finite element analysis of aircraft wing

ANALYSIS OF OF AIRCRAFT AIRCRAFT WING

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 system of 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 structure concerns 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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ANALYSIS OF AIRCRAFT WING

2. Figures and Tables: Figure 3.0 Representation of airfoil Table 4.1: Represents different young’s modulus of Carbon Epoxy UniDirectional 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 invention aeroplanes 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. Lift and weight are two of the four forces acting on an airplane, the other two are drag and thrust.

Figure3.0 Representation of airfoil

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The design and analysis of the wings of aircraft is one of the principal applications of the science of aerodynamics, which is a branch of fluid mechanics. The properties of the airflow around any moving object can - in principle - be found by solving the Navier-Stokes equations of fluid dynamics. However, except for simple geometries these equations are notoriously difficult to 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 is called the "lift" generated by the wing.

4. Material Properties :

The starting point for any materials selection is the identification and specification of design requirements. In this case, we keep the example fairly simple at the level that might be used in an introductory materials engineering course. The requirements for the aircraft wing (illustrated, right) are: A. B. C. D.

High stiffness High strength High toughness 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 the aircraft 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 be made of fibrous materials embedded within a resin matrix. In general, fibres oriented in a specific direction are laminated with fibres characterised by a different orientation in order to obtain the required strength and stiffness.

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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 carbon fibers are pretension and aligned during impregnation and curing. This process assures the efficient utilization of the superior mechanical properties of the carbon fibers. Young’s Modulus: E11 E22 E33

155.8Gpa 8.89Gpa 8.89Gpa

Table 4.1: represents different young’s modulus of Carbon Epoxy Uni-Directional Laminate

Poisson’s Ratio: V12 V13 V23

0.3 0.3 0.3675

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

Density: 1550 kg/m^3 4.2 Titanium: A metallic element, titanium is recognized for its high strength-to-weight ratio. It is a strong metal with low density that is quite ductile (especially in an oxygen-free environment), lustrous, and metallic-white in colour. The relatively high melting point (more than 1,650 °C or 3,000 °F) makes it useful as a refractory metal. It is paramagnetic and has fairly low electrical and thermal. Young’s Modulus: 116.52Gpa Poisson’s ratio: 0.31 Density: 4428.78kg/m^3

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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 an object overcomes the earth’s 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 figure and are also described below.

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

Chord:

Extends from leading edge to trailing edge of the wing

Camber line:

Points halfway between chord and upper wing surface

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 create this pressure difference, the surface of the wing must satisfy one or both of the following 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 the formation 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 the wing. The air passing above the wing gets spread out or expanded and hence the 7


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 in between. 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 as lift (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 pressure than 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 would produce "down lift" and send it crashing to the ground!

5.4 Components of an Airfoil: A leading edge, a trailing edge , a chord and a camber are 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 wind is 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 the Direction 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 turning moment 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, and completed 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 for physical simulation such as finite element analysis or computational fluid dynamics. Three-dimensional meshes created for finite element analysis need to consist of tetrahedral, pyramids, prisms or hexahedra. Those used for the finite volume method can consist of arbitrary polyhedral. Those used for finite difference methods usually need to consist of piecewise structured arrays of hexahedra known as multi-block structured meshes. A mesh is otherwise a discretization of a domain existing in one, two or three dimensions.

Figure 6.2: representing the meshing model of airfoil

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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 response analysis, or a spectrum analysis.

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Modal analysis is the study of the dynamic properties of structures under vibrational 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 an electromagnetic shaker, or the noise 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 if they are defined. You can choose from several mode extraction methods: subspace, Block Lanczos, Power Dynamics, reduced, unsymmetrical, and damped. 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

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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 and solution 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 the available computing power.

Figure 7.2: representing Static pressure contour

Fluid flow is characterized by a velocity vector field in three-dimensional space, within the framework of mechanics. Streamlines, streak lines, and path lines are field lines resulting from this vector field description of the flow. They differ only when the flow changes with time: that is, when the flow is not steady

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Figure 7.3: representing Streamline flow

Figure 7.4: representing Density variation

7.3 STATIC 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 2 3 4 5 6 7 8 9 10

9.9719 51.965 61.923 112.24 171.04 293.21 328.5 338.19 502.6 528.81

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 was positive. Since a particular aircraft's required lift is set by its weight, delivering that lift with lower drag leads directly to better fuel economy, climb performance, 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 density than 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-71 Blackbird manufacturing. 16


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. 149 – 154, 1998 (New Brunswick).

Computational Fluid Dynamic (CFD) Analysis of Cantilevered Aircraft’s Wing Along With Wingtip Missile https://en.wikipedia.org/wiki/Fixed-wing_aircraft seli ,M.UIUC Airfoil coordinates Database, version 2.0, URL selig.ae.illinois.edu/ads/coord_database.html, Nov.11, 2005 [cited March13, 2006]

http://m-

https://depts.washington.edu/amtas/publications/wing/UW%20Wing%20Design.xls

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finite element analysis of aircraft wing

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