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A Project Report on

“STRESS ANALYSIS OF THE LANDING GEAR-

WELL BEAMS AND DAMAGE CALCULATION

DUE TO LANDING CYCLES”

Submitted to

VISVESVARAYA TECHNOLOGICAL UNIVERSITY

BELGAUM -590 018

In Partial Fulfillment Of The Requirements For The Award Of Degree Of

MASTER OF TECHNOLOGY

In

MACHINE DESIGN

By

KARTHIK GOUD R V

USN: 1OX12MMD06

Under the guidance of

Mr. NANDISH R V

Asst. Prof, Mechanical Department

The Oxford College Of Engineering,

DEPARTMENT OF MECHANICAL ENGINEERING

THE OXFORD COLLEGE OF ENGINEERING

BOMMANAHALLI, BANGALORE -560 068

2013-2014

ISSN: 2321-3051

CERTIFICATE OF PUBLICATION

This is to certify that Karthik Goud R V has

published his/her research work entitled

“STRESS ANALYSIS OF THE LANDING GEAR-

WELL BEAMS AND DAMAGE CALCULATION DUE

TO LANDING CYCLES” in International Journal

of Research in Aeronautical and Mechanical

Engineering

Editor-in-chief, IJRAME volume 2 issue 5, May 2014

ii

ABSTRACT

Landing gear is a structure, which supports the aircraft on the ground. Landing

gear structure experiences the load during take-off and landing of the aircraft. These loads

are transferred to the airframe through landing gear beams. Wing box near the root will

have cut-out at the bottom surface to accommodate the retraction of the landing gears.

Landing loads are absorbed by the landing gears and diffused to the larger area of the

wing through connecting members.

In the current project two landing gear beams with a root rib are considered for the

analysis. On either sides of the cut-out region landing gear beams are used to transfer the

landing load from landing gears to the wing and fuselage structure. Landing gear beams

are in the span wise direction of the wing.

Linear static analysis of the beams along with the root rib will be carried out to

identify the fatigue critical location in the structure. Local analysis will be carried to

capture the stress concentration and stress distribution near the high stress location. It is

very rare that these structural members will fail by static over load. Due fluctuating loads

during the service fatigue cracks will get initiated at the high tensile stress location.

Landing gear beams will experience constant amplitude load cycles because of every

landing during service. Fatigue life to crack initiation will be calculated using Miner’s

rule based on the S-N data of the material being used.

iii

ACKNOWLEDGEMENT

Project work is a job of great enormity and it can be accomplished by an

individual all by themselves. Eventually I am grateful to a number of individuals whose

professional guidance, assistance and encouragement have made it a pleasant endeavour

to present this project.

I have a great pleasure in expressing my deep sense of gratitude to the Founder

Chairman SRI. S. NARASA RAJU and to the Executive Director SRI. S.N.V.L.

NARSIMHA RAJU for having provided me with a great infrastructure and well-

furnished labs.

I take this opportunity to express my profound gratitude to the Principal Dr.

NAGARAJ. R for his constant support and encouragement.

I am grateful to the Head of the Department Dr. T NAGESWARA RAO for his

unfailing encouragement and suggestions given to me in the course of the project.

Guidance and deadlines play a very important role in successful project work, I

also convey my gratitude to guide Mr. NANDISH R V, Asst. Professor, Department of

Mechanical engineering.

My sense of gratitude to teaching and non-teaching staff for their encouragement

and help, which was my foundation and I treasure them for my future endeavors.

Finally, I take this opportunity to extend my deep appreciation to my family and

friends; for all that they supported me for the successful completion of my dissertation.

KARTHIK GOUD R V

[USN-1OX12MMD06]

iv

CONTENTS

DECLARATION i

ABSTRACT ii

ACKNOWLEDGEMENT iii

CONTENTS iv

LIST OF FIGURES vi

LIST OF TABLES vii

CHAPTER 1: INTRODUCTION 01

1.1 INTRODUCTION TO AIRCRAFT 01

1.2 PARTS OF AIRCRAFT 01

1.3 COMPONENTS OF WING 07

1.4 STRESSES ON AIRCRAFT 10

1.5 TYPES OF STRUCTURAL STRESS 11

1.6 FATIGUE LIFE 13

1.7 COMPUTATIONAL METHOD 17

CHAPTER 2: LITERATURE SURVEY 19

CHAPTER 3: FINENITE ELEMENT ANALYSIS 28

3.1 FINITE ELEMENT ANALYSIS OF

LANDING GEAR WELL BEAMS 28

3.2 PROCESS FLOW OF FINITE ELEMENT ANALYSI 30

CHAPTER 4: MATERIAL PROPERTIES, LOAD CALCULATION

AND BOUNDARY CONDITION 32

4.1 CHARACTERISTICS OF ALUMINUM 32

v

4.2 LOAD CALCULATION 34

CHAPTER 5: LINEAR STATIC ANALYSIS OF LANDING

GEAR WELL BEAMS 36

5.1 GLOBAL ANALYSIS 37

CHAPTER 6: THEORETICAL VALIDATION 42

6.1 MAXIMUM STRESS IN PLATE WITH HOLE WITH ONE END

FIXED 42

CHAPTER 7: FATIGUE ANALYSIS OF LANDING GEAR WELL BEAMS 46

7.1 CALCULATE MAX STRESS FOR DIFFERENT RANGE 48

7.2 CALCULATION FOR STRESS AND STRESS RATIO 49

CONCLUSION 55

SCOPE FOR FUTURE WORK 56

REFERENCE 57

APPENDIX 59

vi

LIST OF FIGURES

FIGURE NO FIGURE NAME PAGE NO

Fig 1.1 Fuselage and its parts 02

Fig 1.2 Nomenclature of wing 03

Fig 1.3 Parts of tail of aircraft 04

Fig 1.4 Engine of transport aircraft 05

Fig 1.5 Landing gear of typical aircraft 06

Fig 1.6 Components of Wing 07

Fig 1.7 Spar 08

Fig 1.8 Ribs 10

Fig 1.9 The five stresses that may act on-

an aircraft and its parts. 12

Fig 1.10 S N curve 14

Fig 3.1 Process Flow of FEA 31

Fig 4.1 Basic dimension of aircraft 34

Fig 4.2 Meshing and Boundary Condition-

of landing gear well beams. 35

Fig 5.1 Landing Gear beam Catia Model. 38

Fig 5.2 Two Dimensional Model of LG Beams. 38

Fig 5.3 Complete Meshed Model. 39

Fig 5.4 Loaded and Constrained model 39

Fig 5.5 Output of Stress Analysis. 40

Fig 5.6 Location of Maximum Stress in LG beams. 40

Fig 5.7 Elemental values near Maximum Stress Location 41

Fig 6.1 Plate with Hole for Local Analysis 42

Fig 6.2 Mesh and Boundary Condition -

applied to Local Model. 43

Fig 6.3 Local Analysis 44

Fig 6.4 Stress Concentration Factor for Plate with Hole 44

Fig 7.1 Graph for number cycles to failure. 52

vii

LIST OF TABLES

TABLE NO TABLE NAME PAGE NO

Table 4.1 Aluminium Alloy 2024 properties 33

Table 7.1 Variable Load Spectrum for Typical Aircraft 47

Table 7.2 No of cycles and stress ratio 53

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CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION TO AIRCRAFT

When designing an aircraft, it’s all about discovering the right proportion of the

weight of the vehicle and payload. It needs to be robust and rigid enough to withstand the

uncommon circumstances in which it has to operate. Durability is an important factor.

Also, if a part fails, it doesn’t necessarily result in failure of the whole aircraft. The main

sections of an aircraft, the fuselage, tail and wing, gives its external shape. The load

carrying members of the main parts, those subjected to major forces, are called the

airframe. The airframe is what remains if all equipment and systems are disassembled.

In today`s modern aircrafts, the skin plays an vital role in carrying loads. Tension

can only be supported by sheet metals. But if the sheet is folded, it quickly does have the

ability to withstand compressive loads. Stiffeners can be used for that. The combination

of skin and stiffeners is called stringers. An efficient way of using sheet metal skin is in a

thin-walled cylinder, known as monocoque structure. A cylinder with holes, for windows

and doors, is called a semi-monocoque structure. Stiffeners cannot be made from sheet

metal. We can use rolling or drawing process for sheet metal. Usually stiffeners are

attached to the skin. Skin and stiffeners are manufactured from one single solid piece of

material. It is also possible to make some kind of a sandwich structure, in which the skin

has a high rigidity due to its special structure.

1.2 PARTS OF AIRCRAFT

The main parts of an aircraft are

1. Fuselage

2. Wing

3. Tail

4. Engine

5. Landing gear

1.2.1 FUSELAGE

The fuselage should carry the load of passenger and goods, and it is the main

structure to which all other parts are interlinked. It must be able to withstand, torsional

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loads, bending moments and pressurization. The structural robustness and rigidity of the

fuselage must be high enough to withstand the loads. The weight of the aircraft structure

should be as minimum as possible. The shape of passenger aircraft is cylindrical with

tapered nose section. The semi-monocoque construction, which is virtually standard in all

modern aircraft, consists of a stressed skin with added stringers to prevent buckling,

attached to hoop-shaped frames.

The fuselage also has member’s perpendicular to the skin, that supports it and

helps keep its shape. These supports are called frames if they are open or ring-shaped or

bulkheads if they are closed. Doors and window hole in the cylindrical shape fuselage are

called cutouts. They are usually unsuitable to carry many of the loads that are present on

the surrounding structure. Cut-outs are reinforced to withstand the direct loads carrying

on the aircraft. Different aircraft have different doors and window sizes depending on the

necessity. It is therefore necessary for them to transmit some of the loads from the frames

and stringers.

Fig 1.1: Fuselage and its parts.

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1.2.2 WING

The main function of wing is to provide necessary lift for the aircraft. Wing can be

divided into two main parts, First part is internal which consists of spars, ribs and

stringers and second part is skin.

The main aerofoil shape of the wing is given by ribs. Wing consists of control

surfaces, flaps and engines. Presence of ribs provides additional strength, rigidity,

prevents buckling and also separate fuel tanks in the wing. There are many types of ribs,

they are form ribs, plate type ribs, truss ribs, forged ribs, milled ribs and closed ribs.

Stringers run in length wise direction of the wing. Resist bending and axial loads along

with the skin .Divide the skin into small panels and thereby increase its buckling and

failing stresses. Act with the skin in resisting axial loads caused by pressurization.

Spars give the support needed for ribs. These are beams with cross-section usually

of I section. Most of the load is carried by the spars. These are heavily loaded part in the

aircraft structure. More force is acting at the root than at the tip of the wing. Shear force

and bending moment are the major force acting on the spar because it will deflect

upwards due to load acting on wing. Wing undergoes not only bending but also twisting

due to aerodynamic forces acting on it. In order to prevent twisting second spar beam is

introduced. Most of the modern aircraft use torsion box structure which comprises of spar

and strengthened skin. This structure resists both bending and twisting.

Fig 1.2: Nomenclature of wing

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1.2.3 TAIL

The main function of the tail is to provide control and stability of the aircraft. The

ability by which aircraft returns to its original position is called stability. Stability and

control has to be achieved in three directions i.e. longitudinal, lateral and vertical. Aircraft

uses three manoeuvres those are yaw, pitch and roll. Stability for yaw is provided by fin.

Rudder is deflected when aircraft needs to yaw. Stability in pitch is provided by tail

plane. When aircraft needs to climb or descend, rudders are moved. Whenever aircraft

speed is changed, elevator position is changed accordingly.

Fig 1.3: Parts of tail of aircraft

1.2.4 ENGINE

Engines can be of many types like turbo fan, piston engine, turbo prop and ram jet

type. Most transport aircraft use turbo jet engine as they provide high trust. Most engines

are positioned externally, leaving fuselage completely to carry payloads. They can be

wing or rear positioned or both. If the engine is mounted closer to the fuselage more noise

is generated. Transport aircraft which use twin or multi engine must be mounted on the

wing. While for combat aircraft engine can be rear mounted. A turbojet is a type of gas

turbine engine that was originally developed for military fighters during World War II. A

turbojet is the simplest of all aircraft gas turbines. It consists of a compressor to draw air

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in and compress it, a combustion section where fuel is added and ignited, one or more

turbines that extract power from the expanding exhaust gases to drive the compressor, and

an exhaust nozzle that accelerates the exhaust gases out the back of the engine to create

thrust. When turbojets were introduced, the top speed of fighter aircraft equipped with

them was at least 100 miles per hour faster than competing piston-driven aircraft. In the

years after the war, the drawbacks of the turbojet gradually became apparent. Below

about Mach 2, turbojets are very fuel inefficient and create tremendous amounts of noise.

Early designs also respond very slowly to power changes, a fact that killed many

experienced pilots when they attempted the transition to jets. These drawbacks eventually

led to the downfall of the pure turbojet, and only a handful of types are still in production.

The last airliner that used turbojets was the Concorde, whose Mach 2 airspeed permitted

the engine to be highly efficient.

Fig 1.4: Engine of transport aircraft

1.2.5 LANDING GEAR

Landing gear supports aircraft while it is on ground, while takeoff and landing.

For fast aircraft retractable landing gear is used to reduce drag. Aircraft landing gear

include wheels along with shock absorber. In retractable gear system the space where

wheels are stowed is called wheel wells. The larger the aircraft more wheels are added to

the landing gear. The position of landing gear depends on design, type and load of

aircraft. Some landing gear is mounted on wing and some under fuselage. Most of them

are mounted on wing.

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Multiple redundancies are usually provided to prevent a single failure from failing

the entire landing gear extension process. Whether electrically or hydraulically operated,

the landing gear can usually be powered from multiple sources. In case the power system

fails, an emergency extension system is always available. This may take the form of a

manually operated crank or pump, or a mechanical free-fall mechanism which disengages

the uplocks and allows the landing gear to fall due to gravity. Some high-performance

aircraft may even feature a pressurized-nitrogen back-up system.

Malfunctions or human errors (or a combination of these) related to retractable

landing gear have been the cause of numerous accidents and incidents throughout aviation

history. Distraction and preoccupation during the landing sequence played a prominent

role in the approximately 100 gear-up landing incidents that occurred each year in the

United States between 1998 and 2003. A gear-up landing incident, also known as a belly

landing, is an accident that may result from the pilot simply forgetting, or failing, to lower

the landing gear before landing or a mechanical malfunction that does not allow the

landing gear to be lowered. Although rarely fatal, a gear-up landing is very expensive, as

it causes massive airframe damage. For propeller driven aircraft it almost always requires

a complete rebuild of engines because the propellers strike the ground and suffer a sudden

stoppage if they are running during the impact. Many aircraft between the wars – at the

time when retractable gear was becoming commonplace – were deliberately designed to

allow the bottom of the wheels to protrude below the fuselage even when retracted to

reduce the damage caused if the pilot forgot to extend the landing gear or in case the

plane was shot down and forced to crash-land.

Fig 1.5: Landing gear of typical aircraft

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1.3 COMPONENTS OF WING:

Fig 1.6: Components of Wing

Main structural parts of wing:

1. Spar

2. Stringer

3. Ribs

1.3.1 SPAR: The main structural part of wing is spar. It is positioned along

lengthwise direction of wing and perpendicular to fuselage. Weight of wing and flight

loads is carried by spar. There may be one or more spars which depend on design of

aircraft. While single spar carries majority of load. While aircraft is in flight the load is

acting on skin. The load acting on skin is transferred to ribs and then to spar. Most wing

as two spars one is front and other rear spar. Front spar is located at the leading edge and

rear spar is located at trailing edge. Earlier spars are made of wood , but in modern

aircraft spar is made from metal. Spar is build by joining by many small length beams

attached together to provide structural strength and rigidity.

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Fig 1.7: Spar

1.3.2 STRINGER:

Stringer or longeron or stiffener is thin metal strip fastened to skin. In wings

stringer run span wise and are attached between ribs. The basic function of stringer is to

transfer loads to ribs and then to spars. They resist bending and axial loads. These divide

the skin into small blocks, thus increasing the buckling strength. Stringer is not attached

to any parts other than skin. On larger aircraft stringer is more common in spite of

complex to analyze. In aircraft construction, a longeron, or stringer or stiffener is a thin

strip of material to which the skin of the aircraft is fastened. In the fuselage, stringers are

attached to formers (also called frames) and run in the longitudinal direction of the

aircraft. They are primarily responsible for transferring the aerodynamic loads acting on

the skin onto the frames and formers. In the wings or horizontal stabilizer, longerons run

spanwise and attach between the ribs. The primary function here also is to transfer the

bending loads acting on the wings onto the ribs and spar.

Sometimes the terms "longeron" and "stringer" are used interchangeably.

Historically, though, there is a subtle difference between the two terms. If the longitudinal

members in a fuselage are few in number and run all along the fuselage length (usually 4

to 8), then they are called "longerons". The longeron system also requires that the

fuselage frames be closely spaced (about every 4 to 6 in or 10 to 15 cm). If the

longitudinal members are numerous (usually 50 to 100) and are placed just between two

formers/frames, then they are called "stringers". In the stringer system the longitudinal

members are smaller and the frames are spaced farther apart (about 15 to 20 in or 38 to

51 cm). Generally, longerons are of larger cross-section when compared to stringers. On

large modern aircraft the stringer system is more common because it is more weight-

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efficient, despite being more complex to construct and analyze. Some aircraft use a

combination of both stringers and longerons.

Longerons often carry larger loads than stringers and also help to transfer skin

loads to internal structure. Longerons nearly always attach to frames or ribs. Stringers

often are not attached to anything but the skin, where they carry a portion of the fuselage

bending moment through axial loading. It is not uncommon to have a mixture of

longerons and stringers in the same major structural component.

1.3.3 RIBS:

In an aircraft, ribs are forming elements of the structure of a wing, especially in

traditional construction. By analogy with the anatomical definition of "rib", the ribs attach

to the main spar, and by being repeated at frequent intervals, form a skeletal shape for the

wing. Usually ribs incorporate the airfoil shape of the wing, and the skin adopts this shape

when stretched over the ribs.

There are several types of ribs. Form-ribs, plate-type ribs, truss ribs, closed-ribs,

forged ribs and milled ribs, where form-ribs are used for light to medium loading and

milled ribs are as strong as it can get. Form-ribs are made from a sheet of metal bent into

shape, such as a U-profile. This profile is placed on the skin, just like a stringer, but then

in the other direction. Plate-type ribs consist of sheet-metal, which has upturned edges

and (often has) weight-saving holes cut into it. Truss ribs are built up out of profiles that

are joined together. These joints require great attention during design and manufacture.

The ribs may be light or heavy in design, which make them suitable for a wide range of

loads.

Closed-ribs are constructed from profiles and sheet metal and are suitable for

closing off sections of the wing (e.g.: the fuel tank). Here too, particular care must be

taken with the joints and this type of rib is also suitable for application in a variety of

loading conditions.

Forged ribs are manufactured using heavy press-machinery. The result is fairly rough; for

more refined parts, high-pressure presses are required, which are very expensive. Forged

pieces (usually) have to undergo further treatment (for smoother edges and holes). Forged

ribs are used for sections where very high loads apply - near the undercarriage for

example.

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Milled ribs are solid structures. They are manufactured by milling away excess material

from a solid block of metal (usually using computer-controlled milling machines). The

shape of these ribs is always accurately defined. Such ribs are used under similar

conditions as those for forged ribs. Ribs are made out of wood, metal, plastic, composites,

foam. The wings of kites, hang gliders, paragliders, powered kites, powered hang

gliders, ultralights, windmills are aircraft that have versions that use ribs to form the

wing shape. For full size and flying model aircraft wing structures that are usually made

of wood, ribs can either be in one piece (forming the airfoil at that rib's "station" in the

wing), or be in a three-piece format, with the rib web being the part that the one-piece rib

consisted of, with capstrips for the upper and lower edging of the rib, running from the

leading edge to the trailing edge, being the other two component parts.

Fig 1.8: Ribs

1.4 STRESSES ON AIRCRAFT:

Structural integrity is a major factor in aircraft design and construction. No

production airplane leaves the ground before undergoing extensive analysis of how it will

fly, the stresses it will tolerate and its maximum safe capability. Every airplane is subject

to structural stress. Stress acts on an airplane whether on the ground or in flight. Stress is

defined as a load applied to a unit area of material. Stress produces a deflection or

deformation in the material called strain. Stress is always accompanied by strain. Current

production general aviation aircraft are constructed of various materials, the primary

being aluminium alloys. Rivets, bolts, screws and special bonding adhesives are used to

hold the sheet metal in place. Regard less of the method of attachment of the material,

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every part of the fuselage must carry a load, or resist a stress placed on it. Design of

interior supporting and forming pieces, and the outside metal skin all have a role to play

in assuring an overall safe structure capable of withstanding expected loads and stresses.

The stress a particular part must withstand is carefully calculated by engineers.

Also, the material a part is made from is extremely important and is selected by designers

based on its known properties. Aluminium alloy is the primary material for the exterior

skin on modern aircraft. This material possesses a good strength to weight ratio, is easy to

form, resists corrosion, and is relatively inexpensive.

Wings may be either strut braced or full cantilever, depending on whether (as in

many smaller aircraft) an external brace is employed to help transmit loads from the wing

to the fuselage. Cantilever wings must resist all loads with their own internal structure.

Small, low speed aircraft have straight, nearly rectangular wings. For these wings, the

main load is in bending of the wing as it transmits load to the fuselage, and the bending

load is carried primarily by the spars. In fact, the spars are the main structural pieces in a

wing assembly. Attached to the spars are ribs that give the aerodynamic shape to the

wing. During flight, stresses are transmitted first to the wing skin, then to the ribs, and

finally to the spars. Spars also must carry loads distributed by the fuselage, landing gear

and any nacelles. Stress is a fact of life for airplanes; it is always present in one form or

another. The primary concern for the owner/pilot should be to not put any undue stress on

the aircraft. Treat it gently, by operating it within its design limitations. Normal stress

(and occasional abnormal stress) is not a problem for an aircraft that is properly designed.

But, the airplane must be properly flown and maintained in order to keep it airworthy.

1.5 TYPES OF STRUCTURAL STRESS:

The five basic structural stresses to which aircraft are subject are:

1. Tension

2. Compression

3. Torsion

4. Shear

5. Bending

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Tension is the stress that resists a force that tends to pull something apart. The

engine pulls the aircraft forward, but air resistance tries to hold it back. The result is

tension, which stretches the aircraft. The tensile strength of a material is measured in

pounds per square inch (psi) and is calculated by dividing the load (in pounds)

required to pull the material apart by its cross-sectional area (in square inches).

Compression is the stress that resists a crushing force. The compressive strength

of a material is also measured in psi. Compression is the stress that tends to shorten or

squeeze aircraft parts. Torsion is the stress that produces twisting. While moving the

aircraft forward, the engine also tends to twist it to one side, but other aircraft

components hold it on course. Thus, torsion is created. The torsion strength of a

material is its resistance to twisting or torque.

Shear is the stress that resists the force tending to cause one layer of a material to

slide over an adjacent layer. Two riveted plates in tension subject the rivets to a

shearing force. Usually, the shearing strength of a material is either equal to or less

than its tensile or compressive strength. Aircraft parts, especially screws, bolts, and

rivets, are often subject to a shearing force. Bending stress is a combination of

compression and tension. The rod has been shortened (compressed) on the inside of

the bend and stretched on the outside of the bend.

Fig 1.9: The five stresses that may act on an aircraft and its parts.

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Fittings must be made of carefully selected materials because of their importance

of holding the aircraft together under expected stress and loading. The same holds true for

important fasteners such as bolts and rivets. It is essential that these parts not fail under

stress. It is also essential that these parts not weaken with exposure to stress and weather

elements. Corrosion is also a consideration. A fitting made of one metal cannot be

secured to the structure with a bolt or fastener made of another metal. This situation may

result in "dissimilar metal corrosion" over a period of time and result in a weakening of

the assembly to the extent that the assembly is rendered unsafe.

1.6 FATIGUE LIFE:

Because the stress levels of the fatigue critical locations are not known, they are

first approximated with a reference fatigue analysis. The reference fatigue analysis

simulates the original fatigue analysis of the aircraft. The stress values are iterated to such

a value that the fatigue life of the original wing is achieved with the original load spectra.

These reference stresses are transferred to the new fatigue analysis. The modified models

are taken into account when forming the loads. A new fatigue analysis is conducted for

the wing with the survey load spectra and the consumed fatigue life is resolved. Both

analytical fatigue analyses base on the Miner rule. With this process the fatigue life

consumption of the wing is estimated. Also, some representing factors are defined for the

future use. With these factors the operations can be scaled to match the estimated fatigue

life consumption.

The Miner hypothesis, also known as the Miner’s Linear Cumulative Damage

Theory, is widely used in the analytical fatigue analyses. The basic philosophy of this

theory is that the fatigue damage introduced by a given stress level is proportional to the

number of cycles at that stress level divided by the total number of cycles to failure at that

stress level. This ratio is referred as the cycle ratio and it is used to measure damage. The

stress level is here defined as the mean stress and amplitude of the load cycle. All various

cycle ratios are summed together to represent the total damage. The hypothesis states that

the failure occurs when the total damage reaches unity.

Two principal factors govern the amount of time it takes for a crack to start and

grow sufficiently to cause component failure: the component material and stress field.

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Methods for determining fatigue testing of materials go back to August Wöhler who, in

the 19th century, set up and conducted the first systematic fatigue investigation. Standard

laboratory tests apply cyclical loads such as rotating bend, cantilever bend, axial push-

pull, and torsion cycles. Scientists and engineers plot the data resulting from such tests to

show the relationship of each type of stress to the number of cycles of repetition leading

to failure—or S-N curve. Engineers can derive the stress level a material can endure for a

specific number of cycles from the S-N curve.

The curve splits into low and high cycle fatigue. Generally, low cycle fatigue

occurs at fewer than 10,000 cycles. The shape of the curve depends on the type of

material tested. Some materials, such as low-carbon steels, show a flattening off at a

particular stress level—referred to as the endurance or fatigue limit. Materials that contain

no iron show no endurance limit. In principle, components designed so that the applied

stresses do not exceed the known endurance limit shouldn’t fail in service. However,

endurance limit calculations don’t account for localized stress concentrations that may

lead to initiation of cracks, despite the stress level appearing to be below the normal

―safe‖ limit.

Fig 1.10 : S N curve

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Fatigue load history, as determined by testing with rotating bend tests, provides

information about mean and alternating stress. The rate of crack propagation in tests has

been shown to be related to the stress ratio of the load cycle, and the load’s mean stress.

Cracks only propagate under tensile loads. For that reason, if the load cycle induces

compressive stress in the area of the crack, it will not produce more damage. However, if

the mean stress shows that the complete stress cycle is tensile, the whole cycle will cause

damage.

1.6.1 FACTORS THAT AFFECT FATIGUE LIFE:

Cyclic stress state: Depending on the complexity of the geometry and the loading,

one or more properties of the stress state need to be considered, such as stress

amplitude, mean stress, biaxiality, in-phase or out-of-phase shear stress, and load

sequence,

Geometry: Notches and variation in cross section throughout a part lead to stress

concentrations where fatigue cracks initiate.

Surface quality: Surface roughness can cause microscopic stress concentrations that

lower the fatigue strength. Compressive residual stresses can be introduced in the

surface by e.g. shot peening to increase fatigue life. Such techniques for producing

surface stress are often referred to as peening, whatever the mechanism used to

produce the stress. Low plasticity burnishing, laser peening, and ultrasonic impact

treatment can also produce this surface compressive stress and can increase the

fatigue life of the component. This improvement is normally observed only for high-

cycle fatigue.

Material Type: Fatigue life, as well as the behavior during cyclic loading, varies

widely for different materials, e.g. composites and polymers differ markedly from

metals.

Residual stresses: Welding, cutting, casting, grinding, and other manufacturing

processes involving heat or deformation can produce high levels of tensile residual

stress, which decreases the fatigue strength.

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Size and distribution of internal defects: Casting defects such as gas

porosity voids, non-metallic inclusions and shrinkage voids can significantly reduce

fatigue strength.

Air or Vacuum: Certain materials like Metals are more prone to fatigue in air than in

a vacuum. Depending upon the level of humidity and temperature, the lifetime for

metals such as aluminum or iron might be as much as 5 to 10 times greater in a

vacuum. This is mostly due to the effect of the oxygen and water vapour in the air

which will aggressively attack the material and so encourage the propagation of

cracks. Other environments such as oil or seawater may reduce the fatigue life at an

even greater rate.

Direction of loading: For non-isotropic materials, fatigue strength depends on the

direction of the principal stress.

Grain size: For most metals, smaller grains yield longer fatigue lives, however, the

presence of surface defects or scratches will have a greater influence than in a coarse

grained alloy.

Environment: Environmental conditions can cause erosion, corrosion, or gas-phase

embrittlement, which all affect fatigue life. Corrosion fatigue is a problem

encountered in many aggressive environments.

Temperature: Extreme high or low temperatures can decrease fatigue strength.

Fatigue cracks that have begun to propagate can sometimes be stopped

by drilling holes, called drill stops, in the path of the fatigue crack. This is not

recommended as a general practice because the hole represents a stress concentration factor

which depends on the size of the hole and geometry, though the hole is typically less of a

stress concentration than the removed tip of the crack. The possibility remains of a new

crack starting in the side of the hole. It is always far better to replace the cracked part

entirely.

Changes in the materials used in parts can also improve fatigue life. For example,

parts can be made from better fatigue rated metals. Complete replacement and redesign of

parts can also reduce if not eliminate fatigue problems. Thus helicopter rotor blades

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and propellers in metal are being replaced by composite equivalents. They are not only

lighter, but also much more resistant to fatigue. They are more expensive, but the extra

cost is amply repaid by their greater integrity, since loss of a rotor blade usually leads to

total loss of the aircraft. A similar argument has been made for replacement of metal

fuselages, wings and tails of aircraft.

1.7 COMPUTATIONAL METHOD:

In mathematics, the finite element method (FEM) is a numerical technique for

finding approximate solutions to boundary value problems for differential equations. It

uses variational methods (the calculus of variations) to minimize an error function and

produce a stable solution. Analogous to the idea that connecting many tiny straight lines

can approximate a larger circle, FEM encompasses all the methods for connecting many

simple element equations over many small sub-domains, named finite elements, to

approximate a more complex equation over a larger domain.

FE method is an established procedure that enables predictions of deformations

and stresses of products in normal or accelerated loading environments. Although the FE

procedures continue to evolve, there are numerous FE packages that are commercially

available and capable of performing advanced simulations.

Major Input that are needed to perform a FE simulation:

(1) Geometry of the part(s) of interest;

(2) Applied loading and boundary conditions; and

(3) Material behavior of each of the different materials.

The first two of these required inputs are often easy to accurately specify by CAD

software and knowledge about the loading environment. But for the third input,

specification of the material models is typically the most difficult and challenging part of

performing FE simulations.

FEM is best understood from its practical application, known as finite element

analysis (FEA). FEA as applied in engineering is a computational tool for performing

engineering analysis. It includes the use of mesh generation techniques for dividing

a complex problem into small elements, as well as the use of software program coded

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with FEM algorithm. In applying FEA, the complex problem is usually a physical system

with the underlying physics such as the Euler-Bernoulli beam equation, the heat equation,

or the Navier-Stokes equations expressed in either PDE or integral equations, while the

divided small elements of the complex problem represent different areas in the physical

system.

FEA is a good choice for analyzing problems over complicated domains (like cars

and oil pipelines), when the domain changes (as during a solid state reaction with a

moving boundary), when the desired precision varies over the entire domain, or when the

solution lacks smoothness. For instance, in a frontal crash simulation it is possible to

increase hprediction accuracy in "important" areas like the front of the car and reduce it in

its rear (thus reducing cost of the simulation). Another example would be in numerical

weather prediction, where it is more important to have accurate predictions over

developing highly nonlinear.

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CHAPTER 2

LITERATURE SURVEY

Article titled [1] ―Design of an Aircraft Wing Structure for Static Analysis and

Fatigue Life Prediction‖ published by Ramesh Kumar, S. R. Balakrishnan, S. Balaji. In

this paper stress analysis of the wing structure is carried out to compute the stresses at

wing structure and prediction of fatigue life for crack initiation will be carried out at

maximum stress location. The stresses are estimated by using the finite element approach

with the help of ANSYS-12 to find out the safety factor of the structure. It is found out

from the result that maximum stress is identified at wing root which is found out to be

lower than yield strength of the material. It is found that damage accumulated is less than

the critical damage and structure is safe from fatigue. Life of the particular region in wing

structure is predicted to become critical and found out to be 3058 flying hours.

Journal Paper titled [2]―Wing Structure Static Analysis using Superelement‖

published by W Kuntjoro, AMH Abdul Jalil, J Mahmud. In this paper superelement for

the stress and deflection analysis of a typical fighter wing structure were used. Three

methods of analyses were carried out and compared: practical/theoretical analysis; finite

element analysis with the conventional element modelling approach; and finite element

analysis with the superelement modelling. The direct stress and deflection are sought and

to be compared. Result shows a good agreement between the three methods. The

comparison of the stress values between the theoretical approach and the finite element

analysis approaches shows minimal errors. The comparison of the stress values between

the finite element analysis with conventional approach and finite element analysis with

superelement approach shows the same results. The finite element analysis with

conventional approach and superelement approach shows the same results for the

deflection values. This proves that that the superelement approach does not alter the

values obtained from the conventional finite element approach.

Article titled [3] ―Crack Growth Analysis in Aircrft Wing Lug Section and

Fatigue Life Estimation‖ published by K. Mookaiya, S. Balaji, S. R. Balakrishnan. In this

paper a model for estimating the residual fatigue life of attachment lugs is proposed.

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Strength analysis and fatigue life estimation is determined by applying analytical and

numerical methods. This journal work presents a computational model for the crack

growth analysis of the attachment lug with single quarter-elliptical crack as well as with

single through-the-thickness crack. The proposed model examines the stress analysis, the

fatigue life estimation and the crack path simulation. In the stress analysis, both analytical

approaches are employed to determine the stress intensity factor. In the finite element

analyses are conducted using the packages ANSYS and quarter point (Q-P) finite

elements are employed to simulate the stress field around the crack tip.

Journal paper titled [4] ―Fatigue Analysis in Aircraft Landing Gear Axle Shaft To

Develop The Life Cycles‖ published by P. Mohanraj, S. Balaji, S. Senthilkumar. In this

paper the Objective is to analyze main landing gear axle shaft to determine the fatigue

stress behaviour and the displacement of an aircraft landing gear axle during taxing in the

ground. The failure of the left main landing gear of a Boeing 737-400 has been analyzed

in this report the forces and tensions on the landing gear and axle were calculated. The

current material is changed to titanium alloy ASTM Grade 5 which is stronger but also

more expensive. The fatigue cycles are increased to two times greater than the current

axle. The safety factor is also greater than current alloy therefore cost of the new model

compromised by its greater life cycles. So safety is thereby improved.

Article titled [5] ―Fatigue Life Analysis of Aircraft Structural Components‖

published by Stevan Maksimović. This work defines an effective computation procedure

that combines Neuber`s Rule and the finite element method with strain–life criterions in

order to accurately predict fatigue crack initiation life. Miner’s rule was used to calculate

the accumulative damage in the fatigue crack initiation phase. This procedure is then

applied to a plate with a central hole (structural elements with concentrations), and the

results were compared with analytical local strain method and available experimental

data. Fatigue life estimated by the presented procedure closely approximates experimental

results. The defined procedure, for fatigue life prediction of notched aircraft structural

components up to crack initiation, can take into consideration uni-axial and multi-axial

loading with constant and variable amplitude.

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Journal paper titled [6] ―Initial Fatigue Life Predictions of a Notched Structural

Components Under Variable Amplitude Loading‖ published by Slobodanka Boljanovic

and Stevan Maksimovic. This paper presents numerical procedure for initial fatigue life

of structural components under load spectra. Fatigue crack initiation at the notch root is

considered to be due to localized low-cycle fatigue. The cycle behaviour of the steel was

investigated in terms of stress and strain relations. This work presents an effective

procedure to predict fatigue life up to crack initiation. Miner`s rule was used to calculate

the accumulative damage in the fatigue crack initiation phase. Comparative results

demonstrate that the fatigue life estimated by the presented procedure closely

approximates experimental results. It is very important to stress that presented procedure

for prediction of fatigue life up to crack initiation provides good correlation with

experimental data even with low and high fatigue domains. The defined procedure, for

fatigue life prediction up to crack initiation, can take in consideration uni-axial and multi-

axial loading with constant and variable amplitude.

Journal paper titled [7] ―Fatigue Crack Growth Analysis of Damaged Structural

Components Under Mode-I and Mixed Modes‖ Published by Katarina Maksimović, MSc

(Eng). The work presents a life prediction methodology of damaged structural

components under the interspersed mode-I and the mixed-mode (I and II). This work

considers the numerical computation methods and procedures for predicting the fatigue

crack growth life for cracks at notched structural components. The strain energy density

and MTS criteria are used to determine the crack trajectory or the angle of crack growth

in thin walled structures with cracks emanating from holes. Attention in this work is

focused on the crack growth analyses of damaged structural components under fracture

mechanics for mode I and the mixed modes. The aim of this work is to investigate the

strength behaviour of the notched structural elements such as the cracked lugs. In the

fatigue crack growth and the fracture analysis of lugs, an accurate calculation of SIFs is

essential. An analytic expression for the stress intensity factor of the cracked lug is

derived using the correction function. The contact finite element analysis for the true

distribution of the pin contact pressure is used for the determination of stress

concentration factors that is used in the correction function. Good agreement between the

derived analytic SIFs of the cracked lug with finite elements is obtained.

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Journal paper titled [8] ―Stress Analysis for Wing Attachment Bracket of a six

seater Transport Airframe Structure‖ published by Harish E.R.M, Mahesha. K, Sartaj

Patel. In this paper study the stress analysis of wing-fuselage attachment bracket is

considered. Stress analysis will be carried00 out for the given geometry of the wing-

fuselage attachment bracket of a six seater transport airframe structure. Finite element

method is used for the stress analysis. Stress analysis helps in prediction of fatigue life of

structural component of airframe structure. Stress analysis of the wing fuselage lug

attachment bracket is carried out and maximum tensile stress is identified at one of the

rivet hole of I-spar plate.FEM approach is followed for the stress analysis of the wing

fuselage lug attachment bracket.)A validation for FEM approach is carried out by

considering a plate with a circular hole. Maximum tensile stress of 1373N/mm2 (i.e., 140

kg/mm2) is observed in the I-spar plate. Several iterations are carried out to obtain a mesh

independent value for the maximum stress. A fatigue crack normally initiates from the

location maximum tensile stress in the structure, further fatigue life estimation can be

carried out to predict the life of the airframe component.

Article titled [9] ―Fatigue Life Estimation Of Notched Structural Components:

Computation and Experimental Investigations‖ published by S. Maksimović, Z. Burzić,

K. Maksimović. This work considers the analytical/numerical methods and procedures for

obtaining the stress intensity factors and for predicting the fatigue crack growth life for

cracks at notched structural components. A variety of methods have been used to estimate

the SIF values, such as approximate analytical methods, finite element (FE), finite

element alternating, weight function, photo elasticity and fatigue tests. Single through

crack in the attachment lug analysis is considered. For this purpose analytic expressions

are evaluated for SIF of cracked lug structures. For validation of the analytic stress

intensity factors of cracked lugs, FEM with singular finite elements is used. The aim of

this work is to investigate the strength behaviour of the notched structural elements such

as the cracked lugs. In the fatigue crack growth and fracture analysis of lugs, accurate

calculation of SIF is essential. Analytic expression for stress intensity factor of cracked

lug is derived using correction function. The contact finite element analysis for the true

distribution of pin contact pressure is used for determination of stress concentration

factors that is used in correction function. Good agreement between derived analytic SIF

of cracked lug with finite elements is obtained. In this paper the predicted crack trajectory

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using quarter-point singular finite elements together to the strain energy density criteria

were nearly identical to the trajectories predicted with X-FEM.

Journal titled [10] ―Stress Intensity Factors for Elliptical Surface Cracks in Round

Bars and Residual Life Estimation‖ published by Marija Blažić, Mirko Maksimović,

Ivana Vasović, Yasmina Assoul. This work investigates the behaviour of structural

components with surface cracks1,2 . The attention is focused on a circular bar with an

elliptical surface crack under tension load. Stress intensity factors (SIF) are considered

using the finite element method. For that purpose a straight round bar under tension is

investigated. Stress intensity factors of elliptical surface cracks in tensile round bars are

calculated by using three-dimensional finite element analysis (FEA) models with singular

20-node elements arranged around the crack tip. The stress intensity factors are

determined by singular finite elements for various crack depths. Using these discrete

values of the stress intensity factors, a general analytic expression of stress intensity

factors is derived. An empirical expression for the SIFs as a function of crack geometry is

obtained by fitting the numerical results. These analytic expressions are used in the crack

growth analysis of a cracked structural component. Therefore, the empirical expression

can be used conveniently in the life prediction of notched bars with various notch

geometries and stress concentration coefficients at least within the range of parameters

studied in this work.

Journal paper titled [11] ―An Approach to the Fatigue Analysis of Vertical Axis

Wind Turbine Blades‖ published by pauls. Veers sandia natlonal laboratories

albuquerque, new mexico 87185 and livermore, california 94550. Examination of the real

time stress signal from VAWT blades during operation demonstrate that a single

vibratory stress level at each wind speed does not characterize the state of stress of an

operating turbine’s blades. Combining the Rayleigh distribution with the S-N data using

Miner’s Rule results in an expression for the number of operating cycles to failure at each

wind speed. Implementing the cumulative damage rule again to account for the wind

speed distribution provides a method of predicting the total wind turbine life for a given

wind site and given cut-in and cut-out wind speeds.

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Article titled [12] ―Fatigue Life Estimation Considering Damaging and

Strengthening of Low amplitude Loads under Different Load Sequences Using Fuzzy

Sets Approach‖ published by SHUN-PENG ZHU, HONG-ZHONG HUANG* AND

ZHONG-LAI WANG. Based on the Miner rule, this study refers not only to the

damaging and strengthening effect of low amplitude loads below the fatigue limit, but

also the effects of load sequence and load interaction. Compared with the traditional

Miner rule, results of those fatigue tests clearly indicate that the proposed Miner rule

gives more accurate and reliable predictions on fatigue lives. The strengthening and

damaging of low amplitude loads below the fatigue limit are investigated within the

Miner rule.

Article titled1 [13] ―Literature Review on Aircraft Structural Risk and Reliability

Analysis‖ published by Yu Chee Tong Airframes and Engines Division Aeronautical and

Maritime Research Laboratory. Probabilistic Damage Tolerant approach or Structural

Risk and Reliability Analysis have been identified as the potential tool for satisfying these

requirements. It has also been proven that probabilistic method can be extended to

provide very useful information to help managers in making decisions regarding the

operation and inspection time of the fleet in order to maintain airworthiness. It is capable

of identifying the sources of variables affecting the fatigue life and fatigue strength of the

structure in terms of risk.

Practice paper titled [14] ―Structural Stress Analysis” from Goddard Space Flight

Center (GSFC), NASA. This paper describes the general methodology for performing

stress analysis for structures used in space applications. Reliability of spacecraft structural

components is greatly increased, and their cost and weight reduced by the systematic and

rigorous application of sound stress analysis principles as an integral part of the design

process. Structural loads are specified at the maximum expected level and referred to as

the design or limit loads. . A major difference could be absence of ribs and multiple spars

(more than 2) in the vertical tail construction. Vertical tails have symmetrical airfoil cross

sections. Therefore in the absence of rudder deflection there is no aerodynamic load

acting on the fuselage. However significant side loads develop due to rudder deflection

and this is the major design load for the vertical tail

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Article titled [15] ―Design of Constructions with Respects to Fatigue and Fracture

Mechanics” published by Dr Stevan Maksimović, Marija Blažić, Mirko Maksimović. In

this investigation analytic method for determination of the stress intensity factors to

surface cracks at the 3-D solid structural elements is established. Primary attention of this

paper is to establish analytic expressions of SIF’s for surface crack which can be effective

used in crack growth propagations and residual life estimations. Good agreement analytic

with finite element results is obtained in domains static fracture mechanics and crack

growth analyses. The complete computation procedure for crack growth analysis is

illustrated to aircraft nose landing gears. Procedure is based on using finite element

method to determine critical locations with respects to fatigue and fracture mechanics

with one side and to use analytic expressions for determination of SIF’s and residual life

of structural components with other side.

Journal titled [16] ―A Statistical Analysis of the Aircraft Landing Process‖

published by Babak Ghalebsaz-Jeddi, George L. Donohue, John F. Shortle. We obtained

the wake vortex weight class for 98.6% of aircraft landing in peak periods. This paper

extended our initial report where some statistics of the aircraft approach on all runways

collectively were presented, Jeddi et al. (2006). Samples were additionally conditioned on

weight class of follow-lead aircraft and aggregated for the ones with a minimum

separation standard of 3 nm and 4 nm, whereas the initial report was only about 3 nm

pairs under ILS.

Journal paper titled [17] ―Analytical Fuselage and Wing Weight Estimation of

Transport Aircraft‖ published by Mark D. Ardema, Mark C. Chambers, Anthony P.

Patron, Andrew S. Hahn, Hirokazu Miura, and Mark D. Moore. A method of estimating

the load-bearing fuselage weight and wing weight of transport aircraft based on

fundamental structural principles has been developed. This method of weight estimation

represents a compromise between the rapid assessment of component weight using

empirical methods based on actual weights of existing aircraft, and detailed, but time-

consuming, analysis using the finite element method Using statistical analysis techniques,

relations between the load-bearing fuselage and wing weights calculated by PDCYL and

corresponding actual weights were determined.

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Paper titled [18] ―AIRCRAFT LOADS‖ published by Dr. M. Neubauer, G.

Günther. In this paper Structural loads, leading to fatigue as well as corrosion, depending

on the usage environment, are the major reason for degradation of structures. The many

different classes of loads, the generation of loading conditions during the design phase, as

defined in the weapons systems specification, consideration of static and fatigue loads for

structural lay-out and validation concepts are presented. The procedure of converting

overall aircraft loads (―external loads‖) into individual component loads is shown in

principal.

Article titled [19] ―Design and Analysis of A Spar Beam For The Vertical Tail of

A Transport Aircraft‖ published by Vinod S. Muchchandi, S. C. Pilli. IN THIS PAPER

Vertical tail and the rudder are important structural components of an aircraft. Movement

of the rudder controls the yawing of an aircraft. Structurally speaking vertical tail is a

typical mini-wing construction. A major difference could be absence of ribs and multiple

spars (more than 2) in the vertical tail construction. Vertical tails have symmetrical airfoil

cross sections. Therefore in the absence of rudder deflection there is no aerodynamic load

acting on the fuselage. However significant side loads develop due to rudder deflection

and this is the major design load for the vertical tail. For transport aircraft side gust load is

also important from a design point of view. In this project a typical spar of a vertical tail

of a transport aircraft will be analysed. Loads representative of a small transport aircraft

will be considered in this study. An efficient tapered spar beam will be designed for this

load. SOM approach will be used for preliminary sizing of the spar. This will be followed

by FEA for a more accurate stress analysis that will be used to improve the design. The

objective of the present study is to investigate the stresses acting in the spar beam of the

vertical tail with and without cut outs. The analysis shows that increase in the air drag

load increases the maximum stress. The differential air drag load is applied between the

ranges 62 to 620 Kg which varies non-linearly. In this study, the effects of stresses in

aircraft spar beam structure with and without cut outs are determined. A typical spar

beam with and without cut outs of standard configurations is loaded and analysed.

Parametric studies were done to examine the effects of different cut outs. Based on the

results of finite element predictions and by the calculations of the stress analysis

approach, it is apparent that the air drag load has more effect on the top and bottom

flange. From the load cases the maximum stress is compared with yield stress and

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ultimate stress of 2024 T351 aluminium alloy.This study refers not only to the damaging

and strengthening effect of low amplitude loads below the fatigue limit, but also the

effects of load sequence and load interaction. Compared with the traditional Miner rule,

results of those fatigue tests clearly indicate that the proposed Miner rule gives more

accurate and reliable predictions on fatigue lives. The strengthening and damaging of low

amplitude loads below the fatigue limit are investigated within the Miner rule.

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CHAPTER 3

FINITE ELEMENT ANALYSIS

3.1 FINITE ELEMENT ANALYSIS OF LANDING GEAR

WELL BEAMS

Finite Element Analysis is a numerical analysis technique used to obtain solutions

to the differential equations that describe or approximately describe a wide variety of

physical (and non-physical) problems physical problems range in diversity from solid,

fluid and soil mechanics to electromagnetism or dynamics.

FEA uses a complex system of points called nodes which make a grid called

a mesh. This mesh is programmed to contain the material and structural properties which

define how the structure will react to certain loading conditions. Nodes are assigned at a

certain density throughout the material depending on the anticipated stress levels of a

particular area. Regions which will receive large amounts of stress usually have a higher

node density than those which experience little or no stress. Points of interest may consist

of: fracture point of previously tested material, fillets, corners, complex detail, and high

stress areas. The mesh acts like a spider web in that from each node, there extends a mesh

element to each of the adjacent nodes. This web of vectors is what carries the material

properties to the object, creating many elements.

The underlying premise of the method states complicated domain can be sub-

divided into a series of smaller regions in which the differential equations are

approximately solved by assembling the set of equations for each region the behaviour

over the entire problem domain is determined each region is referred to as an element and

the process of subdividing a domain into a finite number of elements is referred to as

discretization elements are connected at specific points called nodes and the assembly

process requires that the solution be continuous along common boundaries of adjacent

elements.

FEA has become a solution to the task of predicting failure due to unknown

stresses by showing problem areas in a material and allowing designers to see all of the

theoretical stresses within. This method of product design and testing is far superior to the

manufacturing costs which would accrue if each sample was actually built and tested.

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FE models can be created using one-dimensional (1D beam), two-dimensional

(2D shell) or three-dimensional (3D solid) elements. By using beams and shells instead of

solid elements, a representative model can be created using fewer nodes without

compromising accuracy. Each modeling scheme requires a different range of properties to

be defined, such as:

Section areas

Moments of inertia

Torsional constant

Plate thickness

Bending stiffness

Transverse shear

To simulate the effects of real-world working environments in FEA, various load

types can be applied to the FE model, including:

Nodal: forces, moments, displacements, velocities, accelerations, temperature and heat

flux

Elemental: distributed loading, pressure, temperature and heat flux

Acceleration body loads (gravity)

Types of analysis include:

Linear statics: linear analysis with applied loads and constraints that are static

Nonlinear statics and dynamics: effects due to contact (where one part of the model

comes into contact with another), nonlinear material definitions (plasticity, elasticity, etc.)

and large displacement (strains that exceed small displacement theory that limits a linear

analysis approach)

Normal modes: natural frequencies of vibration

Dynamic response: loads or motions that vary with time and frequency

Buckling: critical loads at which a structure becomes unstable

Heat transfer: conduction, radiation and phase change

Typical results calculated by the solver include:

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Nodal displacements, velocities and accelerations

Elemental forces, strains and stresses

Benefits of FEA:

FEA can be used in new product design, or to refine an existing product, to ensure

that the design will be able to perform to specifications prior to manufacturing. With FEA

you can:

Predict and improve product performance and reliability

Reduce physical prototyping and testing

Evaluate different designs and materials

Optimize designs and reduce material usage

3.2 PROCESS FLOW OF FINITE ELEMENT ANALYSIS

In practice, a finite element analysis usually consists of three principal steps:

1. Pre-processing: The user constructs a model of the part to be analyzed in which the

geometry is divided into a number of discrete sub regions, or ―elements," connected at

discrete points called ―nodes." Certain of these nodes will have fixed displacements, and

others will have prescribed loads. These models can be extremely time consuming to

prepare, and commercial codes vie with one another to have the most user-friendly

graphical pre-processor to assist in this rather tedious chore. Some of these preprocessors

can overlay a mesh on a pre-existing CAD file, so that finite element analysis can be done

conveniently as part of the computerized drafting-and-design process. Computation of the

mathematical model. The solver runs after you have defined your material, fixtures, and

loads. The solver constructs a system of equations from the elements based on these

parameters and solves for them either directly or iteratively.

2. Analysis: The dataset prepared by the preprocessor is used as input to the finite

element

code itself, which constructs and solves a system of linear or nonlinear algebraic

equations

Kijuj = fi,

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where u and f are the displacements and externally applied forces at the nodal

points. The formation of the K matrix is dependent on the type of problem being attacked,

and this module will outline the approach for truss and linear elastic stress analyses.

Commercial codes may have very large element libraries, with elements appropriate to a

wide range of problem types. One of FEA's principal advantages is that many problem

types can be addressed with the same code, merely by specifying the appropriate element

types from the library.

3. Postprocessing: In the earlier days of finite element analysis, the user would pore

through reams of numbers generated by the code, listing displacements and stresses at

discrete positions within the model. It is easy to miss important trends and hot spots this

way, and modern codes use graphical displays to assist in visualizing the results. Typical

postprocessor display overlays colored contours representing stress levels on the model,

Showing a full-field picture similar to that of photo elastic or moire experimental results.

The general steps followed in a finite element analysis with a commercial FEM package

is as shown in figure 3.1

Fig 3.1 Process Flow of FEA

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CHAPTER 4

MATERIAL PROPERTIES, LOAD CALCULATION

AND BOUNDARY CONDITION

The material taken for the landing gear wells beams is assumed to be made of

aluminium alloy AA 2024 T351. Aluminium alloy 2024 is an aluminium alloy,

with copper as the primary alloying element. This is the most common of the the high-

strength aluminum alloys. It is aircraft quality. 2024-T3 aluminum sheet is thought of as

the aircraft alloy because of its strength. It has excellent fatigue resistance. Welding is

generally not recommended. Typical uses for 2024-T3 Alclad aluminum sheet are aircraft

skins, cowls, aircraft structures, and also for repair and restoration because of its shiny

finish (2024-T3 Alclad). Ultimate strength is 62000 PSI with a shearing strength of 40000

PSI. It is used in applications requiring high strength to weight ratio, as well as

good fatigue resistance. It is weldable only through friction welding, and has

average machinability. Due to poor corrosion resistance, it is often clad

with aluminium or Al-1Zn for protection, although this may reduce the fatigue strength.

Aluminum alloy 2024 has a density of 2.78 g/cm³ (0.1 lb/in³), electrical

conductivity of 30% IACS, Young's Modulus of 73 GPa (10.6 Msi) across all tempers,

and begins to melt at 500 °C (932 °F).

2024 aluminum alloy's composition roughly includes 4.3-4.5% copper, 0.5-

0.6% manganese, 1.3-1.5% magnesium and less than a half a percent of silicon, zinc,

nickel, chromium, lead and bismuth. T3 temper 2024 sheet has an ultimate tensile

strength of 58-62 ksi (400-427 MPa) and yield strength of at least 39-40 ksi (269-276

MPa). It has an elongation of 10-15%.

4.1 CHARACTERISTICS OF ALUMINUM:

At high temperatures (200-250°C) aluminum alloys tend to lose some of their

strength. However, at subzero temperatures strength increases while retaining their

ductility, making aluminum an extremely useful low-temperature alloy, high flying

commercial aircraft commonly fly at -50°C so they profit from this property.

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It also has good electrical (ground for aircraft antenna) and thermal

conductivities and is highly reflective to heat and light. Copper is the more widely

used conductor (copper bus bars and wiring among other things), having a

conductivity of approximately 160% that of aluminum. Aluminum connectors have a

tendency to become loose after repeated usage and this can lead to arcing and fire,

which requires extra precaution and special design when using aluminum wiring in

buildings.

Corrosion resistance: Aluminum alloys also have a good strong resistance to

corrosion which is a result of an oxide skin that forms as a result of reactions with the

atmosphere. These reactions occur very quickly, usually within minutes. This

corrosive skin protects aluminum from most chemicals, weathering conditions. It is a

very versatile metal and can be cast in any form. It can be rolled, stamped, drawn,

spun, roll-formed, hammered and forged. The metal can be extruded into a variety of

shapes and can be turned, milled, and bored in the machining process. Aluminum can

riveted, welded, brazed, or resin bonded (aluminum/composite aircraft are a good

example). For most applications, aluminum needs no protective coating as it can be

finished to look good, however it is often anodized to improve color and strength.

Young`s modulus

73 GPa

Poisson`s ratio

0.33

Yield strength

324 MPa

Ultimate tensile strength

427 MPa

Load factor

1.5

Density

2.78g/cm3

Elongation

10-15 %

Electrical conductivity

30% IACS

Table 4.1: Aluminium Alloy 2024 properties

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4.2 Load calculation:

Type of aircraft used for analysis: 13 seater aircraft

Total weight of aircraft: W= 6.1 ton = 6100 kg

Fig 4.1: Basic dimension of aircraft

Base length of aircraft = B = 6.465 m

Fm=

Hcg =1.88 m

Fmdy=

aT = vertical sink rate.

Hcg = Height from ground to center of gravity.

Fmdy = 2660.79 kg

Total load on main landing gear during normal touch down:

F = 2660.79 + 6100 = 8760.79 kg

Force per landing gear: F = 8760.79/2 = 4380.4 kg

Force acting on pin diameter:

=46.4775 kg/mm.

Force acting on each side of pin:

= 23.23 kg/mm.

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Fig 4.2: Meshing and Boundary Condition of landing gear well beams.

The load is calculated for a 13 seater aircraft. Total weight of aircraft is 6100 kg

or 6.1 ton. The base dimension of aircraft is 6.465 m. The distance between ground and

centre of gravity is 1.88 m. The load calculated by using above equation is total load on

main landing gear during normal touchdown is combination of total weight and dynamic

forces acting on it during flight level which is 8760.9 kg. As there are two landing gears

per aircraft one is main landing gear and other is nose landing. As main landing gear

takes maximum load during landing, hence main landing gear is analyzed. The main

landing gear contains two landing gear hence load is divided equally between the two

landing gear. Total load per landing gear is 4380.4 kg.

The load is acting on pin of diameter is 46.4775 kg/mm. There are two sides in a pin and

hence load acting on each pin hole is 23.23 kg/mm. In the structure the flange of rib is

fixed and load is applied to pin hole.

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CHAPTER 5

LINEAR STATIC ANALYSIS OF LANDING GEAR

WELL BEAMS

Linear analysis is used to solve static problems, such as determining if a structure

will fail under a prescribed load, and can also be used to solve transient problems where

loads change over time. Linear analysis has been used for decades to evaluate structural

performance for applications in a variety of industries, such as understanding how an

airframe reacts to flight loads, determining the amount of pressure a new keypad can

handle on an electronic device, or how much weight beams can hold in a civil structure

before buckling.

A series of assumptions are made with respect to a linear static analysis:

1. Deflections should be small relative to structure.

2. Rotations should be less than 10 degrees to 15 degrees.

3. Material should be linear elastic.

4. Boundary conditions should be constant

Linear static FEA process begins with taking the geometry and discretizing it into

a series of smaller elements. Currently only basic shapes have analytical solutions. CAD

geometry is often complex and must be broken down, or discretized, into a series of

continuous elements which can be solved for displacements and subsequently stresses and

strains.

There are many different types of elements that FEA programs use to handle

different classes of problems. SolidWorks has three main types of elements, 3-D solid

tetrahedral, 2-D triangular shell, and 2-D beam elements. The model of the LG beams

geometry is built up with solid 3D brick elements. The element is defined by eight nodes

having three degrees of freedom at each node. The landing gear beams is modeled using

Catia V5, meshed using Patran and analyzed using the Nastran software.

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5.1 GLOBAL ANALYSIS:

In global analysis the meshed model along with boundary condition applied is

analyzed. The main objective in this analysis is to find maximum stress location, because

cracks are initiated at maximum stress location. Magnitude of maximum stress and stress

distribution is also obtained from global analysis.

STEPS IN LINEAR STATIC STRESS ANALYSIS:

STEP 1: Requirements and loads determination

Loads

-Static (or equivalent static)

-Strength, displacement, cyclic life

STEP 2: Material Characterization

-Structural goals vs. material parameters

STEP 3: Structural modelling

-Discretized numerical model (e.g., finite element model)

-Analytical (closed form) solution of idealized geometry and loading

STEP 4: Determination of structural response

-Linear/non-linear

-Deformations, internal forces and stresses

STEP 5: Failure modes check

-Margin of safety for ultimate failure, yielding, instability etc.

-Safe life for fracture if applicable

STEP 6: Optimization and redesign if necessary

STEP 7: Documentation

Generally the following method is used for doing global analysis, They are:

Importing Solid model designed using modeling software( CATIA V5).

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Fig 5.1: Landing Gear beam Catia Model.

Converting 3D into 2D model.

Fig 5.2: Two Dimensional Model of LG Beams.

Meshing: The 2D model is meshed using Quad 4 and Tria element type.

Meshing is done in patran software.(pre-processor)

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Fig 5.3: Complete Meshed Model.

Cross-section of beams must be assigned.

Material properties must be assigned. Such as young's modulus (7000) and

possion`s ratio (0.33).

Boundary condition and loads are applied to structure.

Fig 5.4: Loaded and Constrained model

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Output.

Fig 5.5: Output of Stress Analysis.

The above figure gives the stress distribution in landing gear beam for given load.

The magnitude of maximum stress is 94.8 N/mm2. The location of maximum stress is at

the lower end of fixed beam. The maximum stress is found to be located at the rivet

location in the beam

.

Fig 5.6: Location of Maximum Stress in LG beams.

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Fig 5.7: Elemental values near Maximum Stress Location

The above fig shows the value of stress of element near maximum stress location.

In the model the rivet is not simulated as a hole instead it is taken as one dimensional

beam element, Hence the load acting as point load. Which results is high stress value at

point load, but in real the stress at the rivet is much lower than the value obtained. To get

the stress value near rivet average stress value in between two adjacent rivets is taken as

shown in box in fig 6.7. The average of four stresses is whose value is 22.725 kg/mm2 is

taken for local analysis or theoretical formulation.

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CHAPTER 6

THEORETICAL VALIDATION

It is very important that the theoretical results should matches with the

experimental or analysis results. Where the convergence of results plays a major role in

the software analysis. Convergence can achieved with the element size and shape which

is called as H-type convergence, in P-type convergence the polynomial order of the

differential equation can be considered to achieve the required result.

6.1 MAXIMUM STRESS IN PLATE WITH HOLE WITH

ONE END FIXED.

In local analysis, the location where maximum stress is found is considered for

analysis. Here maximum stress is obtained at rivet location. A plate with hole is taken to

stimulate the rivet location. The main objective in this analysis is to find the maximum

stress at the cut out rivet region. The model for local analysis is a plate with hole with

length 50mm, width 25mm, thickness 5mm and hole with diameter 5mm

.

Fig 6.1: Plate with Hole for Local Analysis

For local model analysis, a plate with hole is taken of length = 50mm, width = 25mm and

thickness = 8mm.

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Nominal stress acting on global model is 14.9+14.5+29.3+32.2 = 22.725kg/mm2

Load acting on the local model:

Stress average = Load / Area

Load = Stress avg*Area

= 22.725*25*5

= 2840.625 kg

One side of plate with hole is fixed and other end load applied is 2840.6/25= 113.625

kg/mm.

Fig 6.2: Mesh and Boundary Condition applied to Local Model.

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Fig 6.3: Local Analysis

The magnitude of maximum stress in local model is 54 N/mm2. The ultimate

tensile stress for aluminum is 45 N/mm2.

Fig 6.4: Stress Concentration Factor for Plate with Hole

To find Kt value we need to know the ratio d/w, which is 5/25 = 0.2.From stress

concentration graph Kt is found to be 2.5.

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We know that, stress concentration factor is ratio of maximum stress to nominal stress.

Kt =

Maximum stress = Kt * nominal stress

= 2.5*22.725

= 56.8 N/mm2

From the above result we can say that the analysis value almost equal to the

theoretical value obtained from Kt equation. Hence the analysis is considered as valid

process. The present model thickness is not sufficient to withstand the stress generated.

Hence the thickness needs to be increased to 8 mm for the landing gear beams to be safe.

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CHAPTER 7

FATIGUE ANALYSIS OF LANDING GEAR WELL

BEAMS

The definition of fatigue, in fact, is: failure under a repeated or otherwise varying

load, which never reaches a level sufficient to cause failure in a single application Fatigue

life evaluation of mechanical components under complex loading conditions is of great

importance to optimize structural design, and improve inspection and maintenance

procedures. Under variable amplitude loading, every same stress – strain cycle make the

same damage, and is independent of the place in the load spectrum. The mechanism of

fatigue can be broken down into three interrelated processes:

1. Crack initiation

2. Crack propagation

3. Fracture

4. Fits together

FEA stress analysis can predict crack initiation. A number of other technologies,

including dynamic nonlinear finite element analysis, can study the strain issues involved

in propagation. Because design engineers principally want to prevent fatigue cracks from

ever starting,

Fatigue damages under variable amplitude were estimated by Palmgren-Miner rule.

The Miner law is adopted, the damage D is expressed as follows:

D=Σ

Nfi is the cycle count at the time of failure under of axial (multiaxial) loading, the value ni

is the actual cycle count at the adequate stress level. Then the block load spectrum T

when the structure is failure can be expressed as follows:

T =

The above equation represents a statement of the linear damage rules used by the

local strain fatigue life predictions.

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SN curve is based on stress levels only, and uses the Wöhler method only.

Although unsuitable for components with areas of plasticity, and providing poor accuracy

for low cycle fatigue, it is the easiest to implement, has ample supporting data, and offers

a good representation of high cycle fatigue. Most components undergo a varying load

history in real life conditions, in terms of both amplitude and mean stress. Therefore, a far

more general and realistic approach considers variable amplitude loading, in which the

stresses, although repetitive over time, have varying amplitude, making it possible to split

them into load ―blocks.‖

Normally aircraft landing gear beams experiences variable spectrum loading

during takeoff and landing. A typical transport aircraft is considered for flight load

spectrum is for the fatigue analysis of the landing gear well beams structure. Calculation

of fatigue life estimation is carried out by using Miner`s Rule. Damage calculation is

carried out for the full service life of the aircraft. The load factor ―g‖ is defined as the

ratio of the lift of an aircraft to its weight. This gives a measure of the load which aircraft

experiences. As we know the maximum stress value obtained from the analysis is

corresponding to 1.5 g condition.

Therefore the stress value corresponding to 1.5 g condition is obtained as 53.7 N/mm2.

LOAD SPECTRUM FOR FATIGUE LIFE ESTIMATION:

Sl no

G range

Cycles

1

0.5g to 0.75g

57000

2

0.75g to 1g

28000

3

1g to 1.25g

24000

4

1.25g to 1.5g

18000

5

0 to 1.5 g

50

6

-0.5 g to 1.5g

100

Table 7.1: Variable Load Spectrum for Typical Aircraft

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The above table 7.1 gives load spectrum of a typical 13 seater aircraft. This data is

provided by the designer and other various design teams. This is collected from the

existing aircraft during the flight. The table gives various cycles of loading at different

range.

Correction factors for fatigue life calculations of landing gear well beams structure are

• Surface Correction Factor = 1

• Loading Type = 1

• Design Reliability = 0.897

Surface Roughness = 0.8

7.1 CALCULATE MAX STRESS FOR DIFFERENT RANGE:

Case 1: 0.5 g

Local model considering 1.5 g Load = 114 kg/mm

Local model considering 0.5 g Load = 38 kg/mm

After applying 38 kg/mm load to Local model i.e. plate with hole, we get maximum stress

of magnitude 11.3 kg /mm2.

Case 2: 0.75 g

Local model considering 1.5 g Load = 114 kg/mm

Local model considering 0.75 g Load = 57 kg/mm

After applying 57 kg/mm load to Local model i.e. plate with hole, we get maximum stress

of magnitude 16.9 kg /mm2.

Case 3: 1 g

Local model considering 1.5 g Load = 114 kg/mm

Local model considering 1 g Load = 76 kg/mm

After applying 76 kg/mm load to Local model i.e. plate with hole, we get maximum stress

of magnitude 22.6 kg /mm2.

Case 4: 1.25 g

Local model considering 1.5 g Load = 114 kg/mm

Local model considering 1.25 g Load = 95 kg/mm

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After applying 95 kg/mm load to Local model i.e. plate with hole, we get maximum stress

of magnitude 28.2 kg /mm2.

Case 5: 1.5 g

Local model considering 1.5 g Load = 114 kg/mm

After applying 114 kg/mm load to Local model i.e. plate with hole, we get maximum

stress of magnitude 33.8 kg /mm2.

Case 6: 1.75 g

Local model considering 1.5 g Load = 114 kg/mm

Local model considering 1.75 g Load = 133 kg/mm

After applying 133 kg/mm load to Local model i.e. plate with hole, we get maximum

stress of magnitude 37.5 kg /mm2.

For different g condition maximum stress is different, hence it is calculated for

each range. Initially for 1.5 g and load 114 kg/mm, maximum stress obtained is 54

kg/mm2. By using relation with 1.5 g range other range stress can be calculated as shown

above.

7.2 CALCULATION FOR STRESS AND STRESS RATIO:

1. Range 0.5 g to 0.75 g:

σmax = 16.9 kg/mm2

σmin = 11.3 kg/mm2

σ

=

= 22.26 kg/mm2

σ

=

= 14.88 kg/mm2

σamp =

= 3.69 kg/mm2

In ksi

σmax =

= 31.8 ksi

σmin =

= 21.25 ksi

σamp =

= 5.27 ksi

Stress ratio = R=

= 0.6682

2. Range 0.75 g to 1g:

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σmax = 22.9 kg/mm2

σmin = 16.9 kg/mm2

σ

=

= 29.77 kg/mm2

σ

=

= 22.26 kg/mm2

σamp =

= 3.755 kg/mm2

In ksi

σmax =

= 42.5 ksi

σmin =

= 31.8 ksi

σamp =

= 5.36 ksi

Stress ratio = R=

= 0.7482

3. Range 1 g to 1.25 g:

σmax = 28.2 kg/mm2

σmin = 22.6 kg/mm2

σ

=

= 37.15 kg/mm2

σ

=

= 29.77 kg/mm2

σamp =

= 3.69 kg/mm2

In ksi

σmax =

= 53.07 ksi

σmin =

= 42.52 ksi

σamp =

= 5.27 ksi

Stress ratio = R=

= 0.8

4. Range 1.25 g to 1.5 g:

σmax = 33.8 kg/mm2

σmin = 28.2 kg/mm2

σ

=

= 44.53 kg/mm2

σ

=

= 37.15 kg/mm2

σamp =

= 3.69 kg/mm2

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In ksi

σmax =

= 63.61 ksi

σmin =

= 53.07 ksi

σamp =

= 5.27 ksi

Stress ratio = R=

= 0.83

5. Range 0 g to 1.5 g:

σmax = 33.8 kg/mm2

σmin = 0 kg/mm2

σ

=

= 44.53 kg/mm2

σ

=

= 0 kg/mm2

σamp =

= 22.26 kg/mm2

In ksi

σmax =

= 63.61 ksi

σmin =

= 0 ksi

σamp =

= 31.80 ksi

Stress ratio = R=

= 0

6. Range -0.5 g to 1.5 g:

σmax = -11.3 kg/mm2

σmin = 33.8 kg/mm2

σ

=

= 44.53 kg/mm2

σ

=

= -14.88 kg/mm2

σamp =

= 29.705 kg/mm2

In ksi

σmax =

= 63.61 ksi

σmin =

= -21.25 ksi

σamp =

= 42.43 ksi

Stress ratio = R=

= -0.33

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Fig 7.1: Graph for number cycles to failure.

Above fig 7.1 is for design purposes is called master diagram which accumulates

fatigue data under different mean stresses and presents each line as the fatigue life under

the net of maximum and minimum stresses in addition to mean stress and alternating

stress as the reference axises. It is used to check the maximum and minimum stress

directly. Define R is the ratio of minimum stress to the maximum stress. Alternatively,

define A is the ratio of alternating stress to mean stress.

Miner's rule assumes the fatigue life is consumed by the linear combination of

different portion of stress state, both cycles and magnitude. This approximation, which is

simple and straight forward, does not take the sequences of loading history into account.

For example, a serial of high stress loading, which weaken the material, followed by a

serial low stress loading may cause more damage than a serial of low stress loading

followed by a serial of high stress loading. But Miner's rule cannot catch this effect.

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Sl no

Range

Stress ratio(R)

Stress amp(ksi)

Cycles

1

0.5g to 0.75g

0.6682

5.27

infinite

2

0.75g to 1g

0.75

5.36

Infinite

3

1g to 1.25g

0.8

5.27

Infinite

4

1.25g to 1.5 g

0.83

5.27

infinite

5

0 to 1.5 g

0

31.80

2.5*104

6

-0.5g to 1.5g

-0.33

42.43

13750

Table 7.2: No of cycles and stress ratio

Table 7.2 gives number of cycles to failure for different g range. It is obtained by

fig 7.1 by using stress ratio, mean stress and alternating stress. Stress ratio, mean stress

and alternating stress is calculated in above section.

Range 1: 0 to 1.5g

1=

= 0.002

Range 2: -0.5 g to 1.5 g

2=

= 0.007

Total damage accumulated is =

1 +

2

= 0.002+0.007

= 0.009

Total damage accumulated is 0.009, which is less than 1. Therefore a crack will

not get initiated from the location of maximum stress in the landing gear well beams

structure for given load spectrum. Hence total damage is 0.009 for 1 block of loading or

for 100 flights. One flight is considered 10 flying hours which eventually means 100

flights as 1000 flying hours.

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For damage to become critical (D= 1), the number of blocks required is 111.11

blocks or 111110 hours. Hence it is advised to meet the wing structure components

maintenance at least by this required time.

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CONCLUSION

Stress analysis of the Landing gear well beams is carried out and maximum stress

is identified near rivet location at fixed end which is found out to be lower than

yield strength of the material.

Normally the fatigue crack initiates in a structure where there is maximum tensile

stress is located. The fatigue calculation is carried out for the prediction of the

structural life of landing gear well beams. Since the damage accumulated is less

than the critical damage in the well beams structure is safe from fatigue

considerations.

Life of the particular region in landing gear well beams structure is predicted to

become critical and found out to be 111110 flying hours or 111.11 blocks, hence

advised to conduct the maintenance without fail during this period. Fatigue crack

growth analysis can be carried out in the other parts of the landing gear well

beams structure.

In the future work damage tolerance evaluation and structural testing of the

landing gear well beams structure can be carried out for the complete validation of

all theoretical calculations. As well as beam structure optimization can also be

carried out to meet the appropriate factor of safety of landing gear beam section.

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SCOPE FOR FUTURE WORK

The same work can be extended with the modifications of the material in use with

the stress and fatigue properties are more of the materialist in nature.

One can vary cross-section the beams and can perform stress analysis.

Similarly different loading condition can be considered for further analysis. These

are future scope of work which can give the strong knowledge of the failure

analysis like failure prediction and critical usage of materials or part.

Similar analysis can be carried out by using composite material and result may be

compared with conventional materials.

Analysis can for carried for different loads and boundary condition.

STRESS ANALYSIS OF THE LANDING GEAR- WELL BEAMS AND DAMAGE

CALCULATION DUE TO LANDING CYCLES

Dept of Mechanical Engineering, TOCE Page 57

REFERENCE

[1]. A. Ramesh Kumar, S. R. Balakrishnan and S. Balaji ― Design Of An Aircraft

Wing Structure For Static Analysis And Fatigue Life Prediction‖ International

Journal of Engineering Research & Technology Vol. 2 Issue 5, May – 2013 ISSN:

2278-0181

[2]. W Kuntjoro, AMH Abdul Jalil and J Mahmud(2012) ―Wing Structure Static

Analysis using Superelement‖ International Symposium on Robotics and

Intelligent Sensors 2012 (IRIS 2012)

[3]. K. Mookaiya, S. Balaji and S. R. Balakrishnan ―Crack Growth Analysis In

Aircrft Wing Lug Section And Fatigue Life Estimation‖ International Journal of

Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 2 Issue 6,

June - 2013

[4]. P.Mohanraj1, S. Balaji2, S. Senthilkumar3 ―Fatigue Analysis In Aircraft Landing

Gear Axle Shaft To Develop The Life Cycles‖ International Journal of

Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 2 Issue 6,

June - 2013

[5]. Stevan Maksimović ―Fatigue Life Analysis of Aircraft Structural Components‖,

Scientific-Technical Review,Vol.LV,No.1,2005

[6]. Slobodanka Boljanovic and Stevan Maksimovic ― Initial Fatigue Life Predictions

of a Notched Structural Components Under Variable Amplitude Loading‖ 15-

17,2004 BOOK OF PAPERS Printing Faculty of Mathematics, University of

Belgrade 1 - 15

[7]. Katarina Maksimović ―Fatigue Crack Growth Analysis of Damaged Structural

Components Under Mode-I and Mixed Modes‖ Scientific Technical

Review,Vol.LIX,No.1,2009

[8]. Harish E.R.M, Mahesha.K, and Sartaj Patel ― Stress Analysis for Wing

Attachment Bracket of a six seater Transport Airframe Structure‖ International

Journal of Innovative Research in Science, Engineering and Technology Vol. 2,

Issue 7, July 2013

STRESS ANALYSIS OF THE LANDING GEAR- WELL BEAMS AND DAMAGE

CALCULATION DUE TO LANDING CYCLES

Dept of Mechanical Engineering, TOCE Page 58

[9]. S. Maksimović, Z. Burzić, K. Maksimović ‖FATIGUE LIFE ESTIMATION OF

NOTCHED STRUCTURAL COMPONENTS: Computation and Experimental

Investigations‖.

[10]. Marija Blažić, Mirko Maksimović Ivana Vasović and Yasmina Assoul ―Stress

Intensity Factors for Elliptical Surface Cracks in Round Bars and Residual Life

Estimation‖ Scientific Technical Review, 2011,Vol.61,No.1

[11]. Pauls. Veers sandia ―An Approach to the Fatigue Analysis of Vertical Axis

Wind Turbine Blades‖ published by natlonal laboratories albuquerque, new

mexico 87185 and livermore, california 94550.

[12]. SHUN-PENG ZHU, HONG-ZHONG HUANG* AND ZHONG-LAI WANG

published ―Fatigue Life Estimation Considering Damaging and Strengthening of

Low amplitude Loads under Different Load Sequences Using Fuzzy Sets

Approach‖ School of Mechatronics Engineering, University of Electronic Science

and Technology of China, Chengdu, Sichuan, 611731, China.

[13]. ―Literature Review on Aircraft Structural Risk and Reliability Analysis‖

published by Yu Chee Tong Airframes and Engines Division Aeronautical and

Maritime Research Laboratory.

[14]. ―Structural Stress Analysis” from Goddard Space Flight Center (GSFC), NASA.

[15]. Dr Stevan Maksimović * Marija Blažić and Mirko Maksimović”DESIGN OF

CONSTRUCTIONS WITH RESPECTS TO FATIGUE AND FRACTURE

MECHANICS” Paper number: 8(2010)3,184, 181-188

[16]. A Statistical Analysis of the Aircraft Landing Process‖ published by Babak

Ghalebsaz-Jeddi, George L. Donohue, John F. Shortle.

[17]. ―Analytical Fuselage and Wing Weight Estimation of Transport Aircraft‖

published by Mark D. Ardema, Mark C. Chambers, Anthony P. Patron, Andrew S.

Hahn, Hirokazu Miura, and Mark D. Moore.

[18]. Dr. M. Neubauer, G. Günther AIRCRAFT LOADS DaimlerChrysler Aerospace

GmbH Military Aircraft, MT22, Postfach 80 11 60 81663 Munich, Germany

Paper presented at the RTO AVT Lecture Series on 13-16 November 2000, and

published in RTO EN-015.

[19]. Vinod S. Muchchandi1, S. C. Pilli2 Design and Analysis of A Spar Beam For

The Vertical Tail of A Transport Aircraft International Journal of Innovative

Research in Science, Engineering and Technology Vol. 2, Issue 7, July 2013

STRESS ANALYSIS OF THE LANDING GEAR- WELL BEAMS AND DAMAGE

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Dept of Mechanical Engineering, TOCE Page 59

APPENDIX

MSC SOFTWARE

STRUCTURAL ANALYSIS:

It has been nearly 50 years since we created the world's first structural analysis

program, Nastran. Today MSC Software continues its long history by continuously

developing best-in-class structural analysis tools for all types of engineering applications.

MSC Software provides a family of high performance solutions for FEA that meet

the needs of experienced experts and designers, new engineers, and everyone in between.

These solutions help companies meet their business challenges by helping engineers gain

deeper insight in their products through virtual testing. Engineers using MSC's structural

analysis programs are able to evaluate many different types of designs, giving high

confidence that the final design will successfully meet prescribed requirements before the

physical product is built.

From single components to large complex systems, from linear static to highly

non-linear dynamic problems, MSC's structural analysis capabilities are built to grow

with your business, optimize your cost of ownership, and support you in achieving your

goals.

DESCRIPTION ABOUT SOFTWARE USED

MSC NASTRAN:

MSC Nastran is a multidisciplinary structural analysis application used by

engineers to perform static, dynamic, and thermal analysis across the linear and nonlinear

domains, complemented with automated structural optimization and award winning

embedded fatigue analysis technologies, all enabled by high performance computing.

Engineers use MSC Nastran to ensure structural systems have the necessary

strength, stiffness, and life to preclude failure (excess stresses, resonance, buckling, or

detrimental deformations) that may compromise structural function and safety. MSC

Nastran is also used to improve the economy and passenger comfort of structural designs.

STRESS ANALYSIS OF THE LANDING GEAR- WELL BEAMS AND DAMAGE

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Dept of Mechanical Engineering, TOCE Page 60

Manufacturers leverage MSC Nastran’s unique multidisciplinary approach to

structural analysis at various points in the product development process. MSC Nastran

may be used to:

Virtually prototype early in the design process, saving costs traditionally associated with

physical prototyping.

Remedy structural issues that may occur during a product’s service, reducing downtime

and costs.

Optimize the performance of existing designs or develop unique product differentiators,

leading to industry advantages over competitors.

MSC Nastran is based on sophisticated numerical methods, the most prominent

being the Finite Element Method. Nonlinear FE problems may be solved either with built-

in implicit or explicit numerical techniques. A number of optimization algorithms are

available, including MSCADS and IPOPT. The fatigue capability in MSC Nastran has

been developed jointly by nCode International Ltd. and MSC Software.

MSC Nastran Advantages:

Multidisciplinary Structural Analysis.

Structural Assembly Modeling.

Automated Structural Optimization.

Event Simulation.

High Performance Computing.

FIG 1: Example of MSC Nastran Software.

STRESS ANALYSIS OF THE LANDING GEAR- WELL BEAMS AND DAMAGE

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Dept of Mechanical Engineering, TOCE Page 61

MSC PATRAN:

MSC Patran is the world's most widely used pre/post-processing software for

Finite Element Analysis (FEA), providing solid modeling, meshing, analysis setup and

post-processing for multiple solvers including MSC Nastran, Marc, Abaqus, LS-DYNA,

ANSYS, and Pam-Crash.

Patran provides a rich set of tools that streamline the creation of analysis ready

models for linear, nonlinear, explicit dynamics, thermal, and other finite element

solutions. From geometry cleanup tools that make it easy for engineers to deal with gaps

and slivers in CAD, to solid modeling tools that enable creation of models from scratch,

Patran makes it easy for anyone to create FE models. Meshes are easily created on

surfaces and solids alike using fully automated meshing routines, manual methods that

provide more control, or combinations of both. Finally, loads, boundary conditions, and

analysis setup for most popular FE solvers is built in, minimizing the need to edit input

decks.

Patran's comprehensive and industry tested capabilities ensure that your virtual

prototyping efforts provide results fast so that you can evaluate product performance

against requirements and optimize your designs.

Capabilities:

Direct Access of CAD Geometry.

Advanced Geometry Creation, Editing and Feature Recognition.

Support for Multiple FEA Solvers.

Post-processing and Reporting Tools for Easy Results Evaluation.

Patran Command Language.

Fig 2: Example of MSC Patran Software.

INTERNATIONAL JOURNAL OF RESEARCH IN AERONAUTICAL AND MECHANICAL ENGINEERING

Vol.2 Issue.5,

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Karthik Goud R V , Trupti P Wani

61

ISSN (ONLINE): 2321-3051

INTERNATIONAL JOURNAL OF RESEARCH IN

AERONAUTICAL AND MECHANICAL ENGINEERING

STRESS ANALYSIS OF THE LANDING GEAR-WELL BEAMS AND

DAMAGE CALCULATION DUE TO LANDING CYCLES

Karthik Goud R V

1

, Trupti P Wani

2

1

PG student, M .Tech (Machine Design), The Oxford College of

engineering,Bangalore,karthikrv09@gmail.com

2

Asst. prof, Mechanical department, The Oxford College of engineering, Bangalore, wani.trupti@gmail.com

Author Correspondence: PN 57, Bhuvanagiri colony, sirguppa road, Bellary.

8867224289,karthikrv09@gmail.com

Abstract

Landing gear is a structure, which supports the aircraft on the ground. Landing gear structure

experiences the load during take-off and landing of the aircraft. These loads are transferred to the airframe

through landing gear beams. Wing box near the root will have cutout at the bottom surface to accommodate

the retraction of the landing gears. Landing loads are absorbed by the landing gears and diffused to the larger

area of the wing through connecting members. In the current project two landing gear beams with a root rib

are considered for the analysis. On either sides of the cutout region landing gear beams are used to transfer

the landing load from landing gears to the wing and fuselage structure. Landing gear beams are in the span

wise direction of the wing. Linear static analysis of the beams along with the root rib will be carried out to

identify the fatigue critical location in the structure. Local analysis will be carried to capture the stress

concentration and stress distribution near the high stress location. It is very rare that these structural members

will fail by static over load. Due fluctuating loads during the service fatigue cracks will get initiated at the

high tensile stress location. Landing gear beams will experience constant amplitude load cycles because of

every landing during service. Fatigue life to crack initiation will be calculated using Miner’s rule based on the

S-N data of the material being used.

Keywords

: Stress analysis, Finite element method, Fatigue, Fatigue life estimation, Crack initiation.

1. Introduction

An aircraft fly using lift generated by the wing as it is pushed by the thrust developed by the jet engine. Earlier

major focus of structural design in the early development of aircraft was on strength. But at present days

structural designers also deal with fatigue life, corrosion resistance, maintenance, producability and structural

integrity. The rigidity of wing is provided by the spar beams and ribs which gives support to the aircraft

structure. Now a day’s aircraft structures are designed using a semi-monocoque structure concept. It consists of

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load carrying frames, longerons and skin which are in turn supported by spars and ribs members. An aircraft is

to be designed in such a way that it should be light in weight and strong enough to withstand loads acting on it.

An aircraft is subjected to various kinds of loads and forces during takeoff, landing and in flight. These loads

cause high stress in the aircraft structure. The main aim of design is to reduce or completely eliminate stress

concentration, detect critical crack region, arrest crack, and avoid failure of the component under service life of

an aircraft.

Stress analysis is used to locate the critical region in the structure where there is a possibility for the

crack to occur. Stress analysis gives the maximum magnitude of stress in the structure. Crack initiate at the

region of maximum stress.

Fatigue is experienced by the material when it is subjected to repeated loading both cyclic and non

cyclic. Fatigue is progressive and localized structural damage that happens when a material is subjected to

cyclic loading. Fatigue cracks are caused generally by tensile stress but sometimes can occur by compressive

stress also. Fatigue life is influenced by various factors such as surface roughness, temperature, residual stress,

microstructure of material used. Fatigue is a cumulative process, it cannot be reversed. Fatigue failure can be

avoided by various method like fail safe approach, damage tolerant design, choosing correct material etc.

1.1 SOFTWARE DISCRIPTION

Software used in this work is MSC Patran and MSC Nastran.

MSC Patran: It is graphical software pre and post processor used for finite element analysis. It is widely used

in aeronautical industry. It easy to use and gives efficient result. Here three dimensional models can be

converted into two dimensional models. The solid model can be meshed using various elements like tria, quad,

hex etc. material properties and boundary condition can be assigned to the finite element model.

MSC Nastran: It is developed by NASA and later acquired by MSC. It is a finite element solver. It does not

have the meshing capability. MSC Nastran is commonly utilized for performing structural analysis. It is widely

used in aerospace and automobile industries. We can perform various analyses such as dynamic, rotor

dynamic, non linear thermal, impact and fatigue analysis using these software.

1.2 MODEL, MATERIAL PROPERTIES, LOAD CALCULATION AND BOUNDARY

CONDITION:

Fig -1: Model Landing Gear Well Beams

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The material taken for the landing gear wells beams is assumed to be made of Aluminium Alloy AA 2024

T351 and material properties of the Aluminium Alloy AA 2024 T351 are taken as

Young's Modulus 7000 MPa

Poisson's Ratio 0.3

Yield Strength 324. MPa

Ultimate Tensile Strength 427. MPa

Load Factor 1.5 G

Load calculation:

Type of aircraft: 13 seater aircraft

Total weight of aircraft: W= 6.1 ton = 6100 kg

Fig 2: Typical Position Of Landing Gear In Aircraft.

Base =B= 6.465 m

F

m

=

H

cg

=1.88 m

F

mdy

=

aT = vertical sink rate.

Hcg = Height from ground to center of gravity.

F

mdy

= 2660.79 kg

Total load on main landing gear during normal touch down:

F = 2660.79 + 6100 = 8760.79 kg

Force per landing gear : F = 8760.79/2 = 4380.4 kg

Force acting on pin diameter: =46.4775

Force acting on each side of pin: = 23.23

The flange region of rib is constrained with six degree of freedom.

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1.3 FINITE ELEMENT ANALYSIS

The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary

value problems for differential equations. Finite element method uses variational methods (the calculus of

variations) to minimize an error function and produce a stable solution. The main idea that connecting many

tiny straight lines can approximate a larger circle, in the same way FEM encompasses all the methods for

connecting many simple element equations over many small sub domains, named finite elements, to

approximate a more complex equation over a larger domain.

The elements used for meshing of landing gear well beam are QUAD 4 and TRIA. But most of the elements

are QUAD 4 type and only few are TRIA elements. Using more QUAD elements will more accurate result.

Fig 3: Finite Element Model Of LG Well Beams.

2. STRESS ANALYSIS:

After applying the load and boundary condition and running the analysis stress in the model is found.

Maximum stress is found at the region near the rivet location at the beam and rib part neat the fixed end. The

maximum value of stress is found to be 94.2 kg/mm

2

near the rivet location. Since the rivet is not simulated,

the stress value is taken little away from the rivet to get average value of stress which is found to be 22.725

kg/mm

2

.

Fig 5: Meshed Model

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Fig4: Maximum Stress In The Model.

Fig 5: Two Dimentional Model and Analysis Model

From global stress analysis we find the maximum stress location. Mostly crack initiates at the region

of maximum stress location, since tensile stress is high at that region. In this model maximum stress is found

to be at the rivet location. We need to know the stress around the rivet location. For that we need to know

the stress at elements around the maximum stress location. We use marker option for knowing the stress of

individual element and take average stress, since stress is distributed unevenly in the model.

2.2: THEORETICAL VERIFICATION:

For local model analysis, a plate with hole is taken of length = 50mm, width = 25mm and thickness = 8mm.

Nominal stress acting on global model is 14.9+14.5+29.3+32.2 = 22.725kg/mm

2

Load acting on the local model:

Stress average = Load / Area

Load = Stress avg*Area

= 22.725*25*5

= 2840.625 kg

One side of plate with hole is fixed and other end load applied is 2840.6/25= 113.625 kg/mm2

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Fig 7: Mesh and boundary condition applied to local model

.

Fig 8: Local Analysis

The magnitude of maximum stress in local model is 54 N/mm

2

. now we have to compare the stress result with

theoretical value for validation of analysis result.

Fig 9: No Of Cycles To Failure.

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The fig 9 gives the stress concentration for plate with hole. Here y axis represents stress concentration and x

axis represents d/w ratio. Where d is diameter of hole and w is width of the plate. Ratio is calculated and is

checked in the graph and stress concentration is found out.

From the S-N curve of plate with a hole of d/w ratio 0.2.

d/w = 5/25 = 0.2.

Kt = 2.5

Kt= max stress/nominal stress

Max stress = Kt* nominal stress

= 22.725*2.5

Max stress = 56.8 kg/mm2.

3. FATIGUE LIFE ESTIMATION

Normally aircraft landing gear beams experiences variable spectrum loading during takeoff and landing. A

typical transport aircraft is considered for flight load spectrum is for the fatigue analysis of the landing gear

well beams structure. Calculation of fatigue life estimation is carried out by using Miner`s Rule. Damage

calculation is carried out for the full service life of the aircraft. The load factor “g” is defined as the ratio of the

lift of an aircraft to its weight. This gives a measure of the load which aircraft experiences. As we know the

maximum stress value obtained from the analysis is corresponding to 1.5 g condition.

Therefore the stress value corresponding to 1.5 g condition is obtained as 53.7 N/mm

2

. Correction factors

for fatigue life calculations of landing gear well beams structure are

• Surface Correction Factor = 1

• Loading Type = 1

• Design Reliability = 0.897

• Surface Roughness = 0.8

Load spectrum for fatigue life estimation:

Table 1: Variable Load Spectrum for typical aircraft

Sl no

G range

Cycles

1

0.5g to 0.75g

57000

2

0.75g to 1g

28000

3

1g to 1.25g

24000

4

1.25g to 1.5g

18000

5

0 to 1.5 g

50

6

-0.5 g to 1.5g

100

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Fig 10: Graph for No of Cycles To Failure

Table 2: Range \, stress ratio and cycles

Sl no

Range

Stress

ratio(R)

Stress

amp(ksi)

Cycles

1

0.5g to

0.75g

0.6682

5.27

infinite

2

0.75g to

1g

0.75

5.36

Infinite

3

1g to

1.25g

0.8

5.27

Infinite

4

1.25g to

1.5 g

0.83

5.27

infinite

5

0 to 1.5 g

0

31.80

2.5*10

4

6

-0.5g to

1.5g

-0.33

42.43

13750

Range: 0 to 1.5g

Ni/Nf = 50/25000 = 0.002

Range: -0.5g to 1.5 g

Ni/Nf = 100/13750 = 0.007

Total damage accumulated is 0.002+0.007 = 0.009

Total damage accumulated is 0.009 which is less than 1. Hence the structure is safe i.e. structure does not fail

due to fatigue with in service life.

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4. CONCLUSIONS

Stress analysis of the Landing gear well beams is carried out and maximum stress is identified near rivet

location at fixed end which is found out to be lower than yield strength of the material. Normally the fatigue

crack initiates in a structure where there is maximum tensile stress is located. The fatigue calculation is carried

out for the prediction of the structural life of landing gear well beams. Since the damage accumulated is less

than the critical damage in the well beams structure is safe from fatigue considerations. Life of the particular

region in landing gear well beams structure is predicted to become critical and found out to be 111110 flying

hours or 111.11 blocks, hence advised to conduct the maintenance without fail during this period. Fatigue

crack growth analysis can be carried out in the other parts of the landing gear well beams structure. In the

future work damage tolerance evaluation and structural testing of the landing gear well beams structure can be

carried out for the complete validation of all theoretical calculations. As well as beam structure optimization

can also be carried out to meet the appropriate factor of safety of landing gear beam section

References

1) Adarsh Adeppa, Patil M S and Girish K E (2012), “Stress Analysis and Fatigue Life Prediction for Splice

Joint in an Aircraft Fuselage through an FEM Approach”, International Journal of Engineering and Innovative

Technology (IJEIT), Vol. 1, No. 4, pp. 142-144.

2) Maksimović,S., Boljanović,S. and Maksimović,K.: Improved Numerical Procedure in Fatigue Life

Prediction of Structural Components Under Variable Amplitude Loads, IFC-8-Fatigue 2002, Stocholm, 2–

7.June 2002, Vol.1, pp.675–682.

3) S Sarath, Jason Cherian Issac and K E Girish (2013) “Analysis of the Wingbox with Spliced Skin and

Estimation of the Fatigue Life for the Wingbox” International Journal of Mechanical Engineering and Robotics

Research Vol. 2, No. 2, April 2013 (155-163).

[4] Jaap Schijve (2009), “Fatigue Damage in Aircraft Structures Not Wanted but Tolerated”,

International Journal of Fatigue, Vol. 31, No. 6, pp. 998-1011.

[5] F.H.Darwish, G.M.Atmeh, Z. F. Hasan Design (2012) “Analysis and Modelling of a General Aviation

Aircraft” Volume 6, Number 2, ISSN 1995-6665 Pages 183 – 191.

[6] Michael Bauccio (1993), ASM Metals Reference Book, 3rdEdition, ASM International, Materials Park,

OH.

A Brief Author Biography

Karthik Goud R V – is a PG scholar in machine design at The Oxford college of Engineering, Bangalore.

Trupti P Wani – is Asst.Prof in mechanical department at The Oxford college of Engineering, Bangalore.