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International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 6, June 2017, pp. 338–347, Article ID: IJMET_08_06_035

Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=6

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

MODELING AND ANALYSIS OF A COMPOSITE

WING FOR MISSILE STRUCTURE

M. Ganesh

Department of Aeronautical Engineering,

MLR Institute of Technology, Hyderabad, India

G Hima Bindu

Department of Mechanical Engineering,

Malla Reddy Engineering College and Management Science, Hyderabad, India

A. Sai Kumar

Department of Aeronautical Engineering,

MLR Institute of Technology, Hyderabad, India

ABSTRACT

The design and development of satellite launch vehicle and missile are driven by

the need for minimum weight structures. Preliminary design of these structures

requires many optimizations to select among competing structural concepts. Accurate

models and analysis methods are required for such structural optimizations. Model,

analysis, and optimization complexities have to be compromised to meet constraints

on design cycle time and computational resources.

In this work, failure modes and buckling loads of composite plate under uniformly

distributed loading and deflection is investigated by using analytical and theoretical

approaches. A 3-D finite-elements model was also built which takes into consideration

the exact geometric configuration and the orthotropic properties of the composite

plate. Altering the ply sequence for given working conditions alters the deflection of

the particular material. Hence analysis is carried out on such various orientations to

select the most suitable orientation. The composite plate carries out the theoretical

and the FEM results and is found to be around 8-10% difference. The achieved

deflection factor is 5.4 against 4.6 in FEM. They show good agreement at all the

regions. However, the results of FEM show close agreement with theoretical results.

Also, the design stresses are within the safety limits. Sandwich core material is

Polyurethane foam, and Skin material carbon fiber.

Key words: Modeling, Analysis, Composites, Ply Orientation, Laminates etc.

Cite this Article: M. Ganesh, G Hima Bindu and A. Sai Kumar. Modeling and

Analysis of a Composite Wing for Missile Structure. International Journal of

Mechanical Engineering and Technology, 8(6), 2017, pp. 338–347.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=6

M. Ganesh, G Hima Bindu and A. Sai Kumar


1. INTRODUCTION

A composite material consists of two or more constituent materials combined in such a way

that the resulting material has more useful applications than the constituent materials alone.

The constituent materials play a key role in the development of the final material properties.

Advanced composite materials used in structural applications are obtained by reinforcing a

matrix material with continuous fibers having high strength and stiffness properties. The

selection of a composite material for any application will involve selection of reinforcing fibre

and matrix, and their fractional volume in the resulting material. A properly selected

combination will give a composite material with following advantages:

• High strength and stiffness-to-weight ratio.

• Low weight.

• Excellent corrosion resistance.

• Excellent fatigue resistance.

1.1. Lamina and Laminate

Lamina (Plural Laminae) - A lamina is an arrangement of unidirectional or woven fibers in a

matrix as shown in Fig1. The principal axes of the lamina are along the fiber direction and

perpendicular to fiber direction.

Figure 1 Types of Laminae

Laminate- A laminate is a built-up of a stack of laminae having fibers orientated in different

directions. A lay-up of typical laminate is shown in Figure 2. A laminate having plies placed

symmetrically about the centreline is termed as symmetric laminate as shown in Figure 2.

Prepreg, Pre-impregnated- A combination of mat, fabric, fibers with resin, advanced to B-

stage, ready for curing.

Figure 2 Typical Laminate Lay-up (02/±45/0/90/0/±45/02) or (02/±45/0/90)S

The properties in Table 1.1 are for a single ply or lamina of a composite. Because the

transverse properties are so low, practical composite structures consist of laminates built up

from a stack of laminate. To improve the transverse properties of the laminate, the plies are

Fiber Direction Fill Direction

Modeling and Analysis of a Composite Wing for Missile Structure


stacked so the fibers are rotated at various angles�,defined relative to a convenient laminate

coordinate system, as shown in Figure 3.

Figure 3 Laminate coordinate system

In the case of a beam, for example, the x-axis of the laminate coordinate system might be

chosen to coincide with the axis of the beam.

Table 1 Composite Material Systems

2. DESIGN AND MATERIALS

2.1. Design Considerations

A sandwich structure is designed to make sure that it is capable of taking structural loads

throughout its design life. In addition, it should maintain its structural integrity in the in-

service environments. The structure should satisfy the following criteria:

• The face sheets should have sufficient stiffness to withstand the tensile, compressive, and

shear stresses produced by applied loads.

• The core should have sufficient stiffness to withstand the shear stresses produced by applied

loads.

• The core should have sufficient shear modulus to prevent overall buckling of the sandwich

structure under loads.

• Stiffness of the core and compressive strength of the face sheets should be sufficient to

prevent the wrinkling of the face sheets under applied loads.

2.1.1. Geometric details

Length of the wing = 598 mm

Width of the wing = 130mm



2.2. Design Loads

Wing load = 530 kg

Factor of Safety = 1.5

Pressure (UDL) = (530×1.5×10) / (598×130)

= 0.10226 N /��

2.3. Material Properties

The following are properties of the material which are taken for design and analysis of

orthotropic plates and given in Table-2 & Table-3

Table 2 Carbon fiber epoxy composite

S. No

No. Parameter Value

1 Longitudinal modulus, E1 110 GPa

2 Transverse modulus, E2 6.11 GPa

3 Shear modulus, G12 5.8 Gpa

4 Poison’s ratio, ν12 0.3

5 Longitudinal tensile strength, T1 1800 MPa

6 Longitudinal compressive strength, C1 1100 MPa

7 Transverse tensile strength, T2 14 MPa

8 Transverse compressive strength, C2 63 MPa

9 In-plane shear strength, S12 40 MPa

10 Density, ρ 1.40 gm/cm3

Table 3 Carbon fabric epoxy composite

S. No. Parameter Value

1 Longitudinal modulus, E1 66 GPa

2 Transverse modulus, E2 67 GPa

3 Shear modulus, G12 4.5 GPa

4 Poison’s ratio, ν12 0.25

5 Longitudinal tensile strength, T1 540 MPa

6 Longitudinal compressive strength, C1 320 MPa

7 Transverse tensile strength, T2 532 MPa

8 Transverse compressive strength, C2 310 MPa

9 In-plane shear strength, S12 76.3 MPa

10 Density, ρ 1.35 gm/cm3

3. THEORETICAL PREDICTIONS

Figure 4 Shear Stress Distribution (left) in a sandwich plate and the approximate distribution (right).



When the top and bottom face sheets are unsymmetrical with respect to the face sheets

midplane but are symmetrical with respect to the midplane of the sandwich plate, the matrices

of the sandwich plate become

[A]=2[A]t

[B]=0

[D]=0.5d2[A]

t=2[D]

t + 2d[B]

t

The shear stiffness matrix [S] is determined as follows. In the core, as a consequence of

the assumption that the in-plane stiffness’s are negligible, the transverse shear stress τxz is

uniform. In general, in the face sheets the shear stress distribution is as shown in Fig 4(left).

We approximate this distribution by the linear shear stress distribution shown in Fig 3.1

(right). Accordingly, the transverse shear force Vx is

Where the superscripts c, t, and b refer to the core, the top and the bottom face sheets,

respectively. The distance d= c + tt /2 + t

b /2.

Similarly, we have

Vy= τcyzd

The stress-strain relationship for the core material is given by, with the superscript c

identifying the core, these equations give

Where c

ijC are the elements of the core stiffness matrix.

3.1. Stress for Composite using CLT

For 3D Transverse Orthotropic Stiffness Matrix E1=110,000MPa,

E2=9000MPa

E12=-4500MPa

µ12=0.23

µ23=0.32

�=15000Kg /m3

S11= 1/E1 =1/110,000MPa

S11=9.0911� 10-12

m2/N

S12= -µ�/� =-2.09091� 10 ��/N

��= 1/� =1.111��

�

S12= -��

�� 2.

��

�� =2.22×10 �

��

�

�� μ��/��= 3.556� 10 ��

�



� � ��

�� =0.10977N/��

��

�� =-0.00207N/��

��

�� =8.982×10 �N/��

�� =

!!= 45,000$N/��

Laminate plates orientation in 0° & 45°

3.1.1. Prediction of Laminate Stress

=

xy

y

x

xy

y

x

QQQ

QQQ

QQQ

ε

ε

ε

τ

σ

σ

66

_

26

_

16

_26

_

22

_

12

_

_

1612

_

11

_

For the 0°

Ǭ = 0.01977

Ǭ� = −0.00207

Ǭ��= 0.008982

Ǭ� = 0

Ǭ�� = 0

Ǭ�� = 0

For the laminate plate 45°

Ǭ = 22500 $*+

Ǭ� = −45,000$*+

Ǭ�� = 45000$*+

Ǭ� = 0.025197

Ǭ�� = 0.025197

Ǭ�� = 0.030723

W= -./012

3�4+

-./01�

�

P=O.10226Pa, EI= S22 = S

Solving above equation we get

Deflection = bending deflection+ self deflection

W = 3.574+1.591

W = 5.165mm

4. ANALYSIS

A 3-D model was built for a composite sandwich wing using ANSYS 12.0 Finite- elements

software. Initially one 30o

sector was modeled and then the whole structure was generated

using this primary sector.



4.1. Set up

4.1.1. Elements

• Brick 8node 45

• Layered46 (Nodal)

4.1.2. Layer Properties

Table 4 Properties for Solid 46

Layer No Nodal no Orientation Thickness

Layer number 1 1 0 0.2





4.1.3. Mechanical Properties

Table 5 Material Properties

Parameter CFRP PrePreg (fabric)

Εx 120000 67000

Εy 9000 66000

Εz 9000 6900

γxy 0.25 0.25

γyz 0.32 0.32

γzx 0.25 0.25

τxy 3580 3580

τyz 4500 4500

τzx 3580 3580

4.2. Meshed Models

Figure 5 Meshed Model



5. RESULTS

Figure 6 Deflection of sandwich plate

Figure 7 Deflection of sandwich plate

Figure 8 Stress plot



Figure 9 Distribution of deflection

6. CONCLUSIONS

The composite sandwich wing is successfully designed to meet the stipulated loading

condition. The geometry of the wing has been obtained after giving it through a analytical

treatment. The design approach is based on long plate theory. The wing is fabricated using

carbon fiber and fabric epoxy composite by optimum ply orientation. Layup: 0/45/0/45/0. In

design of composite the following configuration are considered:

• Wing with varying thickness is analyzed.

• Different composite material is considered.

• Varying ply orientations.

The sandwich wing was analyzed by SOLID-45 based on analysis following conclusion

are been drawn:

• The composite wing design is meeting the stipulated composite load.

• The new method proposed for analysis of wing worked out to be efficient in accurately

predicting the structural response.

• The FE results and theoretical results are in closed agreement.

• The design stresses are within limits.

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