A Project Report on ANALYSIS OF SUBMARINE RADOME

Submitted in partial fulfillment of the requirement for award of the degree of

BACHELOR OF TECHNOLOGY

IN

AERONAUTICAL ENGINEERING

BY

M.KARTHIKEYA REDDY 08D41A2107 SRIKANTH SINGH 08D41A2111 MD ALIYSHAAN MOHIUDDIN 08D41A2128 K.SUDHEER 08D41A2150

Under the Esteemed Guidance ofMs. P. Nanda Jyothi

(Associate Professor)

DEPARTMENT OF AERONAUTICAL ENGINEERINGSRI INDU COLLEGE OF ENGINEERING AND TECHNOLOGY

Sheriguda village, Ibrahimpatnam, R.R dist.(Affiliated to Jawaharlal Nehru Technological University)

April 2012

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CERTIFICATE

This to certify that this report on “ANALYSIS OF SUBMARINE RADOME” is a

bonafide work successfully carried out at

Sri Indu College Of Engineering & Technology

BY

M.KARTHIKEYA REDDY 08D41A2107 SRIKANTH SINGH 08D41A2111 MD ALIYSHAAN MOHIUDDIN 08D41A2128 K.SUDHEER 08D41A2150

Students of IV year II sem Aeronautical Engineering under our guidance has

submitted in partial fulfillment as the requirement for the award of degree of

BACHELOR OF TECHNOLOGY

IN

AERONAUTICAL ENGINEERING

Internal Guide External Guide

Ms.P.Nanda Jyothi

(Associate professor)

Head of Department

Mr.M.Srinivasa Rao

(HOD)

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ACKNOWLEDGEMENTWe would like to express our deep sense of gratitude and sincere

thanks to Jagadeesh Reddy P, Principal Director of CADD Institute

Hyderabad for giving us the opportunity for the course and project work.

We would also like to express our sincere gratitude to our college

Principal Mr. P. Mallesham for being a constant source of inspiration

and giving us permission to complete our project.

We would like to extend our sincere thanks to our HOD Mr. M.

Srinivasa Rao and our internal guide Ms. P. Nanda Jyothi, who guided

us throughout the course of the project and made it a grand success.

We would like to thank our external guide Mr. Prasad Rao for his

expert guidance and continuous encouragement and express our

gratitudefor priceless guidance and untiring inspiration during planning

and preparation which lead to the successful completion of our project.

Finally, we also thank our friends and staff members of our

institute Sri Indu College of Engineering and Technology, JNTUH and all

others for helping us in all aspects.

M.KARTHIKEYA REDDY 08D41A2107

SRIKANTH SINGH 08D41A2111

MD ALIYSHAAN MOHIUDDIN 08D41A2128

K.SUDHEER 08D41A2150

3

CONTENTS

Abstract

List of figures

1. INTRODUCTION

1.1. Radome configurations 2

1.2. Structural support 3

1.3. Impact of incident angle 4

1.4. Functions of radome 6

2. LITERATURE SURVEY

2.1 Scope of present study 10

3. DESIGN OF SUBMARINE RADOME 12

3.1 PRO/ENGINEER 13

3.2 Modules of PRO/E 13

3.3 Modeling procedure 14

3.4 Modules of PRO/E 16

3.5 Modeling procedure 16

4. FRP MATERIALS 20

4.1 Materials 20

4.2 Reinforcement 21

4.2.1 Glass fibers 21

4.2.2 Various types of sandwich structures 24

4.2.3 Material section 25

4.3 Matrix 26

4.4 Factors influencing composite fibers 27

4.5 Materials 27

4.6 Functions of the matrix 28

4.7 Advantages of composites 28

4.7.1 High specific stiffness and strength 28

4.8 Limitations of composite materials 28

4.9 Applications of composite materials 30

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5. ANALYSIS OF SUBMARINE RADOME 31

5.1 Finite element method 31

5.2 Explanation of finite element method 35

5.3 Types of elements 37

5.3.1 Size of elements 37

5.3.2 Location of nodes 37

5.3.3 Number of elements 38

5.3.4 Nodal degree of freedom 38

5.3.5 Coordinate system 38

5.4 Formation of matrices and vectors 39

5.4.1 Direct approach 39

5.4.2 Variation approach 39

5.4.3 Weighted residual approach 39

5.4.4 General application of the method 40

5.5 Limitations of FEM 42

6. IMPLEMENTATIONS 43

6.1 Introduction 43

6.2 Theoretical analysis 43

6.2.1 Load cases 43

6.3 ANSYS 46

6.3.1 Program overview 47

6.4 Meshing 49

6.4.1 Fully automatic mesh generation 49

6.4.2 Mesh generation using 2D element 49

6.4.3 Mesh generation using 3D element 49

6.5 Approach to analysis 51

6.5.1 Static analysis 51

6.6 Modal analysis 57

7. FABRICATION METHODS FOR RADOMES 62

7.1 Filament winding 62

7.2 Vacuum bag molding 62

7.3 Auto clave molding 63

7.4 Matched die molding 64

8. RESULTS & DISCUSSIONS 65

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9. CONCLUSIONS & FUTURE WORK 67

REFERENCES

ABSTRACT

Radomes are the electromagnetic windows that protect microwave sub-

systems from the environmental effects. The major requirement of radome is its

transparency to microwaves and for most of the cases mechanical properties are also

equally important. Radome for underwater applications has to withstand high water

pressure of the order of 45 bars.

Composite materials owing to their high strength to weight ratio, high

stiffness and better corrosion resistance are potential source for under water

applications. The concept of 'tailoring' the material properties to suit the radome is

obtained by selecting proper reinforcement, resin matrix and their compositions.

The mechanical properties of composite material, evaluated by testing

specimens as per ASTM standards, are utilized in designing the radome. The modulus

properties calculated using classical theories of composite materials and compared

with test results. The theoretical values utilized to carry out the Finite Element

Analysis of the radome.

ANSYS a Finite Element software package used to analyze the problem. As

the cross sectional thickness of radome varies, the complexity in fabrication is

overcome by adopting matched die techniques. The radome design and finite element

analysis validation concluded by conducting the pressure test on radome.

The modal analysis is also carried out on radome to check for the natural

frequency of the radome. So that resonance does not occur if the natural frequency of

the radome coincides with the excitation frequency of the submarine.

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List of figures

1. 1.1 Functioning of radome 2

2. 1.2 Submarine radome 7

3. 3.1 Fly out icons 18

4. 3.2 2D drawing 19

5. 3.3 Isometric view of the radome 20

6. 3.4 Side view of the radome 21

7. 3.5 Top view of the radome 22

8. 6.1 Nodal solution def+undeformed 59

9. 6.2 Nodal solution 59

10. 6.3 Pressure 60

11. 6.4 Vonmisses stress 60

12. 6.5 Graph Sxy-displacement 61

13. 6.6 Vector plot predefined 61

14. 6.7 Vonmisses graph 62

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1. INTRODUCTION

The basic function of a radome is to form a protective cover between an

antenna and the environment with minimal impact to the electrical performance of the

antenna. Under ideal conditions, a radome is electrically invisible. How well a radome

accomplishes this depends on matching its configuration and materials composition to

a particular application and Radio Frequency range.

Radomes can be found protecting a wide range of outdoor terrestrial and

shipboard communications systems and radar installations as well as airborne avionics

system antennas. The proper selection of a radome for a given antenna can actually

help improve overall system performance by:

1. Maintaining alignment by eliminating wind loading, Allowing for all-weather

operations by protecting the system from rain, snow, hail, sand, salt spray, insects,

animals, UV damage, and wide temperature fluctuations.

2. Providing shelter for installation and maintenance personnel

3. Preventing visual observation of system (security)

4. Minimizing downtime, and extending component and system operating life.

Figure 1.1 Functioning of radome

Historically, a variety of materials have been used for constructing radomes,

including balsa and plywood in early structures. Modern ground-based and ship-based

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radomes are manufactured using composite materials such as fiberglass, quartz, and

aramid fibers held together with polyester, epoxy, and other resins, such as the one

shown. Foam and honeycomb cores are often added between inner and outer “skins”

of the radome to function as a low-dielectric-constant spacer material providing

structural strength and rigidity.

1.1 Radome Configurations:

Several radome configurations are used to minimize RF reflections, including

electrically thin, half-wave, A-sandwich, C-sandwich and others. The best

configuration for a particular application depends on the mechanical requirements and

operating frequency.

A radome that is electrically thin (less than 0.1 wavelengths)as shown, will

generally deliver good RF performance. This is because signal reflections at the free-

space/dielectric boundary are cancelled out by out-of-phase reflections from the

dielectric/free space boundary on the other side of the dielectric material. Signal

losses are low and the net transmission from an electrically thin dielectric laminate is

very high. Unfortunately, electrically thin radomes provide very little thermal

insulation and are not suitable for locations with wide temperature extremes and a

requirement for controlled temperatures.

Another radome approach that works well is a configuration based on the

half-wavelength-thick solid laminate shown in Figure 5. It is similar to the electrically

thin configuration because the reflections cancel out. The wave travels 180° through

the laminate, is reflected with a phase shift of -180°, and travels another 180° on the

return trip to achieve the net 180° phase shift required for cancellation. Figure 6

shows the performance of the same laminate described in Figure 4 at higher

frequencies (through 35 GHz) where it is 0.5 wavelengths thick.

  A-sandwich radome configuration consists of low dielectric foam or

honeycomb core sandwiched between two thin laminates. Its operation is similar to

the half-wavelength-thick solid laminate. However, it is 0.25 wavelengths thick

because the reflection coefficients from the skins have the same amplitude and phase.

The round trip for the reflection from the second skin is 0.5 wavelengths. The

reflections, which are 180°, are out of phase.

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A C-sandwich radome consists of three skin layers and two foam layers, as

shown in Figure 9. The thickness of each foam layer, and possibly the skins, can be

tuned for optimal RF performance in the bands of interest. This can lead to many

potential construction combinations that can provide good RF performance and high

mechanical strength. C-sandwich constructions provide better performance than A-

sandwich radomes; however, the added complexity increases material and labor costs.

1.2Structural Support:

Although radomes are used extensively on airframes and missiles, this section

focuses specifically on support structures for terrestrial and shipboard systems.

Ground and shipboard radomes can range in size from very small antenna covers to

massive-structures.

Self-supporting radomes are usually based on an A-sandwich configuration.

They are made of rigid sections that are bolted or latched together. If phase delay and

insertion loss through the seam is matched to the rest of the radome, the seam

becomes largely invisible to the electromagnetic wave front. Unlike other radome

types mentioned in this article, A-sandwich radomes require no air blowers to

maintain pressure and are not dependant on electrical power to maintain their electro-

magnetic or structural performance. A-sandwich radomes generally have lower

overall operation and maintenance costs.

Inflatable radomes are made of electrically thin dielectric cloth. By being

electrically thin, they are capable of achieving very low loss over wide bandwidths.

The tradeoff for high performance, however, is that they require a constant supply of

air. Inflatable radomes must be supported by internally generated air pressure, which

is supplied by air blowers or air compressors. In order to maintain adequate air

pressure, inflatable radomes must be equipped with airlocks at all doors and a standby

power supply to operate the blowers at all times and under all environmental

conditions. Should the membrane suffer damage or if power is interrupted, it’s

possible for the radome to deflate and collapse. Operating and maintenance costs for

this type of radome usually exceed those all other radome types.

Metal space frame radomes support the window portion of the radome

consisting of the electrically thin, half-wave, or A-sandwich configuration, often in

the shape of a geodesic dome. The window portion typically has very low loss.

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However, signal blockage from the frame reduces system gain and reflects noise back

into the system. Because the frame reflects and refracts the RF wave front, it increases

side lobe levels. A method used to prevent large side lobes is the use of a quasi-

random frame pattern. The quasi-random pattern is also used to minimize side lobes

for the other support structure types.

In contrast to metal space frame radomes, dielectric space frame radomes are

supported by dielectric members who are somewhat electrically transparent.

However, the wave front is phase delayed as it passes through the dielectric support,

alternating between in and out of phase, depending on frequency. If the delay is 180°

out of phase with the phase of the incident signal, the energy that passes through the

frame subtracts from the gain. This leads to a frequency dependant sinusoidal ripple in

the insertion loss and the lost energy goes into the side lobes. This makes dielectric

space frame radomes best suited to systems that operate at less than 1 GHz.

Both types of space frame radomes usually require the use of air blowers or

compressors in order to maintain and enhance the structural integrity of their thin

membrane coverings during windy conditions. Failure to maintain positive pressure

can result in membrane damage and failure.

1.3 IMPACT OF INCIDENT ANGLE:

All of the plots and explanations thus far show reflections at normal

incidence. Typically, an electromagnetic wave hits the radome surface at an oblique

angle, or in the case of a spherical radome, a continuous range of oblique angles. The

transmission characteristics of the radome change with the wave incidence angle and

polarization. Electric fields that are parallel to the plane of incidence have much

higher transmission than fields that are perpendicular to the plane of incidence.

Aerodynamic radomes used on aircraft and missiles often see high incidence

angles. This can result in large amounts of axial ratio degradation for circularly

polarized antennas and higher insertion loss. Electromagnetic wave fronts from

parabolic antennas located inside spherically shaped radomes see low incident angles

at the center of the wave front. Out on the edges, however, the incident angle becomes

higher. If the antenna illumination pattern is symmetric, and the antenna is placed at

the center of the spherical radome, the symmetric shape of the radome cancels out

axial ratio degradation from the oblique incidence angles seen by the antenna.

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Composites are gaining wider acceptance for use on board warships and

submarines due to number of advantages viz. high strength to weight ratio, ability to

be moulded into complex shapes, better EMI performance, absence of corrosion

palliatives which otherwise are source for electronic and magnetic signature.

Composite materials made from E-Glass fibers and epoxy resins have become very

popular as a radome material due to its outstanding transparency to microwaves and

having good mechanical properties. The increasing popularity of the material for

underwater application are posing great difficulties to the designer to select right

combination of composition & shape of radome due to the complex nature of the

structure and the loading conditions for the useful operation life.

Mechanical properties of composite materials are influenced by several

factors like reinforcement, fiber orientation, adhesion, composition, manufacturing

process etc. Conducting the tests on standard specimens and evaluating mechanical

properties is the most important aspect in design of composite material applications.

The ASTM guidelines followed in testing and preparation of standard test specimens.

The micro-mechanics and failure mechanism of composite material is very complex

compared to the conventional isotropic materials. Depending on the reinforcement,

composition content & its percentage, appropriate theory & failure mechanism can be

considered for designing the radome.

Finite Element Analysis of radome design is carried-out using (Analysis

System) ANSYS a FEA software package. Geometrical model of radome is generated

as per radome sketch. Suitable elements are selected and optimum size of mesh is

generated. Material properties, evaluated from tests, are assigned. Boundary

conditions, load cases are applied to complete the preprocessing stage. The post

results obtained after FE analysis compared with design requirements.

The main objective of this project is to develop composite radome which protects the

electronic equipment from high water pressure and transparent to electromagnetic

waves.

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Figure 1.2 Submarine radome

The geometric shape of the radome is a cylindrical barrel covered with a

hemi-spherical dome at the top. It has a circular plate at the bottom end of the cylinder

having M6 size holes which acts as a flange. The radome is secured to the submarine

structure with M6 bolts on its flange.

Radome is made of sandwiched construction with glass reinforced plastic

(GRP) as sheet material and syntactic foam as core. E glass woven fabric & Epoxy

resin is used.

1.4 FUNCTIONS OF THE RADOME:

The Functions of the radome are as follows:

1. The Radome protects the installation from the deteriorating effects of environment and extends the durability of antenna and other equipment.

2. The overall performance of the antenna will be increased with the use of radome

3. FRP radome helps to have overall economy and weight reduction.

4. A radome permits the air borne antenna to function with good efficiency under

high head of the water over the submarine.

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2. LITERATURE SURVEY

Although the name of the finite element method was given recently the

concept has been used several centuries back. For example, Ancient mathematicians

found the circumference of a circle by approximating it as a polygon. In terms of the

present day notation each side of the polygon can be called a finite element, by

considering the approximating polygon inscribed or circumscribed, one can obtain a

lower bound or an upper bound for the true circumference. Further, as the number of

sides of the polygon is increased the approximate values coverage to the true value,

these characteristics will hold true in any general finite element application.

In recent times an approach similar to the finite element method, involving the

use of piece wise continuous functions defined over triangular regions, was first

suggested by R. Courant in 1943 in the literature of applied mathematics.

The finite element method as known today has been presented in 1956 by M.J.

Turner, R.W. Clough, and H.C. Martain & L.J. Toop. This paper presents applications

of simple finite elements (pin-joined bar & Triangular plates with in plane loads) for

the analysis of aircraft structure and is considered as the key contributions in the

development of the finite element method. The digital computer provides a rapid

means of performing the many calculations involved in the finite element analysis and

made the method practically viable, along with the development of high speed digital

computers the application of the finite element method progressed at a very

impressive rate.

The book by Przemieniecki, and Zienkievicz and Hoslister presented the finite

element method as the applied to the solutions of the stress analysis problems. The

book by Zienkievicz’s and Cheug” the finite element method in structural and

continuum mechanics” (Mc. graw hill, London, 1971) presented the broad

interpretation of the finite element method and its applicability to any general field

problems. With this broad interpretation of the finite element method it has been

found that the finite element equation also be derived by using a weighted residual

method such as Galerkin method or the least squares method.

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This lead to widespread interest among applied mathematicians in applying

the finite element method for the solution of the linear and non-linear differential

equations. Over the years several papers, conference proceedings and books have

been published on this subject with all this progress today the finite element method is

considered as one of the well established and convenient analysis tool by engineers

and applied scientists.

The history of submarines subsequent to the first truly operational vessel,

Holland, launched in 1899, showed two significant advances as opposed to steady

incremental developments. These resulted from full scientific studies of all the

problems. The first of these advances was made by the Germans at the end of World

War II, when they produced the Type 21 which had major improvements in range and

battery time while their underwater speed increased to 18 knots compared to 5 knots

on previous vessels. Design diving depth was increased dramatically. They could

operate below the Allies Submarine defense weapon systems. The second advance

was made by US designers who produced Albacore in 1953 with a shape suited to full

underwater operation. Its length-to beam ratio was only 7.7 and top underwater speed

was 33 knots. The drag coefficient was only 0.1 compared to 0.35 on previous

submersible designs.

It is clear that scientific studies should be a starting point for any future

submarine design. A review of the literature covers priorities in design and shows

how enhancement of one feature interacts with other features and may even result in

an overall loss of performance despite the perceived advantage of the enhanced

feature. Hydrodynamic aspects are then discussed starting with the shape and reasons

why a length-to-beam ratio of about 7.5 gives the minimum resistance. All features

affecting the resistance are discussed including the boundary layer, laminar flow,

transition, turbulence separation and how the flow over the principle passive sonar

should be as quiet and smooth as possible. Added resistance from sails, masts,

snorkels and appendages need careful streamlining and attention in design. A

proposed profile of a new submarine is presented which has the passive sonar far

forward in the streamlined nose with the torpedo tubes positioned further aft. It should

be a quieter vessel with more effective sonar. The profile requires shortening to

reduce the displacement and then the internals need rearranging. The design process

then begins, which is iterative.

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In order to proceed with such concepts it is vital to have a database. Our

current submarine, the Collins class, should be the base from which all changes and

proposals are measured. It is suggested detailed wind tunnel studies should be

undertaken concurrently with computational fluid dynamic (CFD) evaluations. The

results should then be compared with full scale trials to establish propeller efficiencies

and roughness factors as well as the contributions for each feature, hull, sail, control

fins, masts and snorkels, flood openings and others. This database will allow more

precise comparisons for any improvements which may be considered in a future

design. Glass fiber recycled poly(ethylene terephthalate) composites: mechanical and

thermal properties by A.L.F. de M. Giraldi, Department of Polymer Technology,

College of Chemical Engineering, State University of Campinas, SP, Brazil. Their

Investigations of thermal and mechanical properties of recycled poly(ethylene

terephthalate) (PET) reinforced with glass fiber have been carried out, focusing on the

influence of two variables involved in the extrusion process: screw speed and torque.

A Factorial Experimental Design of the processing conditions during extrusion (screw

speed and torque) was done to get the best thermo mechanical properties versus

processing conditions. Mechanical properties such as Young's Modulus and Impact

Resistance increased after the addition of glass fiber in recycled PET matrix.

Inter laminar fracture of commingled-fabric-based GF/PET composites. L. Ye

and K. Friedrich Department of Mechanical and Mechatronic Engineering at the

University of Sydney, NSW 2006, Australia, Institute for Composite Materials Ltd,

University of Kaiserslautern, Germany. A 45:55 weight% mixture of commingled

glass/polyethylene terephthalate(PET) fabric was selected to study the relationships

between material micro structure, Mode I and Mode II inter laminar fracture

toughness and failure mechanisms. Composite laminates subjected to different

cooling histories were manufactured with in a steel mould using a laboratory heat

press. Mode I and Mode II inter laminar fracture tests were performed using double

cantilever beam and end-notched flexure specimens.PET matrix morphology

appeared to be sensitive to the thermal histories, although this occurred on a

subspherulitic scale (in contrast to observations made with polypropylene-based

composites). The spherulitic textures were generally very fine and no evidence of

inter spherulitic fracture paths could be identified. When the composites were

subjected to low cooling rates or an isothermal crystallization process, many small

matrix cracks developed between fibers within the reinforcing bundles. The lower the

16

cooling rate, the higher the density of matrix cracks per unit volume of material. The

Hybrid Composite inter laminar fracture toughness in the laminates with slow cooling

rates was much lower than in the case where a quasi-quenched condition was applied.

Characterization of thermoplastic poly(ethyleneterephthalate)-glass fiber

composites, crystallization study By Catherine Gauthier , Laboratoire d 'Etudes des

Matriaux Plastiques et des Biomatériaux, Université Claude Bernard, France. They

investigated the influence of glass fibers on crystallization kinetics and on matrix

morphology for poly (ethylene terephthalate) (PET)/glass fiber composites.

The following parameters are also considered: fusion-crystallization

conditions, thermal stability and the addition of nucleating agents in the matrix (talc

or sodium benzoate). It clearly appears that the influence of those additives on the

crystallization of PET is predominant compared to the effect of stiffening fibers.

Moreover, the application of shear stresses at the PET/glass fiber interface promotes

the growth of a different crystalline superstructure.

2.1 SCOPE OF PRESENT STUDY:

A probe by accident into the field of thermosetting polymers has brought

about a quantum growth in its basic as well as technological aspects.

The synthetic thermosetting polymers with the combinational properties of the

existing conventional high strength polymers and glass fibers with a variety of

filler materials have altogether offered a new field of research.

The review of work presented here reveals that large effort has gone into

the understanding of the mechanical, thermal and physical properties of thermo sets.

A thorough literature search reveals that there are no systematic studies on mechanical

properties of thermosetting composites. There is ample scope for fabrication of newer

composites with different weight fractions of glass fiber and PET in polymers and

there characterization for physical, mechanical and thermal properties. With

a variety of filler Materials have altogether offered a new field of research.

Hybrid Composites-the understanding of the mechanical and thermal

properties of thermo sets:

A thorough literature search reveals that there are no systematic studies on

mechanical properties of thermosetting composites. There is ample scope

for fabrication of newer composites with different weight fractions of glass fiber and

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fillers in polymers and their characterization for physical, mechanical and

thermal properties.

In this thesis, a wealth of data on mechanical properties of polymer glass filler

composites has been generated. These data are useful for material technologists,

mechanical engineers and defense engineering, who can make use of this database for

the generation of new materials for specific application. In that respect it has been

used GF and virgin PET fibers in the form of woven mat and epoxy as matrix.

Laminates are obtained from vacuum bag molding technique. Tests carried out to

evaluate Physic-Mechanical and thermal properties according to ASTM standards.

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3. DESIGN OF SUBMARINE RADOME

Design as a noun informally refers to a plan or convention for the construction

of an object or a system (as in blueprints, engineering drawing, circuit

diagrams and sewing patterns) while "to design" refers to making this plan. No

generally-accepted definition of "design" exists and the term has different

connotations in different fields. However, one can also design by directly constructing

an object (as in pottery, engineering, management, and graphic design). More

formally design has been defined as follows.

A specification of an object, manifested by an agent, intended to

accomplish goals, in a particular environment, using a set of primitive components,

satisfying a set of requirements, subject to constraints; to create a design, in

an environment. 

Another definition for design is a roadmap or a strategic approach for

someone to achieve a unique expectation. It defines the specifications, plans,

parameters, costs, activities, processes and how and what to do within legal, political,

social, environmental, safety and economic constraints in achieving that objective.

Here, a "specification" can be manifested as either a plan or a finished product, and

"primitives" are the elements from which the design object is composed. With such a

broad denotation, there is no universal language or unifying institution for designers

of all disciplines. This allows for many differing philosophies and approaches towards

the subject. The person designing is called a designer, which is also a term used for

people who work professionally in one of the various design areas, usually also

specifying which area is being dealt with (such as a fashion designer, concept

designer or web designer). A designer's sequence of activities is called a design

process. The scientific study of design is called DESIGN. Designing often

necessitates considering the aesthetic, functional, economic and sociopolitical

dimensions of both the design object and design process. It may involve

considerable research, thought, modeling, interactive adjustment, and re-

design. Meanwhile, diverse kinds of objects may be designed, including clothing,

skyscrapers, corporate, skyscrapers, corporate identities, business processes and even

methods of designing.

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3.1PRO/E:

Pro-E Design, LLC was founded in Macedonia, Ohio by Brian T. Hengle. A

graduate of Cleveland State University, Brian holds a bachelor of Civil Engineering

with a concentration in Structures. He is registered in the state of Ohio as a

Professional Engineer.

Pro/ENGINEER is a parametric, integrated 3D CAD/CAM/CAE solution

created by Parametric Technology Corporation (PTC). It was the first to market

with parametric, feature-based, associative modeling software. The application runs

on Microsoft-Windows platform, and provides modeling, assembly and drafting,

finite element analysis, and NC and tooling functionality for mechanical engineers.

The Pro/ENGINEER name was changed to Cero element/Pro on October 28, 2010,

coinciding with PTC’s announcement of Cero, new design software.

Pro/ENGINEER (Pro/E for short) is a commercial CAD/CAM package that is

widely used in industry for CAD/CAM applications. It is one of the new generations

of systems that not only offer a full 3-D solid modeler, in contrast to purely 2-D and

surface modelers, but also parametric functionality and full associatively. This means

that explicit relationships can be established between design variables and changes

can be made at any point in the modeling process and the whole model is updated.

The method of constructing a model of an object is very similar to that followed in the

production of a physical component. For example the manufacture of the shaped

block in Figure 1 would start with the choice of construction environment, the

selection of a piece of stock material followed by a series of manufacturing processes,

e.g. milling, drilling, welding/sticking. Pro/E has direct analogues for most of these

operations as various types of FEATURES which can be combined to generate a

complete representation of a PART, Pro/E's terminology for a single component.

Features fall into three main categories, Construction, Sketched and Pick/Placed.

Pro/E is mainly used for CAD.pro/E is generally defined as feature based, associative,

parametric.

3.2 FEATURE BASED:

When you want to create any solid model, you have to create it using number of

features hence it is known as feature base. Pro/ENGINEER is feature-based.

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Geometry is composed of a series of easy to understand features. A feature is the smallest building block in a part model. Things to remember:

• Pro/ENGINEER allows building a model incrementally, adding individual features one at a time.

• This means, as you construct your model feature by feature you choose your building blocks as well as the order you create them in, thus capturing your design intent.

• Design intent is the motive, the all-driving force, behind every feature creation.

• Simple features make your individual parts as well as the overall model flexible and reliable.

The fly-out icons will appears automatically on the right side screen when you

enter the sketcher mode.

These icons are logically grouped together, based on capability.

3.3 ASSOCIATIVE:

Pro/ENGINEER models are often combinations of various parts, assemblies,

drawings, and other objects. Pro/ENGINEER makes all these entities fully

associative. That means if you make changes at a certain level those changes

propagate to all the levels. For example if you change dimensions on a drawing the

change will be reflected in the associated part.

Any modification made in any module will automatically create modification

in the other module. So this type of connection from module to module is known as

associative.

•File: Contains commands for manipulating files

•Edit: Contains action commands

•View: Contains commands for controlling model display and display performance.

•Datum: Creates datum features

21

•Analysis: Provides access to options for model, surface, curve and motion analysis,

as well as sensitivity and optimization studies.

• Info: Contains commands for performing queries and generating reports.

•Applications: Provides access to various Pro/ENGINEER modules,

•Utilities: Contains commands for customizing your working environment.

•Windows: Contains commands for managing various Pro/ENGNEER windows.

figure3.1 Fly-out icons

With fly-out icons, you can access the most frequently used sketching tools with Single click, without having to go to pull down menus.

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3.4 Modules of PRO/E

1 .SKETCHER

2. PART DESIGN

3. ASSEMBLY

4. DRAWING

3.5 MODELLING PROCEDURE:

FOLLWING PROCEDURE IS ADOPTED IN MODELING OF THE SUBMARINE

RADOME

Initially 2D drawings were created using sketcher toolbar; tools in profile tool

bar such As line, circle, rectangle, point, reference lines etc … and sketch

references like grid, vertex, and dimensions are used.

Figure3.2 2D drawing

The created drawings were then completely constrained using the tool in

constraint tool bar like constraint and auto constraint.

Then 2D drawings were converted into 3D using sketch based features tools

such as extrude, swept blend, blend.

3D objects are modified as required using engineering feature tool bar, tools such as edge fillet, chamfer are used.

23

Figure3.3 isometric view of the radome

24

Figure3.4 side view of the radome

25

Figure3.5 top view of the radome

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4. FRP MATERIALS

4.1MATERIAL:

Since the performance of a radome depends on the materials used, the materials

play an important role in the design of the radome.

In the beginning plywood was used for fabrication of radomes. But due to its

moisture absorption tendency now it is not used. Metals cannot be used as radome

materials because they are conductors of electricity which will absorb the transmitted

electromagnetic waves by the antenna.

To avoid moisture absorption resin impregnated glass fabric was applied as thin

layer on the outer surface of the plywood radome. But the performance of this layer is

very much limited. After that polyester foam phenolic resin impregnated cotton

canvas was used to protect moisture absorption even though this exhibits good

strength, its resistance to heavy physical stresses was poor.

To increase the wall strength, the thickness of the radome wall has to be

increased which is not suitable to radar wave length. At this critical stage composite

materials fiber reinforced plastics came into existence.

Composite material is the combination of two or more materials with different

properties and characteristics of the parent material. A composite is a mixture of

materials with adequate bond between the constituents; the constituents retain their

physical identity even after several years.

The composite material mainly contains two components namely reinforcement

and the matrix.

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4.2 REINFORCEMENT :

The main function of the reinforcement is to improve the overall mechanical

properties of the composite. In general this reinforcement material will have higher

tensile strength and young modulus than that of matrix material. These are used in the

form of fibers.

Many materials like glass carbon fiber, graphite, boron fiber, asbestos,

whiskers, Kevlar etc, can be used as reinforcement material, out of these glass fiber is

most versatile. For very high performance applications advanced composites made of

either carbon fibers or boron fibers are used. But in India fibers are used to reduce the

cost of production.

4.2.1 GLASS FIBRES:

These fibers are graded as E,A,C,S,Z,M & D.

‘E’ glass is electrical grade which is having high bulk electrical resistivity and

high surface resistivity.

‘A’ glass in one which is having high alkali content and of very limited use.

‘C’ glass is a chemical quality and used for corrosion resistance to acids.

‘S’ glass has higher strength and elastic module that E glass.

‘Z’ glass is used to reinforce the cement products.

‘M ’glass has high value of young’s modulus but specific strength is low.

‘D’ glass has low dielectric loss value and hence is specifically suited for high

performance electronic applications radomes etc.,

The various forms of glass fiber reinforcement are as continuous strand and roving,

chopped strands, yarns, mats etc.,

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Table 1. Comparison of typical properties for some common fibers:

Materials Density (g/cm3) TensileStrength (MPa)

Young modulus (GPa)

E-Glass 2.55 2000 80

S-Glass 2.49 4750 89

Alumina (Saffil) 3.28 1950 297

Carbon 2.00 2900 525

Kevlar 29 1.44 2860 64

Kevlar 49 1.44 3750 136

CARBON FIBRES: These are used for higher temperature applications compared to

‘E’ glass.

BORON FIBRES:

These are used for light weight aerospace composite structures. The density of

boron fiber is only 2.6 x 10 Micro Kg/Culm. Boron fibers are extremely hard and

have very high tensile strength & Module.

WHISKERS:

Whiskers are strong and the best properties of glass and boron are present in

whiskers. They have the elongation of glass fibers (3 to 4 %) & the modulus of boron

is 410 KN/mm.

MATRIX SYSTEMS:

The plastic phase which holds together the reinforcing fibers is called the

matrix. The plastic material acts as the medium through which load is transferred

from one fiber to the other fiber also the matrix protects the reinforcing fibers from

weather and provides shape and finish to the composite material.

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There are a variety of matrix materials available, some additives are added to

the matrix to get some desired improved properties like hardness, temperature,

resistance etc., and these additives include curing agents, fillers and stabilizers.

The matrix materials/plastic resins which undergo deformation and can be reworked

when heated are known as thermoplastics & the plastics which will not undergo

deformation and cannot be reworked are called thermo setting plastics.

THERMO PLASTICS:

Ex: Polyethylene, Polystyrene, Teflon, PVC, Acrylic etc.,

THERMOSETTING PLASTICS:

Polyster, Epoxy, Phenolics, Silicones, Urea formaldehyde etc., Polymers in a

stage of incomplete polymerization are called resins. A resin must be subjected to

further polymerization during processing by heat or addition of catalyst or harder. The

thermosetting resins are as follows.

POLYSTER:

Polyesters are made in two stages. In the first stage unsaturated moiety is made,

in the second stage the unsaturated base resin is dissolved in a suitable unsaturated

monomer. The cross linking of polymers is called curing and it is achieved by adding

catalyst/ initiator and an accelerator / promoter at room temperature and at elevated

temperature first adding a catalyst suitably the monomers.

EPOXIES:

Epoxy resins in the uncured state are liquids of low melting solids which set to

a solid infusible mass on reacting with a curing agent or hardener. The most widely

used type of epoxy resin in the world is that derived from epichlorohydrin and

Biphenyl ‘A’

Diluents are added to epoxy resins primarily to lower viscosity and thus

improve handling characteristics. Epoxy resins are preferred because of its good

30

electrical properties, excellent chemical properties, outstanding toughness and better

adhesive properties.

PHENOLIC RESINS:

These are used where high strength and high temperatures (up to300 deg.

centigrade) are used. Higher pressures are necessary to cure phenol mouldings.

SILICON RESINS:

Silicons are the first of the inorganic polymers they are the combination of

silicon - oxygen linkages. The outstanding electrical properties of silicon fiber glass

laminates coupled with the retention of mechanical properties at elevated

temperatures have made this type of composite a standard for radomes of supersonic

vehicles.

Glass fibers are bonded to a low density cellular polystyrene material and

used a radome material. For attaining good mechanical properties and better adhesion

between the fabric and resin system epoxide resins are developed. Later on a wide

variety of matrix systems were developed like phenolics, silicon etc., in reinforcement

also different types of fabric are developed to attain desired specific properties. They

are like Kevlar, Carbon Boron etc., for under water applications the Radom has to

withstand high hydrostatic pressures, so sufficient thickness of wall should be

provided. If the thickness of the wall is increased solidly, the transmission losses will

be more because of the high dielectric constants of the wall materials. To overcome

the problem of transmission losses alternate layer of low dielectric constant and high

dielectric constant materials are used. This type of structure is called sandwich wall

and the radome is known as sandwich radome.

4.2.2 VARIOUS TYPES OF SANDWICH STRUCTURES:

The simplest form of laminated construction is two ply sandwiches; this consists

of high dielectric constant thick skin supported internally by a porous low dielectric

material. This suits for low frequencies.

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A sandwich wall consists of an outer and inner skin of high dielectric

material and a core of low dielectric material. The optimum skin spacing or core

thickness is approximately 1/4th wave length. In this construction the strength to

weight ratio is greater than of a solid wall radome and it also has broad band

capabilities. The problem in this is sandwich construction.

4.2.3 MATERIAL SELECTION:

The metals have been the most preferred engineering materials because of

their mechanical properties. Composite materials with high specific modulus and

specific strength are fast becoming the choice of materials for engineering

applications where weight is a crucial factor.

In case of radomes light weight facilitates easy handling and rotation in

required direction which allows power saving, cost saving and greater safety. The

materials must be such that it should not interfere with RF signals. Compared to

metals, composite materials provide better solution to the requirements of masts.

4.2.4 HOW DO COMPOSITES DIFFER FROM METALS:

Composite materials have many characteristics that are different from

conventional engineering materials. Most engineering materials are homogeneous

and isotropic. In contrast composite materials are heterogeneous and orthotropic or

more generally anisotropic.

HOMOGENEOUS:

A homogeneous body has uniform properties throughout i.e. properties are not

a function of position in the body.

ISOTROPIC:

An isotropic body has material properties that are the same in every direction

at a point in the body. i.e. the properties are not a function of orientation at a point in

the body.

HETEROGENOUS:

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A heterogeneous body has non-uniform properties over the body i.e. the

properties are a function of position in the body.

ORTHOTROPIC:

An orthotropic body has material properties that are different in three

mutually perpendicular directions at a point in the body. The properties are a function

of orientation at a point in the body.

ANISOTROPIC:

An anisotropic body has material properties that are different in all directions

at a point in the body. There are no planes of material and property symmetry. Again,

the properties are a function of orientation at a point in the body.

FIBER:

Any material in an elongated form such that it has very high length to diameter

ratio is called a fiber. Fibers are much stiffer and stronger than the same material in

bulk form.

Materials have actual strengths which are several magnitudes lower than the

theoretical strengths. This difference is due to the inherent flaws in the material. As

the fibers become smaller in diameter, it reduces the chances of an inherent flaw in

the material; thereby the strength is increased.

4.3 MATRIX:

A bonding material which adheres to and contains the fibers is called matrix.

Metals, thermoplastics, thermosetting resins, ceramics can be used as matrix

materials. Epoxy resins are the most commonly used matrix materials.

LAMINA:

A lamina is a flat (sometimes curved as in a shell) arrangement of unidirectional

fibers or woven fibers in a matrix.

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LAMINATE:

A Laminate is a stack of laminae with various orientations of principal

material directions in the laminae.

4.4 FIBER FACTORS INFLUENCING COMPOSITE PROPERTIES:

The fibers in a composite material are the major load carrying agents. The

fiber factors which influence the performance of a composite are length, orientation,

shape and material.

LENGTH:

The fibers can be either long or short. Long continuous fibers are easy to

orient and process and have improved surface finish and dimensional stability. The

short fibers cannot be controlled fully for proper orientation however short fibers

provide low cost and have few flaws and therefore have higher strength.

ORIENTATION:

Fibers oriented in one direction give very high stiffness and strength in that

direction. If the fibers are oriented in more than one direction, for the same volume of

fibers per unit volume of the composite, it cannot match stiffness and strength of

unidirectional composites.

SHAPE:

The most common shape of fibers is circular because handling and

manufacturing them is easy. Hexagon and square shaped fibers are possible but their

advantage of strength and high packing factors do not outweigh the difficulty in

handling and processing them.

4.5 MATERIAL:

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The material of the fiber directly influences the mechanical performance of a

composite. Fibers are generally expected to have high elastic modulus and strength.

This expectation and cost have been key factors in graphite, aramids and glass

dominating the fiber market for composites.

4.6 FUNCTIONS OF THE MATRIX:

1. The matrix binds the fibers together, holding them aligned in the important stressed

direction. Loads applied to the composite are then transferred into the fibers, the

principal load bearing component, through the matrix, enabling the composite to

withstand compression, flexural and shear forces as well as tensile loads.

2. The matrix isolates the fibers from each other so that they can act as separate

entities and the failure of one fiber does not result in immediate failure of composite.

3. The matrix should protect the reinforcing fibers from mechanical damage and from

environmental attack. A ductile matrix will provide a means of slowing down or

stopping cracks that might have originated at broken fibers while a brittle matrix may

depend upon the fibers to act as matrix crack stopper.

4. Through the quality of its grip on the fibers the interfacial bond strength the matrix

can also be an important means of increasing the toughness of the composite.

4.7 ADVANTAGES OF COMPOSITES:

Fibrous composites are often the material of choice of designers for variety

of reasons including low weight, high stiffness, high strength, electrical conductivity (

or non conductivity), low thermal expansion, low or high rate of heat transfer and

corrosion resistance.

4.7.1 HIGH SPECIFIC STIFFNESS AND STRENGTH:

Undoubtedly the most often cited advantage of fibrous composites is their

high specific stiffness and high specific strength as compared with traditional

engineering materials. These properties lead to improved performance and reduced

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energy consumption, both vitally important in the design of almost all engineering

structures.

Unlike isotropic materials, composites are directionally dependent. Thus

composites can be designed to have the desired properties in specified directions

without over designing in other directions.

Tailored Design:

Composites can be engineered to meet the specific demands of each particular

application. Available design options include.

i. The choice of materials (fiber and matrix)

ii. The volume fraction of fiber and matrix

iii. Fabrication method

iv. Number of layers in a given direction

v. Thickness of individual layers

vi. Type of layer (unidirectional or fabric)

vii. Layer stacking sequence (symmetric or anti-symmetric)

This vast array of design variables for composites contrasts sharply with more

traditional engineering materials, where the choices are much more limited. The

availability of a wide array of structural materials means that more efficient structures

can be fabricated with less material waste.

The matrix is of considerably lower density, stiffness and strength than the fibers.

However, the combination of fibers and matrix can have very high strength and

stiffness, yet have low density.

4.8 LIMITATIONS OF COMPOSITE MATERIALS:

There are some drawbacks and limitations in use of composites and these include:-

36

i. High cost of fabrication of composites is a critical issue improvement in

processing and manufacturing will lower these costs in the future.

ii. Because of anisotropy of composites, the structural analysis (computational,

experimental) is more complicated and intensive.

4.9 APPLICATIONS OF COMPOSITE MATERIALS:

Composite materials have been successfully applied in a wide variety of fields.

AEROSPACE:-

In aircrafts, spacecrafts & helicopters, the composites have been used

successfully. High specific modules and strength and dimensional stability during

large changes in temperature in space make composites the material of choice in

space applications.

SPORTING GOODS:-

Composites are used in athletic equipment to improve composites through

lighter weight and improved tailoring composites have been used for tennis racket,

boat hulls, speed boats, hockey sticks etc.

MILITARY:-

Helmets, bullet proof vests, lighter weapons, portable bridges are a few

examples of military applications. Apart from these, composites have been used

successfully in automotive industry, medical and electronic applications.

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5. ANLASYS OF SUBMARINE RADOME

5.1 . GENERAL DESCRIPTION OF THE FINITE ELEMENT

METHOD:

5.1.1 FINITE ELEMENT METHOD:

The finite element method is a numerical technique, well suited to digital

computers, which can be applied to solve problems in solid mechanics, fluid

mechanics, heat transfer and vibrations. The procedures to solve problems in each of

these fields are similar; however this discussion will address the application of finite

element methods to solid mechanics problems. In all finite element models the

domain (the solid in solid mechanics problems) is divided into a finite number of

elements. These elements are connected at points called nodes. In solids models,

displacements in each element are directly related to the nodal displacements. The

nodal displacements are then related to the strains and the stresses in the elements.

The finite element method tries to choose the nodal displacements so that the stresses

are in equilibrium (approximately) with the applied loads. The nodal displacements

must also be consistent with any constraints on the motion of the structure.

The finite element method converts the conditions of equilibrium into a set of

linear algebraic equations for the nodal displacements. Once the equations are solved,

one can find the actual strains and stresses in all the elements. By breaking the

structure into a larger number of smaller elements, the stresses become closer to

achieving equilibrium with the applied loads. Therefore an important concept in the

use of finite element methods is that, in general, a finite element model approaches

the true solution to the problem only as the element density is increased (see the

discussion on Limitations of Finite Element Methods)

There are a number of steps in the solution procedure using finite element

methods. All finite element packages require the user to go through these steps in one

form or another.

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1) Specifying Geometry - First the geometry of the structure to be analyzed is defined.

This can be done either by entering the geometric information in the finite element

package through the keyboard or mouse, or by importing the model from a solid

modeler like Mechanical Desk Top.

2) Specify Element Type and Material Properties - Next, the material properties are

defined. In an elastic analysis of an isotropic solid these consist of the Young’s

modulus and the Poisson’s ratio of the material.

3) Mesh the Object - Then, the structure is broken (or meshed) into small elements.

This involves defining the types of elements into which the structure will be broken,

as well as specifying how the structure will be subdivided into elements (how it will

be meshed). This subdivision into elements can either be input by the user or, with

some finite element programs (or add-ons) can be chosen automatically by the

computer based on the geometry of the structure (this is called automeshing).

4) Apply Boundary Conditions and External Loads - Next, the boundary conditions

(e.g. location of supports) and the external loads are specified.

5) Generate a Solution - Then the solution is generated based on the previously input

parameters.

6) Post processing - Based on the initial conditions and applied loads, data is returned

after a solution is processed. This data can be viewed in a variety of graphs and

displays.

7) Refine the Mesh - Finite element methods are approximate methods and, in

general, the accuracy of the approximation increases with the number of elements

used. The number of elements needed for an accurate model depends on the problem

and the specific results to be extracted from it. Thus, in order to judge the accuracy of

results from a single finite element run, you need to increase the number of elements

in the object and see if or how the results change.

8) Interpreting Results - This step is perhaps the most critical step in the entire

analysis because it requires that the modeler use his or her fundamental knowledge of

39

mechanics to interpret and understand the output of the model. This is critical for

applying correct results to solve real engineering problems and in identifying when

modeling mistakes have been made (which can easily occur).

The eight steps mentioned above have to be carried out before any meaningful

information can be obtained regardless of the size and complexity of the problem to

be solved. However, the specific commands and procedures that must be used for

each of the steps will vary from one finite element package to another. The solution

procedure for ANSYS is described in this tutor. Note that ANSYS (like any other

FEM package) has numerous capabilities out of which only a few would be used in

simple Static Analysis problems.

In the finite element method, the actual continuum or body of matter like

solid, liquid or gas is represented as some assemblage of sub divisions called finite

elements. These elements are considered to be interconnected as specified joints

which are called nodes or nodal points. The nodes usually lay on the element

boundaries where adjacent elements are considered to be connected, since the actual

variation of the field variable (like displacement, stress, temperature, pressure &

velocity) inside the continuum is not known. We assume that the variation of the field

variable inside a finite element can be approximated by a simple function. The

approximating functions (also called interpolation models) are defined in terms of the

values at the nodes. When the field equations (like equilibrium equations) for the

while continuum are written the new unknown will be the nodal values of the field

variable, by solving field equations, which are generally in the form of matrix

equations. The nodal values of the field variable will be known once these are known;

the approximating function defines the field variable throughout the assemblage of

elements.

The solution of a general continuum by the finite element method always

follows an orderly step by step process; the step by step procedure for static structural

problem can be stated as follows:

Step1. Discritization of structural domain:

40

The first step in the finite element method is to divide the structure or solution

region into sub divisions or elements.

Step2. Selection of a proper interpolation model:

Since the displacement (field variable) solution of a complex structure under

any specified load condition cannot be predicted exactly, we assume some suitable

solution within an element to approximate the unknown solution. The assumed

solution must be simple from computation point of view and it should satisfy certain

convergence requirements.

Step3. Derivations of element stiffness matrices (Characteristic matrices) and load

vectors:

From the assumed displacement model the stiffness matrix [K(e)] and the load

vector P(e) of element ‘e’ are to be derived by using either equilibrium conditions or a

suitable variation principle.

Step4. Assemblage of element equations to obtain the overall equilibrium equation:

Since the structure is composed of several finite elements, the individual

element stiffness matrices and load vectors are to be assembled in a suitable manner

and the overall equilibrium equation has to be formulated [k]_=P

Where [k] is called assembled stiffness matrix, _ is called vector of nodal

displacements and P is the vector of nodal forces for the complete structure.

Step 5: Solution of system equations to find nodal values of the displacements (field

variable)

The Overall equilibrium equations have to be modified to account for the

boundary conditions of the problem. After the incorporation of the boundary

conditions, the equilibrium equations can be expressed as [K]_ = P.

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For the linear problems, the vector ‘-’ can be solved very easily but for non-

linear problems, the solution has to be obtained in a sequence of steps, each step

involving the modification of the stiffness matrix [K] and for the load vector ‘P’.

Step 6: Computation of element strains & stresses from the known model

displacements:

If required, the element strains & stresses can be computed by using the

necessary equations of solid or structural mechanics. In the steps the words indicated

in brackets implements for the general FEM step by step procedure.

5.2 EXPLANATION OF FEM STEP BY STEP PROCEDURE:

The steps involved in finite element analysis are stated earlier, general

explanation of each step of the step by step procedure of FEM is given below. This

description provides general outlook on bird’s eye view of FEM.

DISCRETIZATION OF DOMAIN:

The discretization of domain of solution region into sub regions (finite

elements) is the first step in the finite element. This is equivalent to replacing the

domain having an infinite number of degrees of freedom by a system having finite

number of degrees of freedom.

The process of discretization is essentially an exercise of engineering

judgment. The shapes, size number & configuration of the elements have to be chosen

carefully such that the original body or domain is simulated as closely as possible

without increasing the computation effort needed for the solution.

BASIC ELEMENT SHAPES:

For any given physical body we have to use engineering judgment in

selecting appropriate elements for discretization. Mostly the choice of the type of the

element is dictated by the geometry of the body and the number of independent spatial

42

coordinates necessary to describe the system. Some of the popularly used are one, two

& three dimensional elements.

When the geometry, material, properties & parameters (like stress,

displacement, pressure & temperature) can be described in terms of only one spatial

coordinate, we can use one dimensional element. Although this element has a cross

sectional area, it is generally schematically as a five segment. Using this type of

elements the cross sectional area along the length may be varied.

When the configuration and the details of the problem can be described in

terms of two independent spatial co-ordinates, we can use the two dimensional

elements. The basic element useful for two dimensional analyses is the triangular

element. Although a quadrilateral for its special forms, rectangle & parallelogram

elements can be obtained by assembling two or four triangular elements, in some

cases the use of quadrilateral elements prove to be advantageous.

If the geometry, material properties and other parameters of the body can be

described by three spatial coordinates. We can idealize the body by using three

dimensional elements. The basic three dimensional, analogous to the triangular

elements in the case of two dimensional problem is the tetrahedron element.

Some problems which are actually three dimensional can be described by

only one or two independent coordinates. Such problems can be idealized by using an

axis-symmetric or ring type elements. The problem that posses axial symmetry like

pistons, storage tanks, Valves, rocket nozzles & re-entry vehicle shield fall into this

category.

The present problem inner casing also comes under the same category. So in

this problem the assume element for discritization is axisymmetric quadrilateral two

dimensional element. For discritization of problems involving curved geometry, finite

elements with curved side are useful. The ability to model curved boundaries has been

made possible by the additional of middle nodes. Finite elements with straight lines

are known as linear elements, while those with curved sides are called higher order

elements.

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5.3 TYPE OF ELEMENTS:

Often the type of elements to be used is evident from the physical problem

itself for example if the problem involves the analysis of a truss structure under a

given set of load conditions the type of elements to be used idealization is obviously

the bar or line elements. However in some cases the type of elements to be used of

idealization may not be apparent and in such cases one has to choose the type of

elements judicially. In certain problems the given body cannot be represented as an

assemblage of only one type of elements. In such cases, we may have to use two or

more types of elements of idealization.

5.3.1 SIZE OF ELEMENTS:

The size of the elements influences the convergence of the solution directly &

hence it has to be chosen with care. If the size of the element is small, the final

solution is expected to be more accurate. However, we have to remember that the use

of the elements of smaller size will also mean more computational time. Sometimes

we may have to use elements of different sizes in the same body. The size

concentration is expected compared to faraway places. In general, use a finer mesh in

that region, another characteristic related element solution is the aspect ratio of the

elements. The aspect ratio describes the shape of the elements in the assemblage of

elements, for two-dimensional elements aspect ratio is taken as the ratio of the largest

dimension of the element to the smallest dimension elements with as aspect ratio of

nearly unity generally yield best results.

5.3.2 LOCATION OF NODES:

If the body has no abrupt changes in geometry, material properties and

external conditions (like load, temperature etc.,) the body can be divided into equal

sub divisions and hence the spacing of the nodes can be uniform. On the other hand, if

there are any discontinuities in the problem nodes have to be introduced obviously at

these discontinuities.

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5.3.3 NUMBER OF ELEMENTS:

The number of elements to be chosen for idealization is related to the accuracy

desired, size of elements and the number of degrees of freedom involved although an

increase in number of elements generally mean more accurate results, for any given

problem there will be certain number of elements reaches the point shown in the

figure so significant improvement will be found. Moreover, since the use of larger

number of elements involves larger number of degrees of freedom, we may not be

able to store the resulting matrices in the available computer memory.

5.3.4 NODAL DEGREES OF FREEDOM:

The basic idea of FEA is to consider a body as composed of several elements

which are connected at specified node points. The unknown solution or the field

variable (like displacement, pressure and temperature) inside any finite element is

assumed to be given by a simple function in terms of the nodal values of the element.

The nodal displacement rotations necessary to specify the deformation of the finite

element are the degrees of freedom of element. The nodal values of the solution, also

known as nodal degree of freedom, are treated as unknowns in formulating the

systems of overall equations, the solution of the system equation (like force

equilibrium equations) gives the values of the unknown nodal degree of freedom.

Once, the nodal degree of freedom are known, the solution with in the any element

(and hence with in complete body) will also be known to us. For having the results in

terms of nodal degrees of freedom the interpolation function must be derived in terms

of nodal degree of freedom.

5.3.5 COORDINATE SYSTEM:

A local coordinate system is not that is defined for a particular element and

necessary for the entire body of structure, the coordinate system for entire body is

called as the “Global Coordinate system”. A natural coordinate system is a local

coordinate system which permits a specification of a point within the element by a set

of dimension less numbers whose magnitude never exceeds unity. The derivation of

element characteristic matrices and vectors involves the integration of the shape

45

functions or their derivative or both over the element. These integrals can be

evaluated easily if the interpolation functions are written in terms of local coordinate

system.

5.4 FORMATION OF ELEMENT CHARACTERISTIC MATRICES AND

VECTORS :

The characteristic matrices and characteristic vectors (also termed as vectors of

nodal actions) of finite elements can be derived by using any of the following

approaches:

5.4.1 DIRECT APPROACH:

In this method, direct physical reasoning is used to establish the element

properties (Characteristic matrices and vectors) in terms of pertinent variables.

5.4.2 VARIATION APPROACH:

In this method, the finite element analysis interpolated as an approximate

means for solving variation problems. Since physical and engineering problems can

be readily applied for finding their appropriate solutions. The variational approach has

been most widely used in the literature in formulating finite element equations.

A major limitation in the method is that it requires the physical or

engineering problem to be stated in variational form which may not be possible in all

cases.

5.4.3 WEIGHTED RESIDUAL APPROACH:

In this method, the element matrices and vectors are directly form the

governing differential equations of the problem without reliance on the variation

statement of the problem, this method offers the most general procedure for deriving

finite element equations and can be applied to almost all practical difference

procedures can be used.

46

They are,

a) Collocation method.

b) Sub domain collocation method.

c) Galerkin method.

d) Least squares method.

Assembly of Element Matrices and vectors and derivation of system equations

5.4.4 GENERAL APPLICATION OF THE METHOD:

Although the method has been extensively in use in the field of structural

mechanics, it has been successfully applied to solve several other types of engineering

problems like heat conduction, fluid dynamics, see page flow and electric and

magnetic fields. The general applicability of the method prompted mathematicians to

use these techniques for the solution of complicated boundary value and other

problems. The general applicability of the finite element methods can be seen by

observing the strong similarities that exist between various types of engineering

problems. For illustration, let us consider the following phenomena

1. One dimensional heat transfer

2. One dimensional fluid flow

HIGHER ORDER AND ISOPARAMETRIC ELEMENT FORMULATIONS:

Whenever the interpolations polynomial is assumed to be of order two or

more, the element is known as a “higher order element”. Thus a higher order element

can be either a complex or a multiplex element. In higher order elements, some

secondary (mid size and / or interior) nodes are introduced in addition to the primary

(Corner) nodes in order to match the number of nodal degrees of freedom with the

number of generalized coordinates in the interpolation polynomial.

47

In general, fewer higher order elements are needful to achieve the same

degree of accuracy in the final results. Although it does not reduce the computational

time, the reduction in the number of elements generally reduces the effort needed in

the preparation of data cards and hence the chances of error in the input data. The

higher order elements are especially useful in those cases where the gradient of the

filed variable is expected to vary rapidly, In these cases the simplex elements, which

approximate the gradient by a set of constant values, do not yield good results. The

combinations of greater accuracy and a reduction in the data preparation effort have

resulted in the widespread uses of higher order elements in practical applications. We

shall consider some of the popularly used higher order elements, in the chapter, some

special interpolation formulae were developed for specific applications.

Problems involving curved boundaries cannot be modeled satisfactorily by

using straight sided elements. The family of elements known as “iso parametric

elements” has been developed for this purpose. The basic idea underlying the

isoparametric elements is to use the same interpolation functions to define the element

shape or geometry as well as the field variable within the element. To derive the

isoparametric element equations; we first introduce a local a natural coordinate

system for each element shape. Then the interpolation or shape functions will have to

be expressed in terms of the natural co-ordinates.

The representation of geometry in terms of (non linear) shape functions can be

considered as a mapping procedure which transforms a regular shape like a straight

sided triangle or rectangle in local coordinates system in to a distorted shape like a

curved sided triangle or rectangle in the global Cartesian coordinate system. This

concept can be used in representing in the problem with curved sided isoparametric

elements. Today isoparametric elements are extensively used in three dimensional and

shell analysis problems. In the later part of this chapter, we shall discuss the

formulation of isoparametric elements. The aspects of numerical integration are

essential for computation with isoparametric elements is also discussed towards the

end of the chapter.

48

5.5 LIMITATIONS OF FINITE ELEMENT METHODS:

Finite element methods are extremely versatile and powerful and can enable

designers to obtain information about the behavior of complicated structures with

almost arbitrary loading. In spite of the significant advances that have been made in

developing finite element packages, the results obtained must be carefully examined

before they can be used. This point cannot be overemphasized.

The most significant limitation of finite element methods is that the accuracy

of the obtained solution is usually a function of the mesh resolution. Any regions of

highly concentrated stress, such as around loading points and supports, must be

carefully analyzed with the use of a sufficiently refined mesh. In addition, there are

some problems which are inherently singular (the stresses are theoretically infinite).

Special efforts must be made to analyze such problems.

An additional concern for any user is that because current packages can solve

so many sophisticated problems, there is a strong temptation to “solve” problems

without doing the hard work of thinking through them and understanding the

underlying mechanics and physical applications. Modern finite element packages are

powerful tools that have become increasingly indispensable to mechanical design and

analysis. However, they also make it easy for users to make big mistakes.

Obtaining solutions with finite element methods often requires substantial

amounts of computer and user time. Nevertheless, finite element packages have

become increasingly indispensable to mechanical design and analysis.

49

6. IMPLEMENTATIONS

6.1 INTRODUCTION:

The finite element method is based on representation of a body by an

assemblage of sub divisions called ‘Finite Elements’. These elements are considered

inter connected at the joint which are called ‘Nodes’. In order to approximate the

distribution of the actual displacements over each of finite elements, simple functions

are chosen. Such assumed functions are called displacement functions. The unknown

magnitudes of these displacement functions are the displacements at the nodes.

The displacement model/functions can be expressed in various simple forms

such as polynomials and trigonometric functions since polynomials offer ease in

mathematical manipulations, they have been employed commonly in finite element

applications.

6.2 THEORETICAL ANALYSIS

6.2.1 LOAD CASES:

The following different load cases considered for designing radome:

Case (i) Water head pressure acting on Radome (due to under water)

Water head Pressure acting on radome (p) = ρgh

ρ = Density of sea water at average temperature of 3.880C with Salinity* of

34.78% = 10270 kg/m3

h = Water head (depth at which object is immersed) = 300m (operational)

= 450m (design)

p = 1,027 x 9.81 x 450m = 45.337 bar

Case (ii) Pressure acting due to Radome platform traveling under water at speed

of 25 knots(12.866m/s)

Pressure acting on radome (p) = Cd ρ V2/2

Where Cd = 0.5 (for the given radome shape)

ρ = 1,027 Kg/m3 (water density)

V = 12.866 m/sec

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p = 42500 kgf/m2 = 4.2 bar

Case (iii) Pressure acting due to wind speed @ 240 kmph (when object

exposed to wind)

Wind Pressure acting on radome (p) = Cd ρ V2/2

Where Cd = 0.5 (for the given radome shape)

ρ = 1.225 Kg/m3 (air density)

V = 66.66 m/sec

p = 1360.83 kgf/m2 = 0.1335 bar

From the above three load cases; water head pressure acting on radome (due to under

water) is predominant. Hence radome is designed to withstand static water head

pressure of 45.337 bars.

( * The salt content of seawater is termed as its ‘salinity’ and measure of total quantity

of all the dissolved substances in a sample of seawater.)

FE ANALYSIS:

ANSYS Ver. XII is used for finite element Analysis of the radome. The

geometric model is generated as per the drawing. The model is shown at Appendix.

The radome is modeled as composite shell element (SHELL 91) suitable fixed

constraints are applied. The FE model is shown at Appendix. The Water Pressure

acting on the surface of the radome is calculated by the emperical formula and is

applied on the whole surface of the radome. 16 layers of 0.75 mm are taken.

Following assumptions are made to analyze the model.

1. Water pressure acting on the periphery of the radome.

2. Material properties taken for E. glass / Epoxy fiber reinforced plastic with fiber -

orientation of O and 900 deg.

3. Mounting flange of radome of assumed rigid body.

51

The following material properties are extracted from literature & applied to the model

Materials Density (g/cm3) Tensile Strength (MPa) Young modulus (GPa)

E-Glass 2.55 2000 80

N (Poisson’s Ratio) 0.29

6.3 ANSYS:

The ANSYS computer software is a large-scale multipurpose finite element

method program that may be used for solving several classes of engineering

problems. The analysis capabilities of ANSYS include the ability to solve static and

dynamic structural analyses , steady state and transient problems, mode frequency and

buckling Eigen value problems, static or time varying magnetic analyses and various

types of field and coupled applications. The program contains many special features

which allow non liberties or secondary effects tube included in the solution such as,

plasticity, large strain, hyper elasticity, creep; swelling, large deflection contact stress

stiffening temperature dependency, material anisotropy and radiation. As ANSYS was

developed, other special capabilities such as, surface structuring, sub modeling,

random vibration, piezo-electrics, coupled field analysis and design optimization was

added to the program. These capabilities contribute further to make ANSYS a

multipurpose analysis tool for varied engineering discipline.

The ANSYS program has been in commercial use since 1970 and it is used

extensively in the aerospace, automotive, construction, electronics, energy, service,

manufacturing, nuclear , oil and steel industries. In addition, many consulting firms

and hundreds of universities use ANSYS for analysis, research and educational use.

6.3.1 PROGRAM OVERVIEW:

The ANSYS element library contains more than 60 elements for static and dynamic

analysis. Over 20 for the heat transform analysis and include numerous magnetic field

and special purpose elements. These varieties of elements are analyzed in the ANSYS

52

program as 3-D shells and non linear problems including contact (interfaces) and

cables.

Analysis of anything in ANSYS has to go through three main steps. They are

Preprocessor

Solution

Postprocessor

The inputs for an ANSYS analysis in prepared using preprocessor .The

generation preprocessor contains powerful solid modeling and mesh generation

capabilities, and is also used to define all other analysis data (geometry) properties

like real constant , material properties , constraints ,load manipulation of analysis

data. Parametric input, used files, macros and extension on line documentation and

graphics capability are available throughout the ANSYS program including

isoperimetric. Perspective section, edge a hidden line displays of 3-D structures. X-y

graphic of input quantities and result and contour displays of solution results. A

graphical user interface to guide new users through the learn 701-15

A static analysis calculation the effects of loads on the structure while ignoring

the inertia and damping effects such as those caused by time varying loads, but it can

accomplish steady inertia load and static equivalent loads. Static analysis is used to

dart ermine. The displacements, stresses, strains and forces in the structures or

component due to loads that do not induce significant inertia and damping effects

steady loading and response conditions are assumed.

The kinds of loading that can be applied in a static analysis include:

Externally applied pressures and forces.

Steady state internal forces (such a gravitational or rotational velocity\

Imposed (non-zero) displacement.

Temperature (for thermal strain)

Fluencies (for nuclear swelling)

A static analysis can be either linear or non-linear. In our present work we are going

to consider linear static analysis.

The procedure for static analysis consists of three main steps:

Building the model obtaining the solution

What is a working plane ?

53

Although your cursor appears as a point on your screen it can be represents a

time through space, normal to the screen. In order to be able to pick a point with your

cursor, you first need to define to imaginary plane that when intersected by normal

line of your cursor, will yield a crippling point in space. This imaginary plane is

called a working plane. Another work to think of the intersection between your cursor

and your working plane is, picture your cursor as a point moves around on your

working plane. Working plane, then acts as a “tablet” on which you write with your

cursor.

MODEL GENERATION:

The ultimate purpose of a F.E.A is to recreate mathematically the behavior of

an actual engineering system. In other words, the analysis must be accurate

mathematical model of a physical prototype. In the bookend this model comprises all

the modes, elements, material properties, real constants, boundary conditions and

other feature that are used to respective the physical system.

The ANSYS program offers you the following approaches to model

Creating a solid model

Using direct generation

Importing a model created in a computer aided design (CAD) system.

6.4MESHING:

ADVANCED MESHING TECHNIQUES:

Mesh generation refers to the generation of nodes and elemental connectivity. It also

includes the automation numbering of nodes and elements based on a minimal amount

of user supplied data.

Mesh generation may be classified into

Semi - Automatic

Fully – Automatic

Semi – automatic:-

The models are sometimes referred to a “interactive mesh generation methods” to

emphasize properly that they require the analysis interaction with the mesh generator

to create the mesh. It can be divided into 2 groups:

Wire – frame and surface based groups.

Solid modelling based group.

54

6.4.1 FULLY AUTOMATIC MESH GENERATION:-

The methods are primarily designed based on the solid modeling theory achieve full

Automation and operate on solid models only a full automatic mesh generation can be

invoked at the users level by using a command such as “mesh solid attitude. Where

mesh solid is the mesh attributes and “d” is a digitize that identifies the solid to be

meshed this implies at mesh automation limits user interaction to defining the solid

and specifying mesh density parameters.

6.4.2 MESH GENERATION USING 2D ELEMENTS:

Majority of the available mesh generation techniques for 2D can be broadly classified

into 6 distinct categories:

1. Topology decomposition approach : The geometry is first defined terms of

vertices and edges. It is decomposed into triangular elements by connecting

the vertices. In the approach, there is no control on the element size and shape

as it is decided by the geometry itself.

2. Node connection approach: The boundary of the geometry is defined and then

nodes are added on the boundary at suitable intervals. The interior nodes are

generated to satisfy mesh penalty requirements. The nodes are then connected

to form the element. Critical comparison of the available mesh generation

methods and choosier the best out of them is a difficult task. Several mesh

generation methods.

6.4.3 MESH GENERATION USING 3-D ELEMENTS :

A generated mesh M must satisfy to following requirements:

Mesh should be topologically and geometrically correct: There should be no

intersecting elements, and the elements should be topologically correct.

The quality of mesh should be as high as possible: M should contain as fel badly

element as pliable. The boundary nodes of M should be positioned exactly on the

edges and faces of the model.

Mesh should be boundary conforming: There should be no element intersecting the

boundary of the object, and there should be no holes in M in the limit of mesh

refinement, M should match the geometric model exactly. With reference to the

second requirement,

55

The quality of a mesh is measured by how will the results of the analysis agree

with an exact, analytical solution (assuming that the FE solution coverage to the exact

solution).

The Quality of the mesh depends upon its density and the shape the elements. For

instance, it is well known that, for triangular elements. Obtuse angles degrade the

accuracy of results. Thus, as few triangles possible with obtuse angles should be

created. Further, the mesh density should be higher where the gradient of the function

being approximated in the geometry is not simplified when a mesh is derived from a

model. It has been shown has been shown that even minor simplification of the

geometry can lead to large error, and therefore this is unacceptable.

Mesh – generation methods for 3D models usually derive a mesh from a B-rep of

the model. Most of these methods are either based on tetrahedrization algorithms for

point sets, or on the cutting of elements from a B-rep

6.4.4 MESHING YOUR SOLID MODEL:

How to mesh your solid model:-

The procedure for generating a mesh of nodes and elements consist of 3 main

steps

1. Set the element attributes

2. Set mesh controls (optional), Ansys offers a large no. of mesh

controls, which you can choose from to suit your needs.

3. Generating the mesh.

The second step, setting mesh controls, is not always necessary, because the

default mesh controls are appropriate for many models. If no controls are used, the

program will use the default settings to produce a free mesh as an alternative, we can

use the smart size feature to produce a better quality for mesh before meshing the

model, and even before building the model. It is important to think about whether a

free mapped mesh appropriate feature analysis.

Free mesh (Automatic):

Coordinate In this type of generation the user does not have to specify in each

node point and element consecutively i.e. no restrictions in terms of element shapes,

are no specified pattern applied to it. This method of generation helps us Faso Fe

meshing and needs only enclosed areas to generate elements.

56

Mapped mesh (user defined):

The user manually controls the mesh generation like shape, size etc i.e.

restricted on terms of the elements shape it contains and the pattern of the mesh. A

mapped area contains either only contains either only quadrilateral or only triangular

elements. While mapped volume only contains hexahedron elements. In addition a

mapped mesh typically has a regular pattern, with obvious row of elements. If this

type of mesh is desired, the user must build the geometry that has a series of fairly

regular volumes and/or area.

6.5 APPROACH TO ANALYSIS:

6.5.1 STATIC ANALYSIS:

ANSYS has been used for the finite element analysis of the radome.

Linear static analysis is carried out to find out the structural response of the model.

Procedure of stress analysis of submarine radome in ANSYS:

The following steps are taken in the analysis

Pre processor:

Fileimportselect Radome IGES fileOK

Preferences→ StructuralOK

Element typeadd/edit/del add

1) Shell elastic 4node63OK

Real constantAdd/edit/deleteadd

Shell thickness 3mm

Material propertiesmaterial modelstructurallinearelasticorthotropic

E1 (Young’s Modules in x-dir) 80Gpa

E2 (Young’s Modules in y-dir) 75Gpa

E3 (Young’s Modules in z-dir) 80Gpa

57

G x y (Shear modules in xy plane) 5Gpa

G x z (Shear modules in xz plane) 5Gpa

G yz (Shear modules in yz plane) 5Gpa

Nu x y (Poissons Ratio) 0.30

Nu y z (Poissons Ratio) 0.30

Nu z x (Poissons Ratio) 0.30

Density =2540ok

Meshing Mesh toolok

Linessetselect all lineselement edge length=2ok

Change mesh options to linesselect linesclick meshok

Setshellareasselect areasmeshok

Loads →Displacement →Apply → on nodes→ select the nodes →all DOF →click

ok

Pressure On nodesselect the nodeok

P=45.337x10^5 Pa

Solution:

SolveCurrent LSok

Solution is done

General post processor:

Plot results counter plot Nodal solution Deformation USUM

deformed+ undeformed shape OKOK

58

Figure 6.1 Nodal solution def+ undeformed

59

Figure 6.2 Nodal solution

Figure 6.3 Pressure

60

Figure 6.4 Von misses stress

Figure 6.5 Graph SXY- displacement

61

Figure 6.6 Vector plot predefined

Figure 6.7 Von misses graph

62

6.6MODAL ANALYSIS :

Modal Analysis is done to find the natural frequency of the radome. The

natural frequency of the radome should be at least four times the excitation

frequency so that resonance does not occur.

Procedure of Modal Analysis of Fuselage in ANSYS:

The following steps are taken in the modal analysis:

Pre processor:

Fileimportselect Radome IGES fileOK Preferences: structural

Element type: 1) Shell elastic-4 node63

Real constant Add/edit/delete Shell thickness 3 mm

Material propertiesmaterial modelsstructuralorthotropic

E1 (Young’s Modules in x-dir) 80Gpa

E2 (Young’s Modules in y-dir) 75Gpa

E3 (Young’s Modules in z-dir) 80Gpa

G x y (Shear modules in xy plane) 5Gpa

G x z (Shear modules in xz plane) 5Gpa

G yz (Shear modules in yz plane) 5Gpa

Nu x y (Poissons Ratio) 0.30

63

Nu y z (Poissons Ratio) 0.30

Nu z x (Poissons Ratio) 0.30

Select Density =2540kg/m3

Sections:

Meshing

Mesh attributes Select SHELLselect areasOK,

Constraining the model

LoadDisplacementApplyOn nodesall DOF on radome

base

Solution:

Analysis Type –Modal

Analysis optionsselect Block lanczosok

Frequency-0-10000

No. of modes to extract=5ok

Solution

SolveCurrent LSok

Solution is done

General post processor:

Read resultsby pickselect modeok

Plot resultsCounter plotNodal solutionDeformation

in USUMOK

64

Figure6.8 Modal 1

65

Figure6.8 Modal 2

Figure6.9 Modal 3

66

Figure6.10 Modal 4

Figure6.11 Modal 5

67

Figure6.12 Modal analysis

7. FABRICATION METHODS FOR RADOMES

The selection of a manufacturing method for a given Radome design

may be based on a number of factors including the Radome performance requirements

and the materials of construction. For example selection of a fabrication method for a

Radome often starts by the consideration of Vacuum bag or Autoclave molding using

glass fabric reinforcement. Frequency requirements for maintaining uniform electrical

properties in the Radome wall might eliminate the less expensive fabrication methods

and dictate a filament winding approach whereby this control is more readily

accomplished.

7.1 FILAMENT WINDING:

A major advantage of the filament winding process is that it lends itself

to automated equipment. Even more important advantage is that it allows very close

control of the resin to glass ratio, which results in a uniform dielectric constant

throughout the radome. The ability to produce on a repeatable basis a radome wall of

68

known dielectric constant makes it possible to machine or grind the radome wall to a

given physical dimension thereby eliminating in many cases, the necessity for

measurement of electrical wall thickness during the final grinding operation. Also the

electrical testing and correction time required for the Radome is reduced when a

uniform electrical wall is present. In addition, the filament winding process allows the

orientation of he fibers in the primary directions of load, thereby providing structural

design flexibility not possible with fabric reinforcements. The glass reinforcement

plastics normally exhibit dielectric constants of the order of 3.5 to 4.5 at X-band

frequency.

7.2 VACUUM BAG MOULDING:

Vacuum bag molding “wet lay-up” of glass reinforced plastic radomes is

one of the earliest techniques employed. This technique involves laying down dry

glass fabric, which is wet with the liquid resin during the lay-up operation. After the

desired thickness has been obtained, a plastic film bag is placed over the lay-up,

sealed to the mould and connected to the vacuum source, which evacuates the air

between the plastic bag and the lay-up. The major advantages of this fabrication

process are its relatively low cost and high quality laminate, which can be produced

by skilled workers.

The removal of excessive resin and air from the aly-up is performed by

squeezing or wiping operation using a rubber soft plastic tool. This squeeze operation

not the vacuum bag pressure, determines the final thickness and resin content at

laminate.

7.3 AUTOCLAVE MOULDING :

The Autoclave molding is similar to vacuum bag molding in that the

lay-up is sealed in plastic bag, which is evacuated by a vacuum pump prior to

application of the autoclave pressure. Autoclave molding of Radome is normally used

with pre-preg materials, which do not allow squeezing to remove entrapped air, and

with resin systems, which generate reaction products during cure. Unlike the vacuum

bag process, the pre-preg lay-up is normally followed with a perforated plastic film or

69

a glass fabric which been treated to prevent adhesion of the resin. This apparatus is

followed by a lay-up dry bleeder material such as glass or other type fabrics which

absorb the excess resin or reaction products or both which are eliminated from the

part during the cure.

Most Autoclave used in the fiberglass plastic industry have operating

pressures between 100 and 200 psi and temperature capabilities upward to 500oF

resin systems such as diallylphthalate and most epoxies may be adequately. Systems

such as silicones, phenolics, polyamides and polybenzidazoles are frequently molded

at pressures of the order of 200 psi. The higher pressure normally yields superior

composites, provided a more reliable manufacturing process and assures greater

reproducibility from part to part.

7.4 MATCHED DIE MOULDING:

The matched die molding involves the use of male and female dies and

offers the advantage of yielding a part having near finished dimension. While this

method has been used for producing reinforced plastics radomes, its use for the

production of the large manned aircraft radomes has been limited. The major factor

which limits the use of this fabrication method is large size normally associated with

aircraft radomes and the resulting cost involved in building precision dies and the

large high capacity presses required to mould a part of this size.

The fabrication technique involves fitting knitted glass socks over a

male mould. As many as 25 glass socks may be used to achieve fiberglass content of

the finished Radome. After the socks have been fixed in place, the female mould is

lowered onto the male mould, located and fixed in place. The cavity between the male

and female mould containing the glass socks is evacuated by use of vacuum pumps to

a vacuum pressure of approximately 25" of mercury and epoxy resin is pumped into

the cavity under pressure of approximately 40 psi. The resin filling operation is

reported to take approximately 4 hrs. After the cavity has been completely filled with

resin, the mould temperature is raised to 150oF for 16 hrs to affect the cure. The

mould is then coded and the part is removed for the post cure.

70

8. RESULTS & DISCUSSIONS

1. Displacement contours and deformed shape of the radome enclosed in

figure6.1. The maximum resultant deformation of 0.2547mm is observed at

the Node No. 409, which is the top most point of the radome.

2. Stress contours Sxy enclosed in figure6.5. From Stress contours found the

maximum Sxy value is 70.398 MPa(Compressive) for layer no.1. The stresses

induced due to water head pressure are within the safe limits.

3. The modal analysis values are taken from the analysis at sub step 5 we have a

frequency of 5.88 cycles / sec and a deflection of 1.763 mm.

4. The natural frequency of the submarine is 5-33 cycles /sec. Hence the obtained

value is about 4 times more than natural frequency of the submarine hence it is

safe.

71

9. CONCLUSIONS & FUTURE WORK

1. The experimental test results and theoretical values are in close agreement

with each other.

2. Deformation and stress values obtained from FE analysis are within the safe

limits.

3. Conducting pressure test on radome verified the design aspects and validated

the FE analysis.

4. To improve the electrical performance of the radome without compromising

the mechanical properties Hybrid composites to be considered in futuristic

radome development.

72

REFERENCES

Dr. Gates PJ & Lynn NM “Ships, Submarines & the Sea” Vol.2, Brassey’s

(UK), 1990.

Bryan Harris “Engineering Composite Materials” 2nd edition, 1999.

Sun CT “Strength Analysis of Unidirectional Composite Laminates”

Comprehensive Composite Materials, Vol.1, Elsevier, 2000.

Robert M Jones “Mechanics of Composite Materials” Mc Graw-Hill Book

Company, 1975.

Timoshenko “Theory of Plates & Shells”.

73

Stephen P Timoshenko, James M Gere “Theory of Elastic Stability” 2nd edition,

Mc Graw-Hill Book Company, 1963.

ANSYS “ANSYS Manuals”, version 12.0

S Ramamrutham “Strength of Materials”.

Prof. P.N. Joubert “Some aspects of Submarine Design”, Australian government

department of defense.

N.Maerz “Experimental non-destructive testing of FRP materials”, University

of Missouri.

Gajic & Zoran “Modern systems engineering”

J. Hall “Radar aids to navigation”

Cady, Karelitz and Turner “Radar scanners and Radomes”

Dennis J. Kozakoff “Analysis of Radome-Enclosed antennas”

Karelitz MB “Submarine Radomes”

Daniel Sjoberg and Mats Gustafsson “Realization of a matching region between a

radome and a ground plane”

www.encyclopedia.com/doc/10233-radome.html

www.wikipedia.com

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