CHAPTER 1 INTRODUCTION
1.1 AIRCRAFT WING The aircraft wings are the primary lift producing device for an aircraft. The aircraft wings are designed aerodynamically to generate lift force which is required in order for an aircraft to fly. Besides generating the necessary lift force, the aircraft wings are used to carry the fuel required for the mission by the aircraft, can have mounted engines or can carry extra fuel tanks or other armaments.
The basic goal of the wing is to generate lift and minimize drag as far as possible. When the airflow passes the wing at any suitable angle of attack, a pressure differential is created. A region of lower pressure is created over the top surface of the wing while, a region of higher pressure is created below the surface of the wing. This difference in pressure creates a differential force which acts upward which is called lift.
In modern commercial, fighter and jet aircrafts, the aircraft wings are not only designed to provide the necessary lift during the different phases of flight, but also have a variety of other roles and functions. In commercial jet aircrafts, the aircrafts wings are used as the primary storage system for the jet fuel required for the flight. The jet fuel is normally carried in a structure placed inside the outer surface of the wing called a wing box. The fuel carried inside the wing box directly delivers fuel to the jet engines.
Modern commercial airplanes like the Boeing 747 and the Airbus A380 amongst many other aircrafts also have podded engines which are placed on the wing. During the flight, the aircraft wing has to deal with aerodynamic, gust, wind and turbulence loads. Also, the aircraft wings have to deal with aero-elastic and structural loads as well. Therefore, the aircraft wings must be designed structurally and aerodynamically well for providing good overall performance in all phases of flight.
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1.1.1 Aircraft Wing Configuration Wings are airfoils that, when moved rapidly through the air, create lift. They are built in many shapes and sizes. Wing design can vary to provide certain desirable flight characteristics. Control at various operating speeds, the amount of lift generated, balance, and stability all change as the shape of the wing is altered.
Both the leading edge and the trailing edge of the wing may be straight or curved, or one edge may be straight and the other curved. One or both edges may be tapered so that the wing is narrower at the tip than at the root where it joins the fuselage. The wing tip may be square, rounded, or even pointed. Figure 1-1 shows a number of typical wing leading and trailing edge shapes.
Figure 1-1: Various wing design shapes yield different performance
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The wings of an aircraft can be attached to the fuselage at the top, mid-fuselage, or at the bottom. They may extend perpendicular to the horizontal plain of the fuselage or can angle up or down slightly. This angle is known as the wing dihedral. The dihedral angle affects the lateral stability of the aircraft. Figure 1-2 shows some common wing attach points and dihedral angle.
Figure 1-2: Wing attach points and wing dihedrals
1.1.2 Wing Structure
The wings of an aircraft are designed to lift it into the air. Their particular design for any given aircraft depends on a number of factors, such as size, weight, use of the aircraft, desired speed in flight and at landing, and desired rate of climb. The wings of aircraft are designated left and right, corresponding to the left and right sides of the operator when seated in the cockpit. [Figure 1-3]
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Figure 1-3: ―Left” and “right” on an aircraft are oriented to the perspective of a pilot sitting in the cockpit
The internal structures of most wings are made up of spars and stringers running span wise and ribs and formers or bulkheads running chord wise. The spars are the principle structural members of a wing. They support all distributed loads, as well as concentrated weights such as the fuselage, landing gear, and engines. It also transfers the stresses to the wing ribs. The ribs, in turn, transfer the loads to the wing spars. [Figure 1-4]
Figure 1-4: Wing structure nomenclature
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In general, wing construction is based on one of three fundamental designs: 1. Mono spar 2. Multi spar 3. Box beam Modification of these basic designs may be adopted by various manufacturers.
The mono spar wing incorporates only one main span wise or longitudinal member in its construction. Ribs or bulkheads supply the necessary contour or shape to the airfoil. Although the strict mono spar wing is not common, this type of design modified by the addition of false spars or light shear webs along the trailing edge for support of control surfaces is sometimes used. The multi spar wing incorporates more than one main longitudinal member in its construction. To give the wing contour, ribs or bulkheads are often included.
The box beam type of wing construction uses two main longitudinal members with connecting bulkheads to furnish additional strength and to give contour to the wing. [Figure 1-5]
Figure 1-5: Box beam construction
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A corrugated sheet may be placed between the bulkheads and the smooth outer skin so that the wing can better carry tension and compression loads. In some cases, heavy longitudinal stiffeners are substituted for the corrugated sheets. A combination of corrugated sheets on the upper surface of the wing and stiffeners on the lower surface is sometimes used. Air transport category aircraft often utilize box beam wing construction.
1.2 WING SPARS Wing spars are long members which run from the root to the tip of the wing. Typically a wing has two spars, a front spar and a rear spar. – Multi-spar designs are used on larger wings and on military aircraft. Spars primarily carry the aerodynamic loads developed by the wing.
Figure 1-6: Wing Spars Construction
The wing spars are the main load carrying structural member of the aircraft wing. The wing spars are used to carry the loads that occur during the flight (flight loads) as well as carry the weight of the aircraft wing while on the ground (ground loads).
The wing spars run throughout the span of the wing from the root to the tip and can be placed perpendicularly or at an angle. Commercial aircrafts sometimes have less number of wing spars than fighter aircrafts, this is due to the fact that, the fighter aircrafts have to deal with much higher flight loads. The structural and forming members of the aircraft wing known as ―wing ribs‖ are also attached to the wing spars. The wing ribs are aerodynamically shaped and thus provide the aircraft wing with a characteristic airfoil shape. The number of wing spars in a wing varies with values between one and more. Other load carrying structural members like the stressed skin construction also helps in carrying the flight loads.
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When the aircraft is on the ground, the weight of the gravity pulls the wings downward. This gravitational load is also carried by the wing spars running through the wing span. If the majority of the load and forces is carried by a single spar in the aircraft wing, it is called as the ―main spar‖. Main spars are common in smaller lightweight aircrafts, where, the wing spar runs from the wing root to the wing tip.
A single aircraft wing (or a monoplane wing) basically acts like a cantilever beam. The wing spars are then used to carry the loads and forces acting on the monoplane wing structure. Wing box which is another important structural member that is placed inside the aircraft wing is attached to the wing spars and is used to provide the requisite stiffness and rigidity to the structure enabling it to carry different loads and forces in flight or in ground.
Aluminum is the most common material from which to construct wings, but they can be wood covered with fabric, and occasionally a magnesium alloy has been used. Moreover, modern aircraft are tending toward lighter and stronger materials throughout the airframe and in wing construction. Wings made entirely of carbon fiber or other composite materials exist, as well as wings made of a combination of materials for maximum strength to weight performance.
Spars may be made of metal, wood, or composite materials depending on the design criteria of a specific aircraft. Wooden spars are usually made from spruce. They can be generally classified into four different types by their cross sectional configuration.
Figure 1-7: Typical wooden wing spar cross-sections 7
As shown in Figure 1-7, they may be (A) solid, (B) box shaped, (C) partly hollow, or (D) in the form of an I-beam. Lamination of solid wood spars is often used to increase strength. Laminated wood can also be found in box shaped spars. The spar in Figure 1-7 (E) has had material removed to reduce weight but retains the strength of a rectangular spar. As can be seen, most wing spars are basically rectangular in shape with the long dimension of the cross-section oriented up and down in the wing.
Currently, most manufactured aircraft have wing spars made of solid extruded aluminum or aluminum extrusions riveted together to form the spar. The increased use of composites and the combining of materials should make airmen vigilant for wings spars made from a variety of materials. Figure 1-8 shows examples of metal wing spar cross-sections.
Figure 1-8: Examples of metal wing spar shapes
In an I–beam spar, the top and bottom of the I–beam are called the caps and the vertical section is called the web. The entire spar can be extruded from one piece of metal but often it is built up from multiple extrusions or formed angles. The web forms the principal depth portion of the spar and the cap strips (extrusions, formed angles, or milled sections) are attached to it. Together, these members carry the loads caused by wing bending, with the caps providing a foundation for attaching the skin. Although the spar shapes in Figure 1-8 are typical, actual wing spar configurations assume many forms. For example, the web of a spar may be a plate or a truss as shown in Figure 1-9.
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Figure 1-9: A truss wing spar
It could be built up from light weight materials with vertical stiffeners employed for strength. [Figure 1-10]
Figure 1-10: A plate web wing spar with vertical stiffeners
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It could also have no stiffeners but might contain flanged holes for reducing weight but maintaining strength. Some metal and composite wing spars retain the I-beam concept but use a sine wave web. [Figure 1-11]
Figure 1-11: A sine wave wing spar can be made from aluminum or composite materials
Additionally, fail-safe spar web design exists. Fail-safe means that should one member of a complex structure fail, some other part of the structure assumes the load of the failed member and permits continued operation. A spar with failsafe construction is shown in Figure 1-12.
Figure 1-12: A fail-safe spar with a riveted spar web
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This spar is made in two sections. The top section consists of a cap riveted to the upper web plate. The lower section is a single extrusion consisting of the lower cap and web plate. These two sections are spliced together to form the spar. If either section of this type of spar breaks, the other section can still carry the load. This is the fail-safe feature.
As a rule, a wing has two spars. One spar is usually located near the front of the wing, and the other about two-thirds of the distance toward the wing‘s trailing edge. Regardless of type, the spar is the most important part of the wing. When other structural members of the wing are placed under load, most of the resulting stress is passed on to the wing spar. False spars are commonly used in wing design. They are longitudinal members like spars but do not extend the entire span wise length of the wing. Often, they are used as hinge attach points for control surfaces, such as an aileron spar.
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CHAPTER-2 LITERATURE REVIEW 2.1 CONCEPT OF SPARS The wing spars are concerned; the wing spar position will be defined by ―point values on curve‖ along the root and tip of the tip of the wing. The point values on curve will range between 0 and 1. 0 means that the spar position will start at the leading edge while, 1 means that the spar position will start at the trailing edge.
There are two approaches for the construction of wing spars inside the wing model. One is that the spars run continuously throughout the wing across all the wing panels while the other is that the wing spars are placed along each wing panel separately and then they are joined together to each other. In either approach, it is important that it is not possible for two spars to intersect each other in any way. Furthermore, it is important that, all new spar positions along the root and the tip of the wing should be modified based on the position of the old spars. The wing spars will have a thickness associated with them, however, this thickness should not protrude inside the thickness of the wing panel skin.
2.2 DESIGN APPROACH The initial design was done using conventional design using strength of materials approach. Selection of the beam cross section is an important activity that was carried out using various cross sections and improving upon the same using iterations. Various iterations of the design were conducted with varying geometries and cross sections, before arriving at the optimized design of the beam with minimal weight, satisfying the given load conditions.
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2.3 A400M & A350 WING SPARS In three short years, GKN Aerospace has taken its wing spar manufacturing strategies to new heights by dramatically reducing part weight, process complexity and production cycle duration.
The GKN Aerospace (U.K.) factory in the Western Approach of the U.K. is dedicated to wing spar manufacturing. It produces the front and rear spars for the Airbus A400M military cargo transport and the rear spar for the Airbus A350. HPC covered A400M spar manufacturing in 2006, when it was produced at GKN‘s site on the Isle of Wight, U.K. Since then, A400M spar production has been transferred to the new dedicated spar facility in Western Approach to take advantage of synergies with the A350 spar operation and benefit from close proximity to the Airbus wing design center in U.K.
2.3.1 The A400M and A350 spars: Different by design Wing spars can be thought of as simple tapered C-shaped channels that make up the front and rear of the wing box. But this is an oversimplification, because it ignores the hidden complexities of the wing design. First, there is the shape of the wing, dictated by aerodynamic, structural and ground-clearance requirements. Close examination of the A350 spars reveals that the inner spar has a very significant curvature. This is because the A350 inner wing is formed into a curved gull-wing shape. By contrast, the A400M‘s wing is virtually straight, making the spar a simpler shape to manufacture.
The structural issues add further complexity to the spar layup, due to the very high load inputs that occur at various points along the length of the spar. Attachments points for the engines, main landing gear (on the A350 only, because the A400M has a fuselage-mounted main undercarriage), flaps and other control surfaces require localized increases in laminate thickness at the attachment points. In other attachment areas, sacrificial woven carbon is added under attachment points or, if the attached component is aluminum, a layer of woven glass is added.
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The length of the A350 spar is considerably longer, at 34m/111.5 ft, than the A400M spar, which measures only 19m/62.3 ft long. Further, the A400M spar is made in two sections, but the A350 spar is made in three.
The manufacturing strategies for each spar also differ, for several reasons: There were five years between the launch of the two programs; during that period the automation of prepare layup by automated fiber placement (AFP) made major progress. The customer changed the material specification from a conventional toughened epoxy to the latest-generation interlayer toughened epoxy. The shape of the A350 spar is much more complex. A more optimized design was desired in the A350 spar; weight savings in commercial applications is now a greater priority in a time period in which fuel savings have grown in importance. The A350‘s C-section spar‘s three segments average 11.5m/37.7 ft in length, with a thickness of 25 mm/0.08 ft at the root end, which tapers to just 5 mm/0.020 inch at the wing tip of the outermost segment. Their size and weight is difficult to convey in words and dimensions. To put it in perspective, the average person could lift one end of the outer spar.
2.4 COMPONENTS OF A400M OUTER WING BOX The figures in this section are representative of the Entry Into Service (EIS) configuration, but analysis requirements of MSN001 to MSN005 are also covered by this document. The outer wing box is a hybrid composite/metallic structure comprising of CFRP front and rear spars, 24 metallic ribs and CFRP upper and lower covers with co-bonded stringers. It transfers aerodynamic, propulsion and inertia loads to the fuselage via the centre wing box and provides structural stiffness to assure aero elastic and flight control performance.
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The interior of the outer wing box forms three sealed fuel tanks (one transfer tank and two engines feed tanks) and a surge tank at the outboard end of the wing. Fuel pressure loads are also carried by the outer wing box structure.
Engine nacelle loads are directly introduced to the outer wing box via three attachment brackets at each engine position. Provision is also made for the mounting of an air-to-air refueling (AAR) pod below the outer wing box outboard of the outer engine pylon. Figure 2-1 shows the general layout of the A400M wing, with the spar locations identified
Figure2-1: General layout of the A400M Outer Wing Box
2.4.1 Wing box loading The primary design load for a wing box is aerodynamic lift. Air pressure variation over the aerodynamic surfaces (covers) creates lift, which is transferred to the spars as vertical shear via the ribs. Spar structures transfer this lift as shear in the spar webs to the root joint, where loads are reacted by the weight of the fuselage. Complementary components of shear are reacted at the wing skins, leading to end load accumulation in the covers.
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The wing box also carry loads from fuel pressure, engine loads and leading and trailing edge attachment loads and other sources.
2.4.2 General description of A400M spar assembly
Front Spar: The front spar (Figure 2-2) is an inward facing C-section configuration similar to existing metallic Airbus spar designs. The basic C-section is manufactured with horizontal stiffeners used to prevent buckling of spar web. A splice joint at rib 10 is used to join the inner front spar to the outer front spar.
Figure 2-2: A400M front spar configuration 16
Rear Spar: The rear spar (Figure 3) uses an inward facing C-section configuration derived from existing metallic Airbus spar designs (similar to the front spar). The basic C-section is manufactured with vertical stiffeners and trailing edge structure used to prevent buckling of the spar web. A splice joint in rib bay 18 joins the inner rear spar and outer rear spar sections.
The inner rear spar is provided with a single horizontal stiffener to prevent buckling of the spar web.
Figure 2-3: A400M rear spar configuration
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CHAPTER-3 PROBLEM DEFINITION
3.1 IDENTIFICATION The wing spar provides the majority of the weight support and dynamic load integrity of cantilever monoplanes, often coupled with the strength of the wing box itself. Together, these two structural components collectively provide the wing rigidity needed to enable the aircraft to fly safely. Biplanes employing flying wires have much of the flight loads transmitted through the wires and inter plane struts enabling smaller section and thus lighter spars to be used.
The wing spars are subjected to a wide variety of aerodynamic, structural, turbulence, gust, wind, flight and ground loads. Some of the forces and loads that the wing spars carry are mentioned below,
Figure 3-1: Forces and moments acting on spar web
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1.
As the aircraft wing rests on the ground, gravity is acting on the wing. The wing weight is
been pulled down due to the gravitational forces acting on the structure and thus a bending moment is produced since, the wing roots are attached to the fuselage while, the wing tips are free. The wing spars running through the wing of the aircraft act as cantilever beams and take these bending loads. Furthermore, not only does the wing spars carry the weight of the wing while on the ground, modern commercial airplanes carry the fuel inside the wing in the wing box. Moreover, they also have mounted engines which are attached below the wing known as ―podded engines‟. 2.
The primary function of an aircraft wing is to generate lift. As, at a suitable angle of
attack, higher pressure exists on the bottom surface of the wing while, a lower pressure exists on the top surface of the wing, a pressure differential is created which results in generation of a differential force which is known as the lift. The lift force generated by the wings of an aircraft creates an upward bending moment. As the wing roots of an aircraft are attached to the fuselage, while, the wing tips are free, they rise upward. The wing spars are then used to resist this upward bending moment. As soon as the wing starts to generate lift, this flight load occurs that has to be carried by the wing spars. 3.
As the aircraft wing flies through the air, a drag force is generated. Drag is a necessary
consequence of flight in a medium such as air since, air or any other fluid has density. The drag increases with speed and at higher Mach numbers, the drag is considerably higher. These drag loads must also be resisted by the wing spars. 4.
The inertial loads must also be taken by the wing spars which act on the aircraft wing
such as the rolling inertial loads, which is generated as the aircraft rolls. 5.
The wing spars are under the effect of both bending and twisting moment. Due to
introduction of wash-out or wash-in and aerodynamic or geometric twist, the wing spars have to carry the twisting loads. Furthermore, due to deflection of the control surfaces such as the aileron, the twisting loads are felt by the wing spars which must be resisted. Moreover, twisting loads and moments are also introduced in the structure by the introduction of podded engines hanging below the wing. The thrust changes in these engines produce the twisting loads and moments.
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3.2 OBJECTIVE Determine the Spar locations with respect to chord length. Determine the dimensions for flange and web of the spars. Estimate the number of ribs and their positioning. To generate the CAD model of wing using the available data and calculate the Bending moment and Shear forces of the front and rear spars.
3.3 SCOPE OF THE PROBLEM Estimation of spar position. Dimension calculations of front and rear spars. Calculations for number of ribs and their positions. Profile creation of the wing using the given NACA standards Creation of the wing geometry using CATIA Analysis the front and rear spars using NASTRAN and PATRAN
3.4 INPUT DETAILS Root chord
:
2400 mm
Tip chord
:
700 mm
Semi Span length
:
5500 mm
Exposed Span
:
4750 mm
Airfoil (root)
:
NACA 64A1215
(Tip)
:
NACA 64A1210
Aircraft weight
:
14000 N
Lift Load
:
6g
Design Factor
:
1.5
Front Spar
:
18-25
Rear Spar
:
62-70
Given Spar Position (in % of chord length)
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3.5 DERIVED INPUT DETAILS Limit load
:
14000 * 6= 84000 N
Design Load
:
84000 * 1.5= 126000 N
Load on semi-span
:
126000 / 2= 63000 N
Exposed wing area
:
7.3625 E6 mm2
Pressure load on wing
:
63000 / 7.3625 E6 = 8556.87 E-6 N/mm2
3.6 WING GEOMETRY
Figure 3-2: Aircraft wing geometry
LEADING EDGE: The foremost edge of an aerofoil, especially a wing or propeller blade. TRAILING EDGE: The rear edge of a moving body, especially an aircraft wing or propeller blade. ROOT CHORD: The chord length of airfoil at Root of Airplane wing. TIP CHORD: The chord length of airfoil at Tip of Airplane wing.
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CHAPTER-4 NUMERICAL ANALYSIS
4.1 MAJOR STEPS INVOLVED
Figure 4-1: Wing area dividing sections
Steps involved in the analysis procedure: 1. Divide the wing area into number of divisions. 2. Calculate the chord length at each section. 3. Determine the C.G of each area. 4. Calculate the shear force, bending moment and Torque at the respective sections. 5. Shear force =pressure*area. 6. Bending moment=shear force*CG distance. 7. Torque = Shear force*Distance b/w CG and CP.
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4.2 ASSESMENT CRITERIA FOR WING SPARS The principal assessment criteria for laminated metallic components of the Trainer wing spar are: Shear force Bending moment Load distribution Moment of inertia Web thickness Torsion Mass Calculations Buckling Calculations Weight Calculations
These criteria are not necessarily applicable to all spar sub-components. The structural assessment must take into account degradation effects from environmental conditioning (moisture and temperature).
Knockdown factors for these are either incorporated within the tools or supplied for analytical methods. These factors must be applied if the load case requires it. Shear forces Unaligned forces pushing one part of a body in one direction, and another part the body in the opposite direction. When the forces are aligned into each other, they are called compression forces. An example is a deck of cards being pushed one way on the top, and the other at the bottom, causing the cards to slide. Another example is when wind blows at the side of a peaked roof of a home - the side walls experience a force at their top pushing in the direction of the wind, and their bottom in the opposite direction, from the ground or foundation.
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A crack or tear may develop in a body from parallel shearing forces pushing in opposite directions at different points of the body. If the forces were aligned and aimed straight into each other, they would pinch or compress the body, rather than tear or crack it.
Bending moment
A bending moment is a measure of the average internal stress induced in a structural element when an external force or moment is applied to the element causing the element to bend.
Figure 4-2: Shear Force and Bending moment representation on a beam
Moment of inertia:
Moment of inertia is the mass property of a rigid body that defines the torque needed for a desired angular acceleration about an axis of rotation. Moment of inertia depends on the shape of the body and may be different around different axes of rotation. A larger moment of inertia around a given axis requires more torque to increase the rotation, or to stop the rotation, of a body about that axis.
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Moment of inertia depends on the amount and distribution of its mass, and can be found through the sum of moments of inertia of the masses making up the whole object, under the same conditions. Torsion: In solid mechanics, torsion is the twisting of an object due to an applied torque. It is expressed in Newton meters (N·m) or foot-pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius. For shafts of uniform cross-section the torsion is:
T=
= Gθ
(4.1)
Figure 4-3: Torsion representation
Buckling : In science, buckling is a mathematical instability, leading to a failure mode. Theoretically, buckling is caused by a bifurcation in the solution to the equations of static equilibrium. At a certain stage under an increasing load, further load is able to be sustained in one of two states of equilibrium undeformed state or a laterally-deformed state.
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4.3 ANALYSIS PROCEDURE
Figure 4-4: Wing box sections
Chord length L 1= Lroot At section 2,
*x
(4.2)
L1 = 2400-((2400-700)/4750)*4275 L1 = 870 mm
Area of Trapezium
A1 = 0.5*(L1+Ltip)*h
(4.3)
A1 = 0.5*(870+700)*475 A1 = 373 E3 mm2
CG of Trapezoid Section = *
(4.4)
CG=475/3*((700+2*870)/ (700+870)) CG = 246 mm from Ltip Limit load
= 84000 N
Design Load
= Limit Load*Design factor
Design load on wing,
= 84000*1.5 = 1,26,000 N
Design load on semi-span wing,
= 63000 N
Pressure load on wing [P] = 8556.87 E-6 N/mm2
Load at Section 2, = P2+P1 = P*A2+P1 = 8557 E-6 * 453625 + 3190.65=7072.25 N
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Bending Moment At Section 2,
M2 = P2 * CG2 + P1 * (CG1 + L2)
(4.5)
M2 = 3881.6 * 230 + 3190.65 * (229 + 475) M2 = 3248260 N-mm
4.3.1 Shear Force By following the same procedure shown in above section about the loads on various sections of the wing we can estimate the Shear force distribution as
Table 1: Shear force distribution
And the above Shear force distribution can be expressed in graphical form as follows
Figure 4-5: Shear force distribution graph
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4.3.2 Bending Moment Distribution Bending moment varies as follows along the wing span as follows
Table 2: Bending moment distribution
The bending moment distribution is again represented in graphical form along with Wing profile as
Figure 4-6: Bending moment distribution graph
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4.3.3 Load Distribution Now we need to get the load distribution over Front and Rear spars and this can be done by calculating CP of the wing and we assume the position of Front spar at 25% from Leading edge and Rear spar is at 62% from Leading edge. Now we will calculate the same for chord length of 870mm Centre of Pressure, CP
= 45% of Chord Length
(C) from LE [870mm]
Front Spar Position
= 25% of C from LE [217.5mm]
Rear Spar Position
= 62% of C from LE [539.4mm]
Figure 4-7: Load distribution of Airfoil chord
Using the position of CP, a, b, c values for various chord lengths we get the values of Shear force and bending moment distributions over front and rear spars.
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4.3.4 Shear force & Bending moment distribution Shear Force on Front Spar
=
Load *
SFFS
=
3190.65 * (148/322)
SFFS
=
1466.507714 N
SFRS
=
3190.65-1466.507714
SFRS
=
1724.137447 N
SF on Front Spar
=
45.9627% of total load
SF on Rear Spar
=
54.03% of total load
At Section 1, Shear Force on Rear Spar
Moment is distributed in same ratio as that of the Shear force. Bending Moment on Front Spar, MFS
=
0.459627 * 730424.4194
MFS
=
335722.7846 N-mm
MRS
=
730424.4194 – 335722.7846
MRS
=
394701.6348N-mm
Bending Moment on Rear Spar,
Table 3: Shear force and bending moment distribution over Front spar
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(4.6)
Table 4: Shear force and bending moment distribution over Rear spar
4.4 MATERIAL PROPERTIES Material
:
AA 2024-T6
Ultimate tensile strength, σ
:
427 Mpa
Shear strength
:
283MPa
Density
:
2.79 E-6 kg/mm3
Young's Modulus, E
:
72400 Mpa
Poisson's Ratio
:
0.33
4.4.1 Moment Of Inertia (4.7) Where,
I = Moment of Inertia, in mm4 M = Bending Moment, in N-mm y = distance b/w neutral axis to top surface, in mm σ = Tensile strength, in Mpa
Now we calculate Moment of Inertia Distribution over the Front and Rear spar as follows Moment of Inertia on Front Spar, 31
IFS
=
IFS
=
44411.22998 mm4
Front spar: Table 5: Moment of Inertia distribution over Front spar
Moment of Inertia on Rear Spar, IRS
=
IRS
=
34154.879.36 mm4
Rear Spar : Table 6: Moment of Inertia distribution over Rear spar
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4.4.2 TORSION
Figure 4-8: Airfoil section with Torsion box
Figure 4-9: Cut view of Torsion box
Area of Torque Box,
A1
= 30980.3 mm2
CG of Torque Box
C.G
= 166.2193429 mm From Rear spar
Distance Between CG & CP
d
= 18.268 mm
Torque,
T
= Load*d = 3190.645161 * 18.17
T
= 57974.022 N-mm
q1
=
Shear flow,
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= 0.93536 N/mm
Table 7: CG of Torque box from Rear spar
Table 8: Torque on each section of the wing
Table 9: Shear flow distribution on wing
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Figure 4-10: Torque distribution graph
4.4.3 Shear Force due to Torsion: Shear force (SF) on Front Spar •
SFFS = q * hFS
•
SFFS = 0.93536*105.602 = 98.7758 N
•
Total SF on FS = 1465.97+98.7758 = 1564.745887 N
(4.8)
On Rear Spar •
SFRS = q*hRS
•
SFRS = 0.93536*86.882
•
SFRS = 81.26594 N
•
Total SF on RS = 1724.676+81.26594 = 1806.405 N
(4.9)
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Front Spar Table 10: Shear flow due to torsion on Front spar
Rear Spar Table 11: Shear flow due to torsion on Rear spar
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4.4.4 Total Shear Force Front Spar Table 12: Total Shear force on Front spar
Rear Spar Table 13: Total Shear force on Rear spar
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4.4.5 Web Thickness Thickness of the Web can be calculated from the following formula,
حshear strength =
(4.10)
Where, حshear strength = Shear strength of the material AA 2024-T6 in MPa A web = Area of the web = (height * thickness) in mm 283 = 1564.745887 / (105.602 * t web ) t web = 0.052358 mm A web = height * thickness
= 105.602 * 0.052358 = 5.52913 mm2
Moment of Inertia of a rectangular section web is given by, I web
= tweb *
= 0.052358 * (105.602)3 / 12
I web = 5138.285518 mm4 Front spar Table 14: Web Thickness of Front spar
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(4.11)
Rear spar Table 15: Web Thickness of Rear spar
4.4.6 Flange Thickness MOIflange = MOIFront Spar - MOIWeb
(4.12)
I flange = IFS – Iweb = 44411.22998 – 5138.285518 = 39272.94446 mm4 Also Moment of Inertia of the flange is given by, I flange = Aflange * (yFS )2
(4.13)
Where, Iflange = Moment of Inertia of flange in mm4 yFS = height from neutral axis to top surface of the flange in mm Hence, Aflange = Iflange / (yFS )2 = 39272.94446 / (52.801)2 Aflange = 14.08669683 mm2
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Front spar Table 16: Flange Thickness of Rear spar
Sections on the Wing from the Root Moment of Inertia on FS Web moment of Inertia on FS Flange moment of Inertia on FS Height of FS Flange Area on FS [mm4] [mm4] [mm4] [mm2] [mm] [mm] 4750 64.492 4275 41514.10137 5140.140358 36373.96101 105.602 13.04686899 3800 237514.76 20667.52088 216847.2391 140.562 43.9013659 3325 717823.9153 50298.79211 667525.1232 169.17 93.299842 2850 1614646.226 95950.29439 1518695.932 192.067 164.6741062 2375 3118139.09 164841.0455 2953298.045 214.551 256.6292667 1900 4179947.258 266864.5695 3913082.689 238.259 275.727693 1425 7498272.6 408492.9294 7089779.671 261.664 414.1949295 950 12203818.71 600347.3166 11603471.39 285.195 570.6424988 475 18618953.79 853277.3942 17765676.4 308.762 745.4079969 0 27099983.81 1179530.227 25920453.58 332.345 938.6945353 Total Volume Rear spar Table 17: Flange Thickness of Rear spar
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Flange volume [mm3] 6197.262771 20853.1488 44317.42495 78220.20046 121898.9017 130970.6542 196742.5915 271055.1869 354068.7985 445879.9043 1670204.074
4.4.7 MASS CALCULATION
AFS = Aflange + Aweb
(4.14)
AFS = 14.08669683 + 5.52913 = 19.61582683 mm2 VFS = AFS * 475 = 19.61582683 * 475
(4.15)
VFS = 9317.517744 mm3 Mass = Density * Total Volume
(4.16)
Mass = 2.78 E-6 * 4233483.491 Mass = 11.7690841kg
4.5 BUCKLING
To check whether the web fails under shear buckling. Condition: Shear stressinduced < Buckling stress (safe design) The thickness calculation is based on iterations, Finduced = Fcritical = k*E* Where,
(4.17) 2
(4.18)
q = shear flow, in N/mm E = Young's Modulus, in MPa b = height of spar, in mm tweb = web thickness, in mm k = shear buckling coefficient from graph
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4.5.1 RIB SPACING -
10 EQUAL DISTANCES OF 475mm
Web thickness's of front spar at section 1 is as follows, Finduced =
= 0.941 / 0.052
(4.19)
Finduced = 18.09 N/mm2 Fallowable
= k*E*
2
(4.20)
17.8647 = 5 * 72400 * (t web / 105.602)2 The value calculated for tweb is re substituted in Eqn.(1) and this loop will continue till we get equal consecutive thickness. Hence, the thickness of the web is 0.5151759603 mm at section 1. Same calculations were repeated for all sections of front spar to optimize the web thickness Front spar Table 18: Shear buckling calculations on Front spar
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Rear spar Table 19: Shear buckling calculations on Rear spar
4.5.2 Mass calculations Table 20: Mass of spars after Buckling
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CHAPTER-5 MODELING AND ANALYSIS 5.1 INTRODUCTION TO CATIA CATIA (Computer Aided Three-dimensional Interactive Application) is a multiplatform CAD/CAM/CAE commercial software suite developed by the French company Dassault Systems and marketed worldwide by IBM. Written in the C++ programming language, CATIA is the cornerstone of the Dassault Systems product lifecycle management software suite. The software was created in the late 1970s and early 1980s to develop Dassault's Mirage fighter jet, then was adopted in the aerospace, automotive, shipbuilding, and other industries. CATIA competes in the CAD/CAM/CAE market with Siemens NX, ENGINEER, Autodesk and Solid Edge. HISTORY: CATIA started as an in-house development in 1977 by French aircraft manufacturer Avions Marcel Dassault, at that time customer of the CAD software. Initially named CATI (Conception Assistée Tri dimensionnelle Interactive — French for Interactive Aided Three-dimensional Design) — it was renamed CATIA in 1981, when Dassault created a subsidiary to develop and sell the software, and signed a non-exclusive distribution agreement with IBM. In 1984, the Boeing Company chose CATIA as its main 3D CAD tool, becoming its largest customer. In 1988, CATIA version 3 was ported from mainframe computers to UNIX.
In 1990, General Dynamics Electric Boat Corp chose CATIA as its main 3D CAD tool, to design the U.S. Navy's submarine. In 1992, CADAM was purchased from IBM and the next year CATIA CADAM V4 was published. In 1996, it was ported from one to four UNIX operating systems, including IBM AIX, Silicon Graphics IRIX, Sun Microsystems SunOS and Hewlett-Packard HP-UX.
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In 1998, an entirely rewritten version of CATIA, CATIA V5 was released, with support for UNIX, Windows NT and Windows XP since 2001.
In 2008, Dassault announced and released CATIA V6. While the server can run on Microsoft Windows, Linux or AIX, client support for any operating system other than Microsoft Windows is dropped.
FEATURES: Commonly referred to as a 3D Product Lifecycle Management software suite, CATIA supports multiple stages of product development (CAx), from conceptualization, design (CAD), manufacturing (CAM), and engineering (CAE).
CATIA can be customized via application programming interfaces (API). V4 can be adapted in the Fortran and C programming languages under an API called CAA. V5 can be adapted via the Visual Basic and C++ programming languages, an API called CAA2 or CAA V5 that is components (COM)-like interface.
Although later versions of CATIA V4 implemented NURBS, V4 principally used piecewise polynomial surfaces. CATIA V4 uses a non-manifold solid engine.
Catia V5 features a parametric solid/surface-based package which uses NURBS as the core surface representation and has several workbenches that provide KBE support.
V5 can work with other applications, including Enovia, Smarteam, and various CAE Analysis applications.
NOTABLE INDUSTRIES USING CATIA:
CATIA is widely used throughout the engineering industry, especially in the automotive and aerospace sectors. CATIA V4, CATIA V5, Pro/ENGINEER, NX (formerly Unigraphics), and Solid Works are the dominant systems.
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Aerospace The Boeing Company used CATIA V3 to develop its 777 airliner, and is currently using CATIA V5 for the 787 series aircraft. They have employed the full range of Dassault System‘s' 3D PLM products — CATIA, DELMIA, and ENOVIA LCA — supplemented by Boeing developed applications. Chinese Xian JH-7A is the first aircraft developed by CATIA V5, when the design was completed on September 26, 2000.European aerospace giant Airbus has been using CATIA since 2001. Canadian aircraft maker Bombardier Aerospace has done all of its aircraft design on CATIA. The Brazilian aircraft company, EMBRAER, use Catia V4 and V5 to build all airplanes. The British Helicopter companies, West lands, use CATIA V4 and V5 to produce all their aircraft. Westland is now part of an Italian company called Finmeccanica the joined company calls themselves Agusta Westland.
Automotive Many automotive companies use CATIA to varying degrees, including BMW, Porsche, Daimler AG, Chrysler, Audi,[11] Volkswagen, Bentley Motors Limited, Volvo, Fiat, Benteler AG, PSA Peugeot Citroën, Renault, Toyota, Ford, Scandia, Hyundai, Škoda Auto, Tesla Motors, Proton,Tata motors and Mahindra & Mahindra Limited. Goodyear uses it in making tires for automotive and aerospace and also uses a customized CATIA for its design and development. Many automotive companies use CATIA for car structures — door beams, IP supports, bumper beams, roof rails, side rails, body components — because CATIA is very good in surface creation and Computer representation of surfaces. Shipbuilding Dassault Systems has begun serving shipbuilders with CATIA V5 release 8, which includes special features useful to shipbuilders. GD Electric Boat used CATIA to design the latest fast attack submarine class for the United States Navy, the Virginia class.[12] Northrop Grumman Newport News also used CATIA to design the Gerald R. Ford class of super carriers for the US Navy.[13] 46
Other Architect Frank Gehry has used the software, through the C-Cubed Virtual Architecture company, now Virtual Build Team, to design his award-winning curvilinear buildings.[14] His technology arm, Gehry Technologies, has been developing software based on CATIA V5 named Digital.[15] Digital Project has been used to design buildings and has successfully completed a handful of projects.
Dassault System‘s S.A. (French pronunciation: [daˈso], Euro next: DSY) is a leading company specializing in 3D and PLM (Product Lifecycle Management) software. Dassault Systèmes develops and markets PLM application software and services that support industrial processes and provide a 3D vision of the entire lifecycle of products from conception to maintenance to recycling. The Dassault Systèmes portfolio consists of CATIA for designing the virtual product, Solid Works for 3D mechanical design, DELMIA for virtual production, SIMULIA for virtual testing, ENOVIA for global collaborative lifecycle management, and 3DVIA for online 3D lifelike experiences.It was created in 1981, and is part of the Groupe Industriel Marcel Dassault.
5.2 CAD MODELING OF THE WING SPAR Taking values from NACA Standards At Root:
Profile: NACA 64A1215. Leading Edge radius = 1.556% c. Slope of mean line at leading edge = 0.0842.
At Tip:
Profile: NACA 64A1210. Leading Edge radius = 0.701% c. Slope of mean line at leading edge = 0.0842.
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Figure 5-1: NACA Airfoils profiles with control points
Figure 5-2: Wing surface generation
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5.3 DESIGNING OF SPAR ON MANUFACTURING BASIS The front spar is placed at 25% of chord length from leading edge. The rear spar is placed at 62% of chord length from leading edge. Thicknesses of the flanges and webs are different. The flanges are made of T-sections and L- sections. The webs are made with sheet metal.
5.4 CROSS SECTION SPAR
Figure 5-3: Cross section of front and rear spars
Skin area,
Where,
As = (b +2*20*ts) mm2
(5.1)
Effective flange area = (Af - As)/2
(5.2)
b = flange width in mm ts = skin thickness in mm Af = designed flange area in mm2
Web thickness is altered as per the availability of sheet metal gages. 49
5.5 FRONT SPAR DIMENSIONS Table 21: Front spar dimensions (All dimensions are in mm)
5.6 REAR SPAR DIMENSIONS Table 22: Rear spar dimensions (All dimensions are in mm)
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5.7 CREATION OF THE SPAR SECTIONS
Figure 5-4: FRONT SPAR
Figure 5-5: REAR SPAR
5.8 FULL PROFILE OF WING
Figure 5-6: Complete wing Skeleton view with spars
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5.9 SPARS REPRESENTATION
Figure 5-7: View of spars
5.10 CRIMP HOLES OR LIGHTENING HOLES The lightening holes are made in the element in order to reduce the weight of the element. The crimp holes are made to the web element of the spar. These holes provided in between the two successive rib locations.
Figure 5-8: Location of Crimp holes
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Figure 5-9: Complete spar representation with lightening holes
5.11 NASTRAN NASTRAN is a finite element analysis (FEA) program that was originally developed for NASA in the late 1960s under United States government funding for the Aerospace industry. The MacNeal-Schwendler Corporation (MSC) was one of the principal and original developers of the public domain NASTRAN code. NASTRAN source code is integrated in a number of different software packages, which are distributed by a range of companies. The NASTRAN program has evolved over many versions. Each new version contains enhancements in analysis capability and numerical performance. Today, NASTRAN is widely used throughout the world in the aerospace, automotive and maritime industries. It has been claimed that NASTRAN is the industry standard for basic types of analysis for aerospace structures, e.g. linear elastic static and dynamic analyses.
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5.12 PATRAN 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 PamCrash. 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.
5.13 FEM MODELING A mesh is a network of line elements and interconnecting nodes used to model a structural system and numerically solve for its simulated behavior under applied loading. First, computational techniques create an analytical model by populating the material domain with a finite-element mesh in which each line element is assigned mathematical attributes (axial, bending, shear, and torsional stiffness, etc.) which simulate the material and geometric properties of the structural system. The system is then restrained within boundary conditions and subjected to mechanical or thermal loading.
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Figure 5-10: Front spar meshing
Figure 5-11: Rear spar meshing
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CHAPTER-6 RESULTS AND DISCUSSIONS 6.1 FRONT SPAR ANALYSIS
Figure 6-1: Front spar displacements
Figure 6-2: Shear force of Front spar
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Figure 6-3: Front spar Thickness plots
Figure 6-4: Principal stresses of front spar
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6.2 REAR SPAR ANALYSIS
Figure 6-5: Rear spar flange displacement
Figure 6-6: Rear spar web displacement
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Figure 6-7: Front spar shear force plot
Figure 6-8: Rear spar Thickness plots
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Figure 6-9: Principal stresses of rear spar
Figure 6-10: Von-mises stresses of rear spar
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CHAPTER-7 CONCLUSION Spars are the main structural members of the wing. They extend from the fuselage to the tip of the wing. The entire load carried by the wing is taken up by the spars. The spars are designed to have great bending strength. Ribs give the wing section its shape, and they transmit the air load from the wing covering to the spars. Front Spar positioning is estimated to 25% and Rear Spar to 62% of the Chord Length. But we can further optimize this configuration by changing Front spar position between 18-25% and select the best possible scenario. We also calculated the various forces acting on the wing and their influences over the entire wing span and the interaction of Shear force with Torsion on spars is very important aspect of wing design and we have calculated this interaction mathematically and included it calculations of Total shear force acting on Front and Rear spars. Flange and web dimensions are calculated and suitable changes in dimensions are incorporated from manufacturing point of view and we have included the Buckling influence in to consideration and we have calculated the weight under buckling environment. Number of Ribs and their positioning for the prevention of bending and buckling of Spars is calculated. We idealized the number of Ribs as 10 with equal spacing. Mass of the spars calculated from iterations is 23.10 kg. The Detail drawings for the front and rear spars are provided using CATIA V5. Now we have decided to validate the Numerical values by finding Shear force and bending moment on the spars analytically using Analysis software.
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CHAPTER-8 FUTURE SCOPE
Spar position can be optimized based on buckling calculations. In our work we specified the location of spars as 25% and 62% for Front and Rear spars but they can be changed from 18% to 25% for Front spar and we can find best possible scenario with much less weight requirements.
Further optimization of Rib is possible. Varying number of Ribs and spacing of Ribs. We used 10 Ribs with equal spacing; then again we can further decrease weight compensations with 15 Ribs and unequal or equal spacing. Use of other materials for the design of spars can be thought of i.e. we can use Composite materials to reduce the weight demands and influence the Moment of Inertia of spars. But care must be taken to consider shock / Impact loads effect on Spars and Fail safe criteria must be increased Detail stress analysis of individual components and its validation with calculations can be carried out.
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BIBLIOGRAPHY 1] Abbot & Albert,'Theory of wing sections',Dover publication,1949. 2] David J. Perry,'Aircraft structures',Mc-Graw Hill publication,1950. 3] E. F. Bruhn,'Analysis and design of flight vehicle structures',1973. 4] Michael C. Y. Niu, 'Airframe Stress Analysis and Sizing', 2001. 5] Michael C. Y. Niu, 'Airframe structural design', Conmilit press Ltd., 1989. 6] Kuethe and Schetzer, 'Foundations of Aerodynamics', 2nd Edition, John Wiley and Sons, New York, 1959. 7] ASM Material Data Sheet 8] S.S.Rao, ‗The Finite Element method in Engineerin’, BH Publications New Delhi, 3rd Edition, 1999. 9] O.C.Zeinkiewicz, ‗The Finite Element method in Engineering Science‘, Tata McGraw Hill, 2nd Edition, 1992. 10] T.R.Chandrupatla, Belegundu A.D., ‗Finite Element Engineering‘, Prentice Hall of India Ltd, 2001. 11] O.P.Gupta, ‗Finite and Boundary element methods in Engineering‘, Oxford and IBH publishing company Pvt.Ltd.New Delhi, 1999. 12] V.Ramamurti, ‗Computer Aided Design in Mechanical Engineering‘, Tata McGraw Hill publishing company Ltd.New Delhi, 1987. 13] C.S.Krishnamoorthy, ‗Finite Element Analysis, Theory and Programming’ 2nd edition, Tata McGraw Hill publishing company Ltd.New Delhi, 2002. 14] Gupta,L., ‗Advanced Composite Materials’, Himalayan Books, New Delhi, 1998. 15] Jones, R.M., ‗Mechanics of Composite Materials‘, McGraw Hill Kogakusha, ltd, Tokyo.
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