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© August 2016 | IJIRT | Volume 3 Issue 3 | ISSN: 2349-6002

IJIRT 143888 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 75

COMPARITIVE STUDY OF CANISTER STRUCTURE

WITH VARIOUS STIFFENING PATTERNS

A. S. Sarath1, Dr. Jason Cherian Issac2 and R. Santhanam3 1Post-graduate student, Saint Gits College of Engineerinig, Kottayam, Kerala

2Professor, Department of Mechanical Engineering, Saint Gits College of Engineerinig, Kottayam,

Kerala 3Scientis E, DOFS, DRDL, DRDO, Hyderabad

Abstract—Analyses of canister structures considering

various stiffening patterns have been carried out. Both

classical and finite element methods have been used for

the analyses. Solid elements are used for idealizing the

canister structures for FEA. Canister structures having

plain shells without any stiffening pattern and canister

structures with different stiffening patterns have been

compared in terms of mass, deformation and stress to

study the effect of stiffening patterns. The study shows

that canister structure with a particular stiffening

pattern gives lesser mass, deformation and stress when

compared to canister structures having plain shells

without any stiffening pattern.

Index Terms—Canister; FEA; Plain shell; Stiffening

pattern.

I. INTRODUCTION

A canister structure is an internal pressure vessel used

in rocket systems for the functions of launching,

storing and transportations. Canister structure may be

of different sections such as rectangular, cylindrical

etc depending upon the configuration of rockets they

are used for. Pressure vessel are designed to hold gases

or liquids at a pressure substantially different from the

ambient pressure. Pressure vessel design,

manufacture, and operation are regulated by

engineering authorities backed by legislation. In the

United States, as with many other countries, it is law

that vessels over a certain size and pressure (15PSIg)

be built to Code, the code is the ASME Boiler and

Pressure Vessel Code (BPVC).

Until late 80’s, the design of rectangular pressure

vessels was usually accomplished by the application

of formulas or structural analysis. Vessels were

assumed to be assumed to be infinitely long

rectangular prisms and unit length was analysed as a

rigid frame. In the 1980 Edition, the ASME Code [1]

include design rules for non-circular pressure vessels,

rectangular and obround, with or without partition

plates, also unreinforced and reinforced vessels. These

rules were based on “infinitely long” vessels of non-

circular cross-section and stresses calculated are based

on a linearized “small deflection” theory of plate

bending.

In actual practice, many pressure vessels can be found

which are of finite length, often operating successfully

under pressures two or three times as high as those

permitted under the Code rules cited. V.S.Hoa et al [2]

in their work had investigated the effects of finite

length on the design formula given by the ASME

Code, and also a design method based on “large

deflection” theory coefficients for short rectangular

pressure vessels. In addition to this certain code books

and technical books published by various authors

signify the importance of pressure vessel theory in the

design of rectangular canister structures [3, 4 and 5].

Extensive experimental and theoretical contributions

are available for the study of open box structures, but

few had dealt with boxes with closed boxes. When a

rectangular box structure is subjected to certain

pressure, stress analysis of rectangular box is required

to avoid the failure during working conditions. Dr

D.V.Bhope et al [6] in their work had proposed a finite

element method to evaluate the stresses in rectangular

boxes by changing the L/B ratio.

Many other works have contributed towards the design

and optimization of aerospace structures using

different analytical and experimental works. These

work had helped to improve the strength of the

structures in optimal working conditions by use of

structural support systems such as, ribs, stiffeners etc.

A design of structures under stiffness requirements

using three different approaches such as, (i) solid/void



topology optimization, (ii) coupled topology

optimization suitable for punched shells and (iii) free

sizing optimization for machine milled shell structures

were developed by P. Cervella et al [7]. The

application of computational methods in structural

design methodology for the wing of an Unmanned

Aerial Vehicle was studied in the work by Farrukh

Mazhar et al [8].

S. Hernandez et al [9] in their work had developed a

structural model that describes very precisely the rear

part of an airplane fuselage used to present the

capabilities of size optimization. Two approaches

were used for the study, in first approach only stress

constraints were used, and in second one both the

stress and strain constraints were considered.

In the present study, first the canister structure is

modelled to be a plain surface and analysed with

calculated thickness using the classical analyses. The

second step is to re-design the canister structure with

additional stiffening elements, thus decreasing the

thickness of the sheet-metal. By this the total weight

of the canister decreases.

II. DESIGN AND ANALYSIS

A. Configuration of structure

The canister structure is a rectangular prism with the

height and width of 340mm and length of 3060mm. It

is a hollow prism with specific thickness used for

different canister structures depending upon the

dimensions of rocket. The canister houses rocket and

its different devices connected to the rockets such as

sensors, umbilical, gas generator etc. The basic

configuration of the canister is given in the fig. 1. All

the dimensions given in figure are in mm. For the

canister structure rectangular structure is preferred

over cylindrical structure because cylindrical structure

occupies more space, and uses more material thereby

increasing the total weight of canister. A super-scribed

circular cross-section of the canister would occupy

more space, whereas if an inscribed circular cross-

section of canister is used it would decrease the space

and weight but would not house the complete rocket

as the fins of the rocket would act as a constraint.

Fig. 1. Configuration and dimensions of canister

structure

B. Materials for Structure

The materials selected for the fabrication of the

structure plays important role, since they affect the

characteristics of canister such as weight, deformation

and stresses. For the present study of comparison

between canister structure without stiffening pattern

and with various stiffening patterns, three materials

are considered namely; alloys of Aluminium (AA

6061), Titanium (Ti6Al4V) and Steel (15CDV6).

These materials are selected since they are widely used

in industry (Table I).

Table I: Material Properties

Materia

l

Young’s

Modulu

s

E

(GPa)

Density

ρ

(kg/m3)

Ultimat

e

Tensile

Strengt

h

UTS

(MPa)

Yield

Strengt

h

YS

(MPa)

AA

6061 72.5

27.96e1

1 290 240

Ti6Al4

V 106

45.12e1

1 920 866

15CDV

6 209

78.50e1

1 1130 980

C. Classical Analysis

For the analyses purpose, an appropriate material and

thickness has to be defined that would satisfy the

considered criteria's such as deformation, weight and

stress of the canister structure. For this purpose the

allowable stress have to be calculated using the

ultimate tensile strength (UTS), yield strength (YS),

factors of safety on UTS and YS, and weld efficiency

of each material. The allowable stress for Aluminium

alloy (AA 6061) is calculated using the eqn. (1),

YSUTSallowable FoS

S.Y,FoS

S.T.UMin (1)



Considering weld efficiency 0.5 of U.T.S and Y.S,

MPa145290*5.0S.T.U MPa120240*5.0S.Y

The allowable stress is calculated using the derived

ultimate tensile strength and yield strength using the

eqn. (1)

15.1120,

5.1145Minallowable

)35.104,67.96(Minallowable

Therefore, the allowable stress for AA 6061 with

respect to weld efficiency 0.5 and factors of safety

(FoS) is 96.67 MPa. Similarly, the allowable stresses

calculated for materials Titanium alloy (Ti6Al4V) and

Steel alloy (15CDV6) are 582 MPa and 715 MPa

respectively.

Every missile has certain working conditions, and

depending upon them the canister conditions are

defined. The loads and boundary conditions for the

present canister structure is:

Weight of missile – 300 kg

Launching Loads

o Internal Pressure – 0.7 MPa

Boundary conditions: both ends of the

canister structure are fixed.

Thickness of the material is important in design point

of view for a canister structure, since they affect the

space for rocket loading, weight of the whole canister

structure, deformation of the structure, stresses

induced in the structure by internal pressure and

fabrication of the structure. The thickness of the

structure with respect to the material is calculated

using the ASME code for non-cylindrical pressure

vessel [2],

2A3

tM6

t2Pl

,Stress (2)

The bending moment MA governing the design for the

canister structure is calculated using the small

deflection theory [2]. For material aluminium alloy

AA 6061 the thickness is calculated using eqn. (2),

2t)4.7687(6

t2340*7.067.96

t4.46124t119t67.96 23 mm46.22t

The thickness required for AA 6061 material to satisfy

the calculated allowable stress is 23mm. Similarly, the

thickness is calculated for Ti6Al4v and 15CDV6

materials and are shown in Table II.

Table II: Thickness of Materials

Materials Thickness (mm)

Aluminium (AA 6061) 23

Titanium (Ti6Al4V) 9

Steel (15CDV6) 8.11

D. Plain Shell Analysis

Plain shell of the canister structure without stiffening

patterns are modelled as first case of our study. They

are modelled for the materials Titanium (Ti6Al4V)

and Steel (15CDV6) of calculated thickness 9mm,

8.25mm respectively. Aluminium is avoided for this

study, since the thickness calculated by classical

analyses is 23mm which would use more space of the

structure. Because of this reason, the volume available

for housing the rocket will be lesser and such thickness

would also increase the total weight of the canister

structure. Hence, only Titanium (Ti6Al4V) and Steel

(15CDV6) materials are used for further studies.

Fig. 2. Mesh of plain shell canister structure



Fig. 3. Boundary conditions of plain shell canister

structure

Fig. 4. Deformation of plain shell canister structure

Fig. 4. von Mises stress of plain shell canister structure

TABLE III: Results of Set-1 Analysis

Materials

(Thickness)

Deflection

(mm)

Weight

(Kg)

von Mises Stress

(MPa)

15CDV6 (8.11)

3.15 264.94 715

15CDV6 (9)

1.79 294.02 495.81

Ti6Al4V (9)

3.42 168.99 495.81

The plain shell canister structure is analysed in

ANSYS Workbench v14.5, and the figs. (2-5)

illustrate the mesh, boundary conditions, deflections

and von Mises stresses for 8.11 mm 15CDV6 material.

Both the materials (15CDV6 and Ti6Al4V) were used

for the analysis of the plain shell canister structure and

are given same working and boundary conditions. The

results of 15CDV6 with thickness 8.11mm, 9mm and

Ti6AL4V of 9mm are tabulated in Table III for

comparison.

The aim of the study is to model a new canister

structure of lesser thickness with different stiffening

patterns so as meet the design criteria such as the

induced stresses are lesser than the estimated

allowable stresses(𝜎𝑖𝑛𝑑𝑢𝑐𝑒𝑑 < 𝜎𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒), at the

same time decreasing the total weight of the structure

with minimal deformations. The canister structure

with 9mm thickness and Titanium alloy (Ti6Al4V)

material has lesser weight, deformation and induced

stresses of all cases in the plain shell analyses. But,

when the canister structure of lesser thickness of same

material is analysed with added stiffening pattern, it

would result in higher induced stresses of the structure

(𝜎𝑖𝑛𝑑𝑢𝑐𝑒𝑑 > 𝜎𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒), since the induced stresses

would increase as the thickness decreases. Hence

Titanium alloy (Ti6Al4V) is avoided due to these

reasons. And 15CDV6 material of 8.11mm satisfies

our criteria of consideration from design point of view.

A limit on the deflection is set, that is to be met by the

new model using various stiffening elements.

Deformation, δ≤ 10mm

E. Canister structure with various stiffening pattern

The canister is modelled with various stiffening

patterns to meet the limits set on deformation and

stress after the analysis of plain shell of canister

structure. The new model is made of lesser thickness

(3mm) i.e approximately one by third of thickness of

the plain shell structure and various stiffening patterns

is added to the surface of the canister. Here seven

different cases are considered with respect to the

change in the orientations of rib along the longitudinal

axis of the canister structure.

Complexity is faced during the modelling of the ribs

used as the stiffening pattern in the canister structure.

For the proper imprinting of the ribs or stiffeners on

the sheet metal, the ribs had to be separately modelled

with higher radius of curvature. The modelling steps

used for the design of the ribs are Sketch, Base

Extrude, Boss Extrude, Boss Revolve, Fillet and Cut

Extrude. Here two ribs are modelled, where the length

of Rib-2 is twice as that of Rib-1 shown in fig. 5.

The canister structure with the ribs imparted on it is

considered as seven different cases with respect to the

orientations of the ribs as illustrated in figs. 6-12.

Case-1: Pattern orientation is parallel to longitudinal

axis (only Rib-1 is used).



Case 2: Pattern orientation is parallel to longitudinal

axis (only Rib-2 is used).

Case 3: Pattern orientation is parallel to longitudinal

axis (both Rib-1 & Rib-2 are used).

Case 4: Pattern orientation is perpendicular to

longitudinal axis (both Rib-1 and Rib-2 are used).

Case 5: First, last quarter of pattern orientation is

perpendicular to longitudinal axis and second, third

quarter of pattern orientation is parallel to longitudinal

axis (both Rib-1 and Rib-2 are used).

Case 6: First, third quarter of pattern orientation is

perpendicular to longitudinal axis and second, last

quarter of pattern orientation is parallel to longitudinal

axis (both Rib-1 and Rib-2 are used).

Case 7: Pattern orientation is 45° inclined to

longitudinal axis (both Rib-1 and Rib-2 are used).

Fig. 5. Ribs modelled for set-2 analysis

Fig. 6. Case-2

Fig. 7. Case-3

Fig. 8. Case-4

Fig. 9. Case-5

Fig. 10. Case-6



Fig. 11. Case-7

The analyses of the canister structure with various

stiffening patterns are carried out using ANSYS

Workbench (illustrated figs. 13-16). Solid (quad)

elements are used for the analyses. Fine mesh is

considered for better results and the mesh size of

25mm is take after mesh convergence study. The quad

element has three degrees of freedom (3 translations

along each axis).

In the analyses, the stiffening patterns are considered

to be integrated part of the canister structure and are of

smooth curvature. This reduces the complexity in

meshing of the canister structure with stiffening

patterns, otherwise the mesh would be of improper

surface leading to unreliable results through analyses.

Elements and nodes of each cases considered changes

as the geometry as the whole changes when the

stiffening pattern orientations are changed. Number of

elements are maintained above 250000 in every case

so as to get better results. Stress analyses is carried out

and the factors such as deformation, stress are found

out for all cases. Stress and deformation depends on

geometry, material, loading conditions and

end/support conditions.

Fig. 12. Mesh of set-2 (Case-4 shown in figure)

Fig. 13. Boundary conditions of set-2 (Case-4 shown in

figure)

Fig. 14. Deformation of set-2 (Case-4 shown in figure)

Fig. 15. von Mises stress of set-2 (Case-4 shown in

figure)

Similarly all cases were analysed, and are compared

with each other with respect to deflection, stresses

induced in structure and weight of the canister. The

results are shown in Table IV.

Table IV: Comparison of Set-2 Analysis



Cases Deformation

(mm)

Weight

(kg)

von Mises Stress

(MPa)

Case-1 16.02 137.27 1156.5

Case-2 16.83 137.31 1093.5

Case-3 18.15 137.29 957.93

Case-4 7.91 143.83 714.6

Case-5 18.17 140.56 1009.6

Case-6 15.55 140.56 1124

Case-7 20.624 134.01 1209.2

From the above table and we could compare the

various cases analysed by using the internal pressure

of a canister structure. All the seven cases have their

own characteristics and advantage over each other

with respect to deflection, weight or induced stresses.

But the best of these cases satisfying all the design

criteria’s has to be selected. From the results of FEA

analyses; case-4 has minimum deformation and stress

thus satisfying the design criteria, whereas case-7 has

minimum weight when compared to other cases. But

we neglect case-7 as the deformations are too high

when compared to the thickness of the sheet-metal and

the stress induced are above the allowable stress of

steel (15CDV6) which would ultimately lead to the

failure of the canister structure. Hence, case-4 with the

pattern orientations perpendicular to the longitudinal

axis is proposed.

For comparison of the materials, the selected case-4

was analysed with Titanium alloy (Ti6Al4V) as well,

and the results were deformations of 14.81mm, weight

of canister as 83kgs and induced stresses as 714.6MPa.

The weight of the canister structure with Titanium

alloy (Ti6Al4V) is least out of all cases, but the

structure would ultimately fail as the induced stress

(714.6MPa) are above the maximum allowable stress

(582MPa) of the material calculated by classical

analyses.

III. RESULTS AND DISCUSSIONS

From the FEA results of all seven configurations for

structural loads alone, it is seen that when the number

of stiffening elements are increased the stresses and

deformation have come down. The canister structure

with case-4 that is pattern orientation perpendicular to

the longitudinal axis gives lesser deformation and

stresses with a minimal weight when compared with

the plain shell structure of canister. All the cases could

be compared to propose the best design for a canister

structure.

The plain shell and the patterned shell canister

structure are compared with respect to the thickness,

deformation, weight and von miser stress and are

given in table V

Table V: Comparison of Plain Shell with Patterned

Shell of Canister Structure

Material

Thickness

(mm)

Deformation

(mm)

Weight

(kg)

von Mises Stress

(MPa)

15CDV6 8.11 3.15 264.94 715

15CDV6 3 7.91 143.83 714.6

Hence, we could conclude that the proposed model

with patterned stiffening of case-4 and 3mm thickness

is on par with the plain shell model of canister

structure and satisfies our criteria’s of thickness,

weight of canister structure, deflections, and induced

stresses.

IV. CONLUSIONS

Canister structures having plain shells without any

stiffening pattern and canister structures with different

stiffening patterns have been analysed using both

classical and finite element methods. Three different

materials such as Aluminium (Al 6061), Titanium

(Ti6Al4V) and Steel (15CDV6) have been considered

for analyses. Initially classical analyses have been

carried out to estimate the minimum thickness

required for canister structures having plain shells

without any stiffening pattern. Classical analyses

shows that the minimum thickness required to meet

the strength and stiffness requirement for aluminium

material is around 23mm, which leads to reduce in

internal volume of space which in turn affects the

housing of rocket inside the canister as the outer

dimensions are fixed due to the space constraints. But

for Titanium and Steel materials the minimum

thickness required are 9 and 8.25mm respectively by

classical analyses. With these basic thickness

requirements estimated by classical analyses, canister

structures have been analysed using finite element



analyses. Canister structures with reduced thickness

(approximately one third of plain shell thickness) and

with different stiffening patterns have been analysed

using FEA aiming to reduce the weight of the structure

and also to meet strength and stiffness requirements.

In this process, it is found that the 3mm thickness of

15CDV6 material canister structure with pattern

oriented perpendicular to longitudinal axis shows the

lesser weight, deflection and stress. This study shows

that canister structure with a stiffening pattern gives

lesser mass, deformation and stress when compared to

canister structures having plain shells without any

stiffening pattern.

ACKNOWLEDGMENT

I would like to sincerely thank my P.G coordinator

Sailesh. K. S, Assistant professor, Department of

Mechanical Engineering, Saintgits College of

Engineering, Kottayam who took time out of his

busy schedule and, guided and encouraged me in

the conduct of study.

REFERENCES

[1] ASME Boiler and Pressure Vessel Code, Section

VIII, Division I, Pressure Vessels, 2013 Edition,

The American Society of Mechanical Engineers,

New York.

[2] Hoa. V. S, Blach. A. E, Kwok. C. K, Ahmed. A.

K. W (February 1990), “Rectangular Pressure

Vessels of Finite Lenght”, Journal of Pressure

Vessel Technology, Volume 112, pp. 50-56.

[3] Eugene F. Megysey, “Pressure Vessel

Handbook”, 12th ed., Pressure Vessel Publishing

Inc., July 2001, pp. 213-230.

[4] Clemens Kaminski, “Stress Analysis & Pressure

Vessels”, University of Cambridge, 2005, pp. 1-

74.

[5] Guy Baylac, Danielle Koplewicz, “Unfired

Pressure Vessels – Background to Design Rules”,

-European National Standards, Paris 2006, pp. 47-

52.

[6] Dr. D. V. Bhope, D. G. Lokhande (April 2014),

“Stress Analysis of Rectangular Boxes Using

FEM”, Journal of Engineering Research and

Applications, Vol. 4, pp. 51-59.

[7] P. Cervellera, M. Zhou, U. Schramm,

“Optimization Driven Design of Shell Structures

under Stiffness, Strength and Stability

Requirements”, presented at 6th World

Congresses of Structural and Multi-disciplinary

Optimization, Brazil, June 2005

[8] Farrukkh Mazhar, Abdul Munem Khan,

“Structural Design of a UAV Wing using Finite

Element Method”, Proc. Structures, Structural

Dynamics and Materials Conference, April 2010,

pp. 12-15

[9] S. Hernandez, A. Baldomir, J. Mendez, “Size

Optimization of Aircraft Structures”, presented at

26th International Congress of the Aeronautical

Sciences, La Coruna, Spain, May 2008.

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