finite element analysis of aircraft wing

7/24/2019 finite element analysis of aircraft wing

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ANALYSIS OF AIRCRAFT WING

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FINITE ELEMENT ANALYSIS OF AIRCRAFT

WING

1. ABSTRACT:

This deals with bending Finite Element Analysis of composite aircraft wing

using commercial software ANSYS. Stress analysis and finite element solution

for a composite shell structure are presented in this study. An aircraft wing is

made of composite with fibre angles in each ply aligned in different direction.

Various air foil thickness and ply angles were considered to study the effect of

bending-torsion decoupling. A typical composite structure consists of a systemof layer bonded together. The layers can be made of different isotropic or

anisotropic materials, and have different structure, thickness, and mechanical

properties. The laminate characteristics are usually calculated using the number

of layer, stacking sequence, geometric and mechanical properties. A finite

number of layers can be combined to form so many laminates, the laminates

characterized with 21 coefficients and demonstrating coupling effect. The

behaviour of laminates as a system of layer with given properties. The only

restriction that is imposed on the laminate as an element of composite structureconcerns its total thickness which is assumed to be much smaller than the other

dimensions of the structure.

Aircraft wing model as per the plan should be made in FEA and the model is

subjected to various loading. The loading given by the self-weight or due to

acceleration due to gravity was discussed and the deflection over here should be

calculated. The wing model is severely affected by the loads on along wing

direction, across wing direction, vertical direction. Moreover the combined

loading is the real case. An individual loading for example the load only on X

direction and its deflection in X, Y and Z directions, also the stress acting on X,

Y, and Z directions should be determine. Von misses stress is calculated in

order to know the maximum stress levels and minimum stress levels on the

wing.


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2. Figures and Tables:

Figure 3.0 Representation of airfoil

Table 4.1: Represents different youngs modulus of Carbon Epoxy Uni-

Directional Laminate

Table 4.2: Represents different poisons ratios of Carbon Epoxy Uni-Directional

Laminate

Figure 5.1: Typical Aerofoil (Cross-Sectional Shape) of an Airplane Wing

Figure 5.2: a) Flat Bottom b) Slightly Curved Bottom c) Symmetrical

Figure 5.3: wind streamline flow over airfoil

Figure 5.4: Represents the schematic diagram of naca4415 airfoil profile

Figure 6.1: representation of model aircraft wing

Figure 6.2: Representing the meshing model of airfoil

Figure 6.3: Representing the CFD meshing including surrounding

Figure 7.1: Representing the deformation using modal analysis

Figure 7.2: Representing Static pressure contour

Figure 7.3: Streamline flow representation

Figure 7.4: Representing Density variation

Figure 7.5: representing static structural analysis

Figure 7.6: representing Von-misses stress


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3. Introduction:

In the earliest days, when man was yet living in the lap of nature, the only

means of locomotion was his legs. Gradually, we have achieved faster and more

luxurious ways of travelling, latest being the air transport. Since, its inventionaeroplanes have been getting more and more popularity as it is the fastest mode

of transportation available. It has also gained popularity as a war machine since

World War II. This popularity of air transport has led to many new inventions

and research to developed faster and more economical planes. This project is

such an attempt to determine how we can derive maximum performance out of

an air foil section. An air foil is a cross-section of wing of the plane. Its main

job is to provide lift to an aeroplane during take-off and while in flight. But, it

has also a side effect called Drag which opposes the motion of the aeroplane.The amount of lift needed by a plane depends on the purpose for which it is to

be used. Heavier planes require more lift while lighter planes require less lift

than the heavier ones. Thus, depending upon the use of aeroplane, air foil

section is determined. Lift force also determines the vertical acceleration of the

plane which in turns depends on the horizontal velocity of the plane. Thus,

determining the coefficient of lift one can calculate the lift force and knowing

the lift force and required vertical acceleration one can determine the required

horizontal velocity. Provide enough lift to counter the weight of the plane. Liftand weight are two of the four forces acting on an airplane, the other two are

drag and thrust.

Figure3.0 Representation of airfoil
http://www.sciencekids.co.nz/pictures/physics/forcesoflift.html


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The design and analysis of the wings of aircraft is one of the principal

applications of the science ofaerodynamics, which is a branch of fluid

mechanics. The properties of the airflow around any moving object can - in

principle - be found by solving theNavier-Stokes equations offluid dynamics.

However, except for simple geometries these equations are notoriously difficultto solve. Fortunately, simpler explanations can be described. The lower air

pressure on the top of the wing generates a smaller downward force on the top

of the wing than the upward force generated by the higher air pressure on the

bottom of the wing. Hence, a net upward force acts on the wing. This force iscalled the "lift" generated by the wing.

4.Material Properties:

The starting point for any materials selection is the identification andspecification of design requirements. In this case, we keep the example fairly

simple at the level that might be used in an introductory materials engineeringcourse.

The requirements for the aircraft wing (illustrated, right) are:

A.High stiffness

B.High strengthC.High toughnessD.Low weight

Aluminium alloys, in thin sheets (.016 to .125 of an inch) provide an excellent

two dimensional material used extensively as shear webs, with or without

stiffeners and also as tension/compression members when suitably formed

(bent).In addition to metals, composite materials are also used within theaircraft industry due to their strength, relatively low weight and corrosion

resistance. Composites are created by the combination of different materials,

which have been selected on the basis of their structural properties. They can bemade of fibrous materials embedded within a resin matrix. In general, fibres

oriented in a specific direction are laminated with fibres characterised by adifferent orientation in order to obtain the required strength and stiffness.
https://en.wikipedia.org/wiki/Aerodynamicshttps://en.wikipedia.org/wiki/Fluid_mechanicshttps://en.wikipedia.org/wiki/Fluid_mechanicshttps://en.wikipedia.org/wiki/Navier-Stokes_equationshttps://en.wikipedia.org/wiki/Fluid_dynamicshttps://en.wikipedia.org/wiki/Fluid_dynamicshttps://en.wikipedia.org/wiki/Navier-Stokes_equationshttps://en.wikipedia.org/wiki/Fluid_mechanicshttps://en.wikipedia.org/wiki/Fluid_mechanicshttps://en.wikipedia.org/wiki/Aerodynamics


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4.1 Carbon Epoxy Uni-Directional Laminate:

A light weight laminate composed of continuous unidirectional carbon fiber in

an epoxy matrix, providing high strength and stiffness and in which all carbonfibers are pretension and aligned during impregnation and curing. This process

assures the efficient utilization of the superior mechanical properties of the

carbon fibers.

Youngs Modulus:

E11 155.8Gpa

E22 8.89Gpa

E33 8.89Gpa

Table 4.1:represents different youngsmodulus of Carbon Epoxy Uni-Directional Laminate

Poissons Ratio:

V12 0.3

V13 0.3

V23 0.3675

Table 4.2:represents different poisons ratios of Carbon Epoxy Uni-Directional Laminate

Density: 1550 kg/m^3

4.2 Titanium:

Ametallicelement, titanium is recognized for its high strength-to-weight

ratio. It is a strong metal with lowdensity that is quite ductile (especially in

anoxygen-free environment), lustrous, and metallic-white incolour.The

relatively high melting point (more than 1,650 C or 3,000 F) makes it useful

as arefractory metal. It isparamagnetic and has fairly lowelectrical and

thermal.

Youngs Modulus: 116.52Gpa

Poissons ratio: 0.31

Density: 4428.78kg/m^3
https://en.wikipedia.org/wiki/Metalhttps://en.wikipedia.org/wiki/Chemical_elementhttps://en.wikipedia.org/wiki/Densityhttps://en.wikipedia.org/wiki/Oxygenhttps://en.wikipedia.org/wiki/Colorhttps://en.wikipedia.org/wiki/Refractory_metalshttps://en.wikipedia.org/wiki/Paramagnetismhttps://en.wikipedia.org/wiki/Electrical_conductivityhttps://en.wikipedia.org/wiki/Electrical_conductivityhttps://en.wikipedia.org/wiki/Paramagnetismhttps://en.wikipedia.org/wiki/Refractory_metalshttps://en.wikipedia.org/wiki/Colorhttps://en.wikipedia.org/wiki/Oxygenhttps://en.wikipedia.org/wiki/Densityhttps://en.wikipedia.org/wiki/Chemical_elementhttps://en.wikipedia.org/wiki/Metal


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5. AIRFOIL:

One of the most spectacular things to view is the structure and the body of an

aircraft. Its concept has always been scintillating and technical. It all started

with the answer to how birds can fly. All of us do know that only when anobject overcomes the earths natural gravitational pull, it tends to fly.

The wing of an aircraft helps in gliding it through the wind and also in its

landing and take-off. The shape of such an important component of the aircraft

makes a lot of impact on its movements. This shape is what is called an aerofoil.

5.1 GEOMETRY/STRUCTURE:

The airplane generates lift using its wings. The cross-sectional shape of the

wing is called an aerofoil. A typical airfoil and its properties are shown in figureand are also described below.

Figure 5.1: Typical Aerofoil (Cross-Sectional Shape) of an Airplane Wing

Chord:Extends from leading edge to trailing edge ofthe wing

Camber line:Points halfway between chord and upper wingsurface

Angle of

attack:

Angle between direction of airflow and the

chord


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5.2 EXPLANATION OF AIRFOIL:

The wings provide lift by creating a situation where the pressure above the wing

is lower than the pressure below the wing. Since the pressure below the wing is

higher than the pressure above the wing, there is a net force upwards. To createthis pressure difference, the surface of the wing must satisfy one or both of thefollowing conditions. The wing surface must be:

Figure 5.2: a) Flat Bottom b) Slightly Curved Bottom c) Symmetrical

Viscosity is essential in generating lift. The effects of viscosity lead to theformation of the starting vortex which, in turn is responsible for producing the

proper conditions for lift.

Figure 5.3: wind streamline flow over airfoil

5.3 How does an Airfoil Work:

When a wing moves through the air, it splits and moves above and below thewing. The air passing above the wing gets spread out or expanded and hence the


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pressure decreases, while the air passing below the wing moves straight enough

to maintain its speed and pressure. To maintain equilibrium higher air pressure

usually moves towards a region which has lower air pressure. The air above the

wing has lower air pressure as compared to air below the wing. Thus the air

below is pushed upwards which in turn lifts the wing, sandwiched inbetween. This lift is due to the angle of attack and shape.

When the air hits the wings it results in an opposite force to the direction of

Deflection.Its components are called aslift(perpendicular) and drag(parallel.)

As the speed of the plane increases, more the lift and eventually when the force

Of motion (lift) is greater than the gravitational pull, the plane starts flying.

When air rushes over the curved upper wing surface, it has to travel further and

go slightly faster than the air that passes underneath. According to a basic

theory of physics called Bernoulli's law, fast-moving air is at lower pressurethan slow-moving air, so the pressure above the wing is lower than the pressure

below, creating the lift that holds the plane up. Although this explanation of

how wings work is widely repeated, it's not the whole story. If it were the only

factor involved, planes couldn't fly upside down. Flipping a plane over wouldproduce "down lift" and send it crashing to the ground!

5.4 Components of an Airfoil:A leading edge, a trailing edge, a chordand a camberare the components of

an airfoil. The end which meets the air first is the leading edge and the trailing

Edge is at the end of the airfoil which is where the air with high pressure (below

The wing) meets the air with lower pressure (above the wing). The chord is the

Imaginary line from the leading to the trailing edge. The camber is the curve on

Top and bottom of the airfoil.

Relative windis defined as the direction of air flowing past the airfoil with

Respect to the direction of the flight. It is always parallel and opposite to theDirection of flight.

Turning moment:

An airfoil has 3 forces. Lift, weight and drag. The lift is usually placed on the

same spot as the weight, which is when the airfoil is stable and the plane has no

problem, but usually when the lift is placed after weight force it produces

instability in the airfoil which in turn produces a turning moment. This turningmoment is compensated with the downward pushing force.


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Figure 5.4: represents the schematic diagram of naca4415

6. GEOMETRY OF MODEL:

Model of wing and its structure was build using CATIA V5 designing software.

By considering the real-time profile of airfoil its co-ordinates were formed and

they were imported to CATIA by EXCEL- MACROS importing format. Then

required dimensioned aircraft wing was formed by using that profile, andcompleted model was imported to ANSYS V12.1 for analysis of model.

Figure 6.1: representation of model aircraft wing


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6.1 MESHING OF MODEL:

Mesh generation is the practice of generating a polygonal or polyhedral mesh

that approximates a geometric domain. The term "grid generation" is often used

interchangeably. Typical uses are for rendering to a computer screen or forphysical simulation such as finite element analysis or computational fluid

dynamics. Three-dimensional meshes created forfinite element analysis need to

consist of tetrahedral,pyramids,prisms orhexahedra. Those used for thefinite

volume method can consist of arbitrary polyhedral. Those used forfinitedifference methods usually need to consist of piecewise structured arrays of

hexahedra known as multi-block structured meshes. A mesh is otherwise adiscretization of a domain existing in one, two or three dimensions.

Figure 6.2: representing the meshing model of airfoil
https://en.wikipedia.org/wiki/Finite_element_analysishttps://en.wikipedia.org/wiki/Pyramid_(geometry)https://en.wikipedia.org/wiki/Prism_(geometry)https://en.wikipedia.org/wiki/Hexahedronhttps://en.wikipedia.org/wiki/Finite_volume_methodhttps://en.wikipedia.org/wiki/Finite_volume_methodhttps://en.wikipedia.org/wiki/Finite_difference_methodhttps://en.wikipedia.org/wiki/Finite_difference_methodhttps://en.wikipedia.org/wiki/Finite_difference_methodhttps://en.wikipedia.org/wiki/Finite_difference_methodhttps://en.wikipedia.org/wiki/Finite_volume_methodhttps://en.wikipedia.org/wiki/Finite_volume_methodhttps://en.wikipedia.org/wiki/Hexahedronhttps://en.wikipedia.org/wiki/Prism_(geometry)https://en.wikipedia.org/wiki/Pyramid_(geometry)https://en.wikipedia.org/wiki/Finite_element_analysis


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6.2 CFD MESHING INCLUDING SURROUNDING:

Figure6.3: representing the CFD meshing including surrounding

7. ANALYSIS TYPES:

MODAL

CFD

STATIC STRUCTURAL

7.1 MODAL ANALYSIS:

7.1.1 Definition of Modal Analysis

You use modal analysis to determine the vibration characteristics (natural

Frequencies and mode shapes) of a structure or a machine component while it is

being designed. It also can be a starting point for another, more detailed,

dynamic analysis, such as a transient dynamic analysis, a harmonic responseanalysis, or a spectrum analysis.


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Modal analysisis the study of the dynamic properties of structures

undervibrational excitation.

Modal analysis is the field of measuring and analysing the dynamic response of

structures and or fluids during excitation. Examples would include measuring

the vibration of a car's body when it is attached to anelectromagnetic shaker, or

thenoise pattern in a room when excited by a loudspeaker.

7.1.2 Uses for Modal Analysis

You use modal analysis to determine the natural frequencies and mode shapes

of a structure. The natural frequencies and mode shapes are important

parameters in the design of a structure for dynamic loading conditions. They are

also required if you want to do a spectrum analysis or a mode superposition

harmonic or transient analysis. You can do modal analysis on a prestressed

structure, such as a spinning turbine blade. Another useful feature is modal

cyclic symmetry, which allows you to review the mode shapes of a cyclically

symmetric structure by modelling just a sector of it.

Modal analysis in the ANSYS family of products is a linear analysis. Any

nonlinearities, such as plasticity and contact (gap) elements, are ignored even ifthey are defined. You can choose from several mode extraction methods:

subspace, Block Lanczos, Power Dynamics, reduced, unsymmetrical, anddamped. The damped method allows you to include damping in the structure.Details about mode extraction methods are covered later in this section.

Figure 7.1: representing the deformation using modal analysis
https://en.wikipedia.org/wiki/Vibrationhttps://en.wikipedia.org/wiki/Electromagnetismhttps://en.wikipedia.org/w/index.php?title=Noise_pattern&action=edit&redlink=1https://en.wikipedia.org/w/index.php?title=Noise_pattern&action=edit&redlink=1https://en.wikipedia.org/wiki/Electromagnetismhttps://en.wikipedia.org/wiki/Vibration


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7.2 CFD ANALYSIS:

Computational Fluid Dynamics (CFD) provides a qualitative (and sometimes

even quantitative) prediction of fluid flows by means of mathematical

modelling (partial differential equations), numerical methods (discretization andsolution techniques).software tools (solvers, pre- and post-processing utilities)

CFD enables scientists and engineers to perform numerical experiments (i.e.

computer simulations) in a virtual flow laboratory.

CFD gives an insight into flow patterns that are difficult, expensive or

impossible to study using traditional (experimental) techniques

The results of a CFD simulation are never 100% reliable because the input data

may involve too much guessing or imprecision the mathematical model of the

problem at hand may be inadequate the accuracy of the results is limited by theavailable computing power.

Figure 7.2: representing Static pressure contour

Fluid flow is characterized by avelocityvector field inthree-dimensional space,

within the framework of mechanics. Streamlines, streak lines, and path

lines arefield lines resulting from this vector field description of the flow. Theydiffer only when the flow changes with time: that is, when the flow is notsteady
https://en.wikipedia.org/wiki/Fluid_flowhttps://en.wikipedia.org/wiki/Velocityhttps://en.wikipedia.org/wiki/Vector_fieldhttps://en.wikipedia.org/wiki/Three-dimensional_spacehttps://en.wikipedia.org/wiki/Field_linehttps://en.wikipedia.org/wiki/Steady_flowhttps://en.wikipedia.org/wiki/Steady_flowhttps://en.wikipedia.org/wiki/Field_linehttps://en.wikipedia.org/wiki/Three-dimensional_spacehttps://en.wikipedia.org/wiki/Vector_fieldhttps://en.wikipedia.org/wiki/Velocityhttps://en.wikipedia.org/wiki/Fluid_flow


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Figure 7.3: representing Streamline flow

Figure 7.4: representing Density variation

7.3STATIC STRUCTURAL ANALYSIS:

A static analysis calculates the effects of steady loading conditions on a

structure, while ignoring inertia and damping effects, such as those caused

by time-varying loads. A static analysis can, however, include steady inertia

loads (such as gravity and rotational velocity), and time-varying loads that

can be approximated as static equivalent loads such as the static equivalent

wind and seismic loads.


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Figure 7.5: representing static structural analysis

Figure 7.6: representing Von-misses stress


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8. Results:

Lift obtained: 8301.9902 N

Drag obtained: 7029.4521 N

Modal Frequency:

S.NO Mode Frequency [Hz]

1 9.9719

2 51.965

3 61.923

4 112.24

5 171.046 293.21

7 328.5

8 338.19

9 502.6

10 528.81

Maximum deformation 6.149e-007 m

Von misses equivalent stress:

Min: 162.93 Pa

Max: 18977 Pa

9. Conclusion:

Lift and drag obtained by the model were reasonable, lift to Drag ratio waspositive.Since a particular aircraft's required lift is set by its weight, delivering

that lift with lower drag leads directly to better fuel economy, climbperformance, and ratio. But it depends on fuselage design too.

Structural deformation was more in titanium when compared to carbon-epoxy

unidirectional laminate (composite material) because titanium has more densitythan carbon-epoxy unidirectional laminate even it has high ultimate tensile

strength and titanium has the highest weight-to-strength ratio so better than any

other metals for aviation applications. Titanium was mostly used in SR-71Blackbird manufacturing.


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10. References:

http://airfoiltools.com/airfoil/naca5digit

http://www.mh-aerotools.de/airfoils/hdi_plotairfoils.htm

Douglas, C.C., Ern, A. and Smooke, M.D., Numerical simulation of flames using multigrid methods.In Iterative Methods in Scientific Computation, edited by J. Wang, M.B. Allen, B.M. Chen and T.Mathew, 4, pp. 149154, 1998 (New Brunswick).

Computational Fluid Dynamic (CFD) Analysis of Cantilevered Aircrafts Wing Along With

Wingtip Missile

https://en.wikipedia.org/wiki/Fixed-wing_aircraft

seli ,M.UIUC Airfoil coordinates Database, version 2.0, URL http://m-

selig.ae.illinois.edu/ads/coord_database.html,Nov.11, 2005 [cited March13, 2006]

https://depts.washington.edu/amtas/publications/wing/UW%20Wing%20Design.xls
http://airfoiltools.com/airfoil/naca5digithttp://airfoiltools.com/airfoil/naca5digithttp://www.mh-aerotools.de/airfoils/hdi_plotairfoils.htmhttp://www.mh-aerotools.de/airfoils/hdi_plotairfoils.htmhttps://en.wikipedia.org/wiki/Fixed-wing_aircrafthttps://en.wikipedia.org/wiki/Fixed-wing_aircrafthttp://m-selig.ae.illinois.edu/ads/coord_database.htmlhttp://m-selig.ae.illinois.edu/ads/coord_database.htmlhttp://m-selig.ae.illinois.edu/ads/coord_database.htmlhttps://depts.washington.edu/amtas/publications/wing/UW%20Wing%20Design.xlshttps://depts.washington.edu/amtas/publications/wing/UW%20Wing%20Design.xlshttps://depts.washington.edu/amtas/publications/wing/UW%20Wing%20Design.xlshttp://m-selig.ae.illinois.edu/ads/coord_database.htmlhttp://m-selig.ae.illinois.edu/ads/coord_database.htmlhttps://en.wikipedia.org/wiki/Fixed-wing_aircrafthttp://www.mh-aerotools.de/airfoils/hdi_plotairfoils.htmhttp://airfoiltools.com/airfoil/naca5digit

finite element analysis of aircraft wing

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