Evaluation of Buckling Stability of the Front Spar in an Aircraft Wing

Evaluation of Buckling Stability of the Front Spar in an Aircraft Wing

Priyadarsh S J1, Anjana Unnikrishnan2, and M.Venkataramana3

1Student, Department of Aeronautical Engineering, MLR Institute of Technology, Hyderabad, INDIA

2Student, Department of Aerospace Engineering, IIAEM, Jain University, Bangalore, INDIA

3Associate Professor, Department of Aeronautical Engineering, MLR Institute of Technology, Hyderabad, INDIA

AbstractWing spars are basically the members that carry bending loads acting on the wing. Buckling failure of Spar web is a common problem associated with most of the wing designs. In this research, buckling stability of the spar is verified through both Classical and Finite element approaches. The location critical to buckling was identified and Critical Eigen value was obtained. Also the critical buckling mode shape is studied for further design modifications. The detailed geometry of the Spar is modeled using CATIA; Finite element model of the Spar was generated in MSC Patran and analyzed in MSC Nastran.

KeywordsBuckling, Buckling stability, Bending, Eigen value, Finite Element approach

INTRODUCTION

Spars are the main members of the wing. They extend lengthwise of the wing (crosswise of the fuselage). The entire load carried by the wing is ultimately taken by the spars. In flight, the force of the air acts against the skin. From the skin, this force is transmitted to the ribs and then to the spars. Most wing structures have two spars, the front spar and the rear spar. The front spar is found near the leading edge while the rear spar is about two-thirds the distance to the trailing edge.

Obtaining Critical region dimensions and elemental stresses

Solve

The function of spar web is to resist the shearing forces between the spar caps and to hold the spar cap on the compression side of the spar in column so that it doesn't buckle.

The finite element model of spar need to be analyzed and critical buckling factors need to be obtained. The critical value obtained from finite element approach is verified through plate buckling formulae.

BUCKLING ANALYSIS

The major goal here is to verify whether the current design is safe under anticipated buckling loads. For this, Eigen value buckling analysis of the model is carried out in MSC Nastran. The flowchart of the procedure followed is shown in Fig.1

The various steps followed during the buckling analysis are shown hereunder.

Build Finite element model

Assigning Material and Properties

Applying Loads and B.Cs

PROBLEM STATEMENT

Reading Results

Wing Spar is a critical component in wing structure which plays a key role in the structural integrity of the wing. The objective of this paper is to study the buckling behavior of the spar under lift load.

The detailed specifications of the aircraft considered and magnitude of estimated loads are specified hereunder.

Category: Light Aircraft Total weight of the aircraft: 18.76kN

Lift load on wing: 45.03kN

Load on each wing: 22.5kN

Load on front spar: 16.9kN

Total length of spar: 3600 mm

Wing span: 8000mm

Aspect ratio: 6.0

Taper ratio: 0.50

Obtaining Critical Buckling factor from FE analysis

Calculating Critical Buckling factor based on Plate Buckling theory

Comparison of FE results and results from Classical formulae

Fig.1 Block Diagram for Buckling analysis

The material used for both Spar web and Spar caps is Aluminium alloy 2024-T3.The material properties used are listed hereunder:

Properties	Values
Elastic modulus	73000 N/mm2
Poissons ratio	0.33
Density	2.77 g/cm3
Yield stress in tension	275 N/mm2

Table.1 Material Properties

The loads are applied at eight different stations along the length of spar based on data from Ref [1] as shown in Table 2.

RESULTS AND DISCUSSIONS

The results of the Eigen value buckling analysis points out that the spar is safe in buckling. It identifies an Eigen factor of

10.51.The most critical region is the spar web region near to the root. The stress results obtained from the buckling analysis are shown in Fig.3.

Fig.3 Eigen value stress plot

A thin sheet may buckle in a variety of modes depending upon its dimensions, the loading and the method of support. Usually, buckling loads are much lower than those likely to cause failure in the material of the plate. Therefore, plasticity factor need not be considered for those calculations. Crippling stress in such a case is given by,

Station no.	Span (mm)	Dimensionless span wise coordinate	Loading coefficient	Force(N)
1	450	1.25	1.28	2510.51
2	900	2.50	1.24	2432.05
3	1350	3.75	1.16	2275.15
4	1800	5.00	1.08	2118.24
5	2250	6.25	0.97	1902.49
6	2700	7.50	0.84	1647.52
7	3150	8.75	0.64	1255.25
8	3600	10.00	0.10	196.13

2kc E t

cr 12(1 2 ) b2

Table.2 Spanwise Loads

These calculated loads are applied on the finite element model and constraints were applied at the root as well as at different stations as shown in Fig.2

Fig.2 Finite Element Model of Spar

where:

Kc= Buckling coefficient which depends on edge boundary conditions and sheet aspect ratio (a/b).

E = Modulus of elasticity

= Elastic Poisson's ratio b = Loaded edge.

t= Sheet thickness.

The critical region identified from buckling analysis is shown in Fig.4

a b

Fig.4 Critical region under buckling

From Fig.4, a=b=200 mm; Elemental stresses = 3245.0 N

cr

2kc E t

12(1 2 ) b2

[3] Static stress distribution throughout the spar web, from station 2 to station 7 is found to be lesser than 80 N/mm2.Hence removal of more material is suggested in those locations after performing dynamic and fatigue analyses.

2 * 4.0 * 71000

12(1 0.332 )

3

2002

58.93N / mm2

REFERENCES

1. Franklin, W.Diederich, Martin Zlotniok (1958) Calculated Spanwise

   Pcr * A 58.93* 600 35351.2N

   Lift Distributions, Influence Functions and Influence Coefficients for Unswept wings in Subsonic Flow NACA Report 1228

   e Pcr Papp

   35351.2/3245.0 = 10.89

2. Faruk ELALDI. Buckling, post-buckling and failure analysis of hat stiffened composite panel international Fracture Conference, vol 35, 2007, pp 345-465

The theoretical buckling calculations are performed to validate

the result from the FE analysis and Eigen factor is found to be

10.89, which is a closer value.

CONCLUDING REMARKS

Eigen value buckling analysis points out that the spar is safe in buckling. It identifies an Eigen factor of 10.51.

Theoretical buckling calculations are performed to validate the result from the FE analysis and Eigen factor is found to be

10.89, which is a closer value.

Mustafa Özakça et al, Buckling and post-buckling of sub-stiffened or locally tailored aluminium panels, international congress of the aeronautical sciences, vol 24, 2001, pp 243-254

Radha P. et al. Ultimate strength of submarine pressure hulls with failure governed by inelastic buckling vol 15, 2005, pp 503-528

Chang-Sun Hong et al Buckling Behavior Monitoring of Composite Wing Box Model Using Fiber Bragg Grating Sensor System national conference, vol 7, 2006, pp 106-118

WilliamsP.A. et al. Bimodal Buckling of Optimized Truss-Lattice Shear Panels international Conference , vol 31, 2009

C.M Wang, C.Y Wang, J.N Reddy(2005) Exact solutions for Buckling of Structural members CRC Press.