses
Structural Analysis of dished end of the multi layer
pressure vessel with hydrostatic pressure 27.3 N/mm2
Fig. 9.Vector sum displacement Fig10.Von-
misses stresses
Structural Analysis of dished end of the multi layer
pressure vessel with burst pressure 64.52 N/mm2
Fig 11.Von-misses stresses
.
VII. CONCLUSION
The following conclusions have been drawn from the
present work.
1. At present multilayered vessels are being used
extensively in many industries when compare to
solid wall pressure vessels. Because, there is a
huge difference in weight of the vessel and
uniform stress distribution among the vessel wall
thickness.
2. There is a percentage saving in material of
28.48% by using multilayered vessels in the
place of solid walled vessel when both the
vessels are manufactured with same material i.e.
SA515 Grade 70 steel .
3. There is a percentage saving in material of
91.62% by using multilayered CFRP material
vessels when compared to multilayered SA515
Grade 70 steel material vessels.
4. This decreases not only the overall weight of the
component but also the cost of the material
required to manufacture the pressure vessel. This
is one of the main aspects of designer to keep the
weight and cost as low as possible.
5. The Stress variation from inner side to outer side
of the multilayered pressure vessel is around
11.76%, where as to that of solid wall vessel is
17.32%. This means that the stress distribution is
uniform when compared to that of solid wall
vessel.
6. Minimization of stress concentration is another
most important aspect of the designer. It also
shows that the material is utilized most
effectively in the fabrication of shell.
7. Owing to the advantages of the multi layered
pressure vessels over the conventional single
walls pressure vessels, it is concluded that multi
layered pressure vessels are superior for high
pressures and high temperature operating
conditions.
8. The burst pressures for various fiber orientations
are predicted using the Tsai-Wu failure criteria.
The ± 25° fiber orientation angle is obtained as
the optimum fiber orientation angle for the
composite pressure vessel subjected to high
internal pressure loading.
FUTURESCOPE
1. Analysis on different layer materials to reduce
cost of production
2. Optimization of shell thickness for the given
conditions
REFERENCES
[1] “Finite Element Analysis of Pressure Vessels”
David Heckman, University of California,
© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002
IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 115
Davis Mentor: Gene Massion, Mark Greise
Summer 1998
[2] “Reduction of Stresses in Cylindrical Pressure
Vessels Using Finite Element Analysis” Farhad
Nabhani, Temilade Ladokun and Vahid Askari
Teesside University, School of Science and
Engineering, Middlesbrough, TS1 3BA, UK.
[3] “Design and analysis of multilayer high
pressure vessels” department of mechanical
engineering qis college of engineering
&technology ongole, andhra Pradesh.
[4] “Design and structural analysis of pressure
vessel due to change of nozzle location and
shell thickness” shaik abdul lathuef department
of mechanical engineering, qis college of
engineering and technology, ongole, andhra
pradesh.
[5] “Finite Element Analysis of Pressure Vessel
and Piping Design”Bandarupalli Praneeth,
Dept. of M.E, Nimra Institute of Science &
Technology, Vijayawada, A.P., India
[6] Mechanics of solids by ROGER .T. FENNER.
[7] Machine Design by SHIGLEY.
[8] Mechanics of solids by EGOR. POPOV
[9] Machine Design by Dr.P.C.SHARMA &
Dr.D.K.AGGARWAL.
[10] Machine Design by V.BHANDARI.
[11] Strength of materials by B.C.PUNMIA.Design
Data book by P.S.G.
[12] Mechanics of solids by SADHU SINGH
[13] www.pressurevessels.com
[14] www.thick pressurevessels.com