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The International Journal Of Engineering And Science (IJES)
||Volume|| 3 ||Issue|| 01 || Pages || 38-43 || 2014 ||
ISSN (e): 2319 – 1813 ISSN (p): 2319 – 1805

 Stress Analysis on Bulkhead Model for BWB Heavy Lifter
Passenger Aircraft
Vigneshwaran R1, Maniiarasan P2, Arulselvan K3, Senthilkumar S4
1

Post Graduate Scholar, Department of Aeronautical Engineering,
2, 3,
Professor, Department of Mechanical Engineering,
4
Assistant Professor, Department of Aeronautical Engineering,
Nehru Institute of Engineering and Technology, T.M. Palayam, Coimbatore – 641 105, Tamil Nadu, India.

-----------------------------------------------------------ABSTRACT--------------------------------------------------------In modern aviation for passenger and military transportations, a new and efficient design in fuselage is
necessary. BWB fuselage will confidently satisfy this requirement. BWB centerbody is the most load
withstanding component among the full length of BWB fuselage structure. Unlike a conventional cylindrical
pressurised Fuselage, the centre body of a BWB suffers from both internal cabin pressurisation and spanwise
wing bending loads. The combined loading results in non-linear stress behaviour, whose complexity is
undesirable for the design process. This project is fully concentrating on the stress analysis of rear structural
pressure Bulkhead component used for the BWB centerbody configuration for passenger fuselage. A New
combination of Multi-bubble and Box type Bulk head is proposed for the ultra heavy lifter by Boeing & NASA.
In this project initially the Bulkhead is modeled for their given specifications and the stress analysis carried out
in Ansys analysis software tool for the same configuration. Theoretical calculations for the bending stress and
the values are validated with the numerically stimulated values. It is expected to prove that the BWB model with
the multi bubble combined with Box type centerbody is more suited for the future ultra heavy lifter passenger
aircrafts.

Keywords - BWB, bulkhead, panel stress.
------------------------------------------------------------------------------------------------------------------------------------------Date of Submission: 22 December 2013
Date of Acceptance: 15 January 2014
-------------------------------------------------------------------------------------------------------------------------------------------

I. INTRODUCTION
It is generally known to provide a pressure bulkhead for enclosing, in a pressure tight manner, the tail
end of the pressurized interior of an aircraft fuselage. The pressure bulkhead includes all structural components
that are necessary for achieving an airtight and pressure-tight seal of the pressurized interior of the fuselage, and
for taking up and further transmitting into the fuselage structure all of the forces that result from the pressure
difference on the two opposite sides of the bulkhead. Generally, two types of bulkhead structures are known in
the art. Pressure bulkheads of the first type are embodied as curved, stiffened membrane structures, for example
in the form of a semi-spherical cup. Pressure bulkheads of the second type are embodied as a planar, skinnedover grid frame structures. The choice between these two types of pressure bulkheads is based on the respective
prevailing boundary conditions, and especially, for example, the available space, the size of the cross-sectional
area that is to be enclosed, and the like. Since the curved form of the first type of pressure bulkhead is
advantageous for supporting, transferring and counteracting the arising forces, this type of pressure bulkhead can
have a lighter weight and simpler construction. Namely, a membrane structure that is subjected to a pressure
supports the resulting loads in directions along its curved surface only in the form of meridian forces and
circumferential forces. The circumferential forces are all internal forces within the pressure bulkhead. On the
other hand, the meridian forces must be taken up and supported by the surrounding structures of the aircraft
fuselage around the edge of the membrane structure. Moreover, the meridian forces of the membrane structure
have an outwardly directed force component around the edge of the membrane at the area of the transition or
junction with the aircraft fuselage.

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Stress Analysis on Bulkhead Model for BWB Heavy Lifter Passenger Aircraft
1.1 Theory involved in modeling
Unlike the traditional aircraft tubular fuselage, the high stress and weight problem associated with
BWB pressurized cabin can be explained using the sketch in Figure 1. This figure illustrates a cylindrical and a
square box fuselage under internal pressure p. In a cylindrical pressure vessel of radius R and skin thickness t,
the pressure is resisted by uniform stretching resulting membrane stress is equal to p(R/t). In BWB box like
fuselage, the nearly flat upper cabin wall resists the pressure by bending deformation. Let us model it as a simply
supported beam or plate of length l, thickness t, then the maximum bending stress is equal to 0.75p(l/t)2.
Assuming R is of same order as l, the bending stress is one order of magnitude higher. The problem is
aggravated by the non-linear effect of compressive load acting on the deflected beam or plate. So in order to
obtain an efficient structure, one must increase the bending stiffness using deep sandwich shell with light weight
high-strength composite skin with Composite deep stiffener. The alternative is to use a multi-bubble concept
with proper design; the adjacent bubble membrane stress resultant is balanced by tension in the intra-cabin wall.

Fig.1 High bending stress associated with a non-cylindrical pressure vessel.
1.2 Simple plate theory for thin panels
In this area the Fig.2 shows the Plate with two edges free and 2 edges fixed:

Fig 2. Plate with two edges free and 2 edges fixed
From plate theory the required maximum bending stress and shear force values for thee specified thin plate can be
calculated as:

1. Max. Bending stress at x=0, y=b

b2
f   1 ( p 2 )( psi)
t

Eq. (1)

2. Shear force at x= a and y= 0

V  k1 pb(lbs / in)

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Eq. (2)

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3. Bending stress at free edges, x=0 and y= b

f  2 ( p

b2
)( psi)
t2

Eq. (3)

4. Max.shear force are free edges, x= 0, y= b

V  k2 pb(lbs / in)

Eq. (4)

Where, co-efficient β1, β2, k1, k2 are taken from [2].
1.3 Ideal beam- column analysis
A simple nonlinear beam-column analysis may provide some initial sizing information. Consider a
cabin roof segment, as shown in Fig. 1, where P is the axial load, q is the distributed running load due to normal
cabin pressure, and EI is the beam bending stiffness over the span- length L. The critical bucking load Pcr for a
simple-supported boundary condition is given by Pcr = π 2 EI/L2 . From beam-column theory (Ref.), the
maximum deflection, bending moment, and bending stress at mid-span are given by equations (5) through (7).

wmax 

5q.L4 12(2sec   2   2 )
384 EI
5 4

Eq (5)

qL2 5q.L4 12(2sec   2   2 )
M max 

p Eq (6)
8 384 EI
5 4
y P
Eq (7)
 max  M max 
2I A
Where,




2

p
pcr

1.4 Stiffened plate analysis
Consider the biaxial stiffened plate shown in Fig. 2. The equivalent bending stiffness Dx, Dy along the
x and y directions and the torsional stiffness H of a biaxially stiffend plate of thickness t can be
approximately defined by equations (4) through (6). Let us assume that the plate-theory assumptions are
applicable to a stiffened plate [1].

Dx 

Dy 

Ex t 3
ExtZ 0 x 2
E' I

 x x
12(1  x y ) 12(1  x y )
b

Eyt 3

E y tZ oy 2

E'y I y



12(1  x y ) 12(1  x y )
a

Gxy t 3
1
H  ( Dx y  Dy x 
)
2
3

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Eq (8)

Eq (9)

Eq (10)

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II. STRESS ANALYSIS
2.1 Analysis for case-1
Case-1 is having only 3 frame members and 2 stringer members as shown in fig below. The stringers
are arranged along y- direction. Frames are formed along x- axis. Material property for the elements is constant
for all of the members including plate with 5 mm thickness. Material is modeled with shell93 element.
Boundary conditions for x=0 & y= 0 lines are symmetry BC. For x=250, y=750 are having clamped
edge BC. The uniform pressure load is given on the plate member.
Table: 1- Dimension specification: Units are in ‘mm’
Item

Stringer(W1)

Frame(L1)

number of members

2

3

spacing

125

250

total length

250

750

height

15

20

thickness

2

2

The contours values correspond to σxx values for the face sheet bottom. Value is -56 MPa. The
negative sign indicates compression. (See Fig.4), the values are shown in the x-component stress model fig.4 at
the face sheet center; σxx varies from a tensile stress of 51 MPa at the top to a compressive stress of 56 MPa at
the bottom. Following values for the bottom of the face sheet is for the y-component stress:
i. At the center, σyy= -28 MPa.
ii. At the clamped edge location (x=0, y=L1), σyy= 77 MPa.
The head-to-head comparison of the analytical values with the FEA values at the center of the structure
is presented in the following table.2
Table: 2. Comparison at the center of the structure
Entity

Location

Theory

3.8mm

W

FEA

3.6mm

Σxx

Bottom

-56MPa

-50MPa

Σxx

Top

312MPa

350MPa

Σyy

Bottom

-28MPa

-20MPa

Σyy

Top

38MPa

105MPa

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2.2 σfor Stiffeners
σxx values at the top of the x-stiffener closest to the center & the following values at the top of this stiffener (see Fig.6):

i. At (x=0, y=L1/6), σxx= 312 MPa.
ii. At the clamped edge location (x=W1, y=L1/6), σxx= -653 MPa.
The head-to-head comparison of the edge stresses is given in the following table.3
Table: 3- comparison of the edge stresses
Entity

Location

FEA

Theory

Σxx

Bottom

116 MPa

100 MPa

Σxx

Top

-653 MPa

-704 MPa

Σyy

Bottom

77 MPa

78 MPa

Σyy

Top

-300 MPa

-403 MPa

Fig.4 deformation of the structure

Fig.5 face sheet stress components

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Fig.6 stiffener stress components

III. CONCLUSION
The deflection at the center is about 8% larger than the theoretical value due to shear deformation in the
FEA model that is not accounted for in the analytical result. Correlation of stresses in the center is reasonably
good. It might improve if solution for anisotropic plate were used. Also, the stiffeners are not at the centerline of
the model, while maximum stresses in theory are calculated at the center. There is good correlation of the edge
stress on the bottom of face sheet but the edge stress at the top of the stiffeners is overestimated by the theory.
This is possibly due to the stiffeners not being at the centerline of the model while the maximum stresses in
theory are calculated at the center. To get much stress concentration and stiffness for the given structural
member, composite materials with high strength give possible static stability and good stiffness over higher
internal pressure levels.

REFERENCES
[1]
[2]
[3]
[4]

Timoshenko, S. P. and Gere, J. M., Theory of Elastic Stability, 2nd ed., Dover Publication, 2009, pp.145. Reprinted from McGraw
Hill Book Co., New York, 1961.
Michael C.Y. Niue, Airframe stress analysis and sizing, 2nd edition, Hongkong conmilit press limited, Hongkong.
Vivek Mukhopadhyay, Hybrid Wing-Body (HWB) Pressurized Fuselage Modeling, Analysis, and Design for Weight Reduction,
NASA Langley Research Center, Hampton, Virginia, 23681-2199.
Sung Hwan Cho, BWB Military Cargo Transport Fuselage Design and Analysis.ICAS2008.

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